Modified Einstein and Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Bulyzhenkov, I. É.

2018-05-01

The appearance of inertial rest mass-energy is associated with the kinematic slowing-down of time and with the vortex state of the elementary massive space with zero integral of its kinetic and potential energies. An analog of the Einstein equation is found for moving densities of a non-empty metric space in the concept of the Einstein-Infeld material field. The vector consequences of this tensor equation for a metric medium of overlapping elementary carriers of continuous mass-energies allow us to modify the Navier-Stokes equation under inertial motion of the matter of the nonlocal field in the nonrelativistic limit. The nonlocality of massenergy generates kinematic accelerations of feedback to Newtonian acceleration, which impedes asymptotic divergence of energy fluxes. Stabilization of inertial media by dynamic Bernoulli pressure corresponds to nonlocal self-organization of Einstein-Infeld non-empty space and invalidates Newtonian localization of masses in empty space.

Modified Einstein and Navier–Stokes Equations

NASA Astrophysics Data System (ADS)

Bulyzhenkov, I. É.

2018-05-01

The appearance of inertial rest mass-energy is associated with the kinematic slowing-down of time and with the vortex state of the elementary massive space with zero integral of its kinetic and potential energies. An analog of the Einstein equation is found for moving densities of a non-empty metric space in the concept of the Einstein-Infeld material field. The vector consequences of this tensor equation for a metric medium of overlapping elementary carriers of continuous mass-energies allow us to modify the Navier-Stokes equation under inertial motion of the matter of the nonlocal field in the nonrelativistic limit. The nonlocality of massenergy generates kinematic accelerations of feedback to Newtonian acceleration, which impedes asymptotic divergence of energy fluxes. Stabilization of inertial media by dynamic Bernoulli pressure corresponds to nonlocal self-organization of Einstein-Infeld non-empty space and invalidates Newtonian localization of masses in empty space.

Liquid Aluminum: Atomic diffusion and viscosity from ab initio molecular dynamics

PubMed Central

Jakse, Noel; Pasturel, Alain

2013-01-01

We present a study of dynamic properties of liquid aluminum using density-functional theory within the local-density (LDA) and generalized gradient (GGA) approximations. We determine the temperature dependence of the self-diffusion coefficient as well the viscosity using direct methods. Comparisons with experimental data favor the LDA approximation to compute dynamic properties of liquid aluminum. We show that the GGA approximation induce more important backscattering effects due to an enhancement of the icosahedral short range order (ISRO) that impact directly dynamic properties like the self-diffusion coefficient. All these results are then used to test the Stokes-Einstein relation and the universal scaling law relating the diffusion coefficient and the excess entropy of a liquid. PMID:24190311

Stokes-Einstein relation in liquid iron-nickel alloy up to 300 GPa

NASA Astrophysics Data System (ADS)

Cao, Q.-L.; Wang, P.-P.

2017-05-01

Molecular dynamic simulations were applied to investigate the Stokes-Einstein relation (SER) and the Rosenfeld entropy scaling law (ESL) in liquid Fe0.9Ni0.1 over a sufficiently broad range of temperatures (0.70 < T/Tm < 1.85 Tm is melting temperature) and pressures (from 50 GPa to 300 GPa). Our results suggest that the SER and ESL hold well in the normal liquid region and break down in the supercooled region under high-pressure conditions, and the deviation becomes larger with decreasing temperature. In other words, the SER can be used to calculate the viscosity of liquid Earth's outer core from the self-diffusion coefficients of iron/nickel and the ESL can be used to predict the viscosity and diffusion coefficients of liquid Earth's outer core form its structural properties. In addition, the pressure dependence of effective diameters cannot be ignored in the course of using the SER. Moreover, ESL provides a useful, structure-based probe for the validity of SER, while the ratio of the self-diffusion coefficients of the components cannot be used as a probe for the validity of SER.

Structural origin of fractional Stokes-Einstein relation in glass-forming liquids

NASA Astrophysics Data System (ADS)

Pan, Shaopeng; Wu, Z. W.; Wang, W. H.; Li, M. Z.; Xu, Limei

2017-01-01

In many glass-forming liquids, fractional Stokes-Einstein relation (SER) is observed above the glass transition temperature. However, the origin of such phenomenon remains elusive. Using molecular dynamics simulations, we investigate the break- down of SER and the onset of fractional SER in a model of metallic glass-forming liquid. We find that SER breaks down when the size of the largest cluster consisting of trapped atoms starts to increase sharply at which the largest cluster spans half of the simulations box along one direction, and the fractional SER starts to follows when the largest cluster percolates the entire system and forms 3-dimentional network structures. Further analysis based on the percolation theory also confirms that percolation occurs at the onset of the fractional SER. Our results directly link the breakdown of the SER with structure inhomogeneity and onset of the fraction SER with percolation of largest clusters, thus provide a possible picture for the break- down of SER and onset of fractional SER in glass-forming liquids, which is is important for the understanding of the dynamic properties in glass-forming liquids.

Stokes-Einstein relation for pure simple fluids.

PubMed

Cappelezzo, M; Capellari, C A; Pezzin, S H; Coelho, L A F

2007-06-14

The authors employed the equilibrium molecular dynamics technique to calculate the self-diffusion coefficient and the shear viscosity for simple fluids that obey the Lennard-Jones 6-12 potential in order to investigate the validity of the Stokes-Einstein (SE) relation for pure simple fluids. They performed calculations in a broad range of density and temperature in order to test the SE relation. The main goal of this work is to exactly calculate the constant, here denominated by alpha, present in the SE relation. Also, a modified SE relation where a fluid density is raised to a power in the usual expression is compared to the classical expression. According to the authors' simulations slip boundary conditions (alpha=4) can be satisfied in some state points. An intermediate value of alpha=5 was found in some regions of the phase diagram confirming the mode coupling theory. In addition depending on the phase diagram point and the definition of hydrodynamics radius, stick boundary condition (alpha=6) can be reproduced. The authors investigated the role of the hydrodynamic radius in the SE relation using three different definitions. The authors also present calculations for alpha in a hard-sphere system showing that the slip boundary conditions hold at very high density. They discuss possible explanations for their results and the role of the hydrodynamic radius for different definitions in the SE relation.

Rotation driven translational diffusion of polyatomic ions in water: A novel mechanism for breakdown of Stokes-Einstein relation

NASA Astrophysics Data System (ADS)

Banerjee, Puja; Yashonath, Subramanian; Bagchi, Biman

2017-04-01

While most of the existing theoretical and simulation studies have focused on simple, spherical, halide and alkali ions, many chemically, biologically, and industrially relevant electrolytes involve complex non-spherical polyatomic ions like nitrate, chlorate, and sulfate to name only a few. Interestingly, some polyatomic ions in spite of being larger in size show anomalously high diffusivity and therefore cause a breakdown of the venerable Stokes-Einstein (S-E) relation between the size and diffusivity. Here we report a detailed analysis of the dynamics of anions in aqueous potassium nitrate (KNO3) and aqueous potassium acetate (CH3COOK) solutions. The two ions, nitrate (-NO3) and acetate (CH3-CO2 ), with their similar size show a large difference in diffusivity values. We present evidence that the translational motion of these polyatomic ions is coupled to the rotational motion of the ion. We show that unlike the acetate ion, nitrate ion with a symmetric charge distribution among all periphery oxygen atoms shows a faster rotational motion with large amplitude rotational jumps which enhances its translational motion due to translational-rotational coupling. By creating a family of modified-charge model systems, we have analysed the rotational motion of asymmetric polyatomic ions and the contribution of it to the translational motion. These model systems help clarifying and establishing the relative contribution of rotational motion in enhancing the diffusivity of the nitrate ion over the value predicted by the S-E relation and also over the other polyatomic ions having asymmetric charge distribution like the acetate ion. In the latter case, reduced rotational motion results in lower diffusivity values than those with symmetric charge distribution. We propose translational-rotational coupling as a general mechanism of the breakdown of the S-E relation in the case of polyatomic ions.

Rotation driven translational diffusion of polyatomic ions in water: A novel mechanism for breakdown of Stokes-Einstein relation.

PubMed

Banerjee, Puja; Yashonath, Subramanian; Bagchi, Biman

2017-04-28

While most of the existing theoretical and simulation studies have focused on simple, spherical, halide and alkali ions, many chemically, biologically, and industrially relevant electrolytes involve complex non-spherical polyatomic ions like nitrate, chlorate, and sulfate to name only a few. Interestingly, some polyatomic ions in spite of being larger in size show anomalously high diffusivity and therefore cause a breakdown of the venerable Stokes-Einstein (S-E) relation between the size and diffusivity. Here we report a detailed analysis of the dynamics of anions in aqueous potassium nitrate (KNO 3 ) and aqueous potassium acetate (CH 3 COOK) solutions. The two ions, nitrate (NO3-) and acetate (CH 3 CO2-), with their similar size show a large difference in diffusivity values. We present evidence that the translational motion of these polyatomic ions is coupled to the rotational motion of the ion. We show that unlike the acetate ion, nitrate ion with a symmetric charge distribution among all periphery oxygen atoms shows a faster rotational motion with large amplitude rotational jumps which enhances its translational motion due to translational-rotational coupling. By creating a family of modified-charge model systems, we have analysed the rotational motion of asymmetric polyatomic ions and the contribution of it to the translational motion. These model systems help clarifying and establishing the relative contribution of rotational motion in enhancing the diffusivity of the nitrate ion over the value predicted by the S-E relation and also over the other polyatomic ions having asymmetric charge distribution like the acetate ion. In the latter case, reduced rotational motion results in lower diffusivity values than those with symmetric charge distribution. We propose translational-rotational coupling as a general mechanism of the breakdown of the S-E relation in the case of polyatomic ions.

On the theory of Brownian motion with the Alder-Wainwright effect

NASA Astrophysics Data System (ADS)

Okabe, Yasunori

1986-12-01

The Stokes-Boussinesq-Langevin equation, which describes the time evolution of Brownian motion with the Alder-Wainwright effect, can be treated in the framework of the theory of KMO-Langevin equations which describe the time evolution of a real, stationary Gaussian process with T-positivity (reflection positivity) originating in axiomatic quantum field theory. After proving the fluctuation-dissipation theorems for KMO-Langevin equations, we obtain an explicit formula for the deviation from the classical Einstein relation that occurs in the Stokes-Boussinesq-Langevin equation with a white noise as its random force. We are interested in whether or not it can be measured experimentally.

Communication: Fast dynamics perspective on the breakdown of the Stokes-Einstein law in fragile glassformers

NASA Astrophysics Data System (ADS)

Puosi, F.; Pasturel, A.; Jakse, N.; Leporini, D.

2018-04-01

The breakdown of the Stokes-Einstein (SE) law in fragile glassformers is examined by Molecular-Dynamics simulations of atomic liquids and polymers and consideration of the experimental data concerning the archetypical ortho-terphenyl glassformer. All the four systems comply with the universal scaling between the viscosity (or the structural relaxation) and the Debye-Waller factor ⟨u2⟩, the mean square amplitude of the particle rattling in the cage formed by the surrounding neighbors. It is found that the SE breakdown is scaled in a master curve by a reduced ⟨u2⟩. Two approximated expressions of the latter, with no and one adjustable parameter, respectively, are derived.

Relationship between structural and dynamic properties of Al-rich Al-Cu melts: Beyond the Stokes-Einstein relation

NASA Astrophysics Data System (ADS)

Jakse, N.; Pasturel, A.

2016-12-01

We perform ab initio molecular dynamics simulations to study structural and transport properties in liquid A l1 -xC ux alloys, with copper composition x ≤0.4 , in relation to the applicability of the Stokes-Einstein (SE) equation in these melts. To begin, we find that self-diffusion coefficients and viscosity are composition dependent, while their temperature dependence follows an Arrhenius-type behavior, except for x =0.4 at low temperature. Then, we find that the applicability of the SE equation is also composition dependent, and its breakdown in the liquid regime above the liquidus temperature can be related to different local ordering around each species. In this case, we emphasize the difficulty of extracting effective atomic radii from interatomic distances found in liquid phases, but we see a clear correlation between transport properties and local ordering described through the structural entropy approximated by the two-body contribution. We use these findings to reformulate the SE equation within the framework of Rosenfeld's scaling law in terms of partial structural entropies, and we demonstrate that the breakdown of the SE relation can be related to their temperature dependence. Finally, we also use this framework to derive a simple relation between the ratio of the self-diffusivities of the components and the ratio of their partial structural entropies.

On the nonlinear variation of dc conductivity with dielectric relaxation time

NASA Astrophysics Data System (ADS)

Johari, G. P.; Andersson, Ove

2006-09-01

The long-known observations that dc conductivity σdc of an ultraviscous liquid varies nonlinearly with the dielectric relaxation time τ, and the slope of the logσdc against logτ plot deviates from -1 are currently seen as two of the violations of the Debye-Stokes-Einstein equation. Here we provide a formalism using a zeroth order Bjerrum description for ion association to show that in addition to its variation with temperature T and pressure P, impurity ion population varies with a liquid's equilibrium dielectric permittivity. Inclusion of this electrostatic effect modifies the Debye-Stokes-Einstein equation to log(σdcτ )=constant+logα, where α is the T and P-dependent degree of ionic dissociation of an electrolytic impurity. Variation of a liquid's shear modulus with T and P would add to the nonlinearity of σdc-τ relation, as would a nonequivalence of the shear and dielectric relaxation times, proton transfer along the hydrogen bonds, or occurrence of another chemical process. This is illustrated by using the data for ultraviscous acetaminophen-aspirin liquid.

Derivation of Einstein-Cartan theory from general relativity

NASA Astrophysics Data System (ADS)

Petti, Richard

2015-04-01

General relativity cannot describe exchange of classical intrinsic angular momentum and orbital angular momentum. Einstein-Cartan theory fixes this problem in the least invasive way. In the late 20th century, the consensus view was that Einstein-Cartan theory requires inclusion of torsion without adequate justification, it has no empirical support (though it doesn't conflict with any known evidence), it solves no important problem, and it complicates gravitational theory with no compensating benefit. In 1986 the author published a derivation of Einstein-Cartan theory from general relativity, with no additional assumptions or parameters. Starting without torsion, Poincaré symmetry, classical or quantum spin, or spinors, it derives torsion and its relation to spin from a continuum limit of general relativistic solutions. The present work makes the case that this computation, combined with supporting arguments, constitutes a derivation of Einstein-Cartan theory from general relativity, not just a plausibility argument. This paper adds more and simpler explanations, more computational details, correction of a factor of 2, discussion of limitations of the derivation, and discussion of some areas of gravitational research where Einstein-Cartan theory is relevant.

Entropy density of spacetime and the Navier-Stokes fluid dynamics of null surfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Padmanabhan, T.

2011-02-15

It has been known for several decades that Einstein's field equations, when projected onto a null surface, exhibit a structure very similar to the nonrelativistic Navier-Stokes equation. I show that this result arises quite naturally when gravitational dynamics is viewed as an emergent phenomenon. Extremizing the spacetime entropy density associated with the null surfaces leads to a set of equations which, when viewed in the local inertial frame, becomes identical to the Navier-Stokes equation. This is in contrast to the usual description of the Damour-Navier-Stokes equation in a general coordinate system, in which there appears a Lie derivative rather thanmore » a convective derivative. I discuss this difference, its importance, and why it is more appropriate to view the equation in a local inertial frame. The viscous force on fluid, arising from the gradient of the viscous stress-tensor, involves the second derivatives of the metric and does not vanish in the local inertial frame, while the viscous stress-tensor itself vanishes so that inertial observers detect no dissipation. We thus provide an entropy extremization principle that leads to the Damour-Navier-Stokes equation, which makes the hydrodynamical analogy with gravity completely natural and obvious. Several implications of these results are discussed.« less

Gravitational Stokes parameters. [for electromagnetic and gravitational radiation in relativity

NASA Technical Reports Server (NTRS)

Anile, A. M.; Breuer, R. A.

1974-01-01

The electromagnetic and gravitational Stokes parameters are defined in the general theory of relativity. The general-relativistic equation of radiative transfer for polarized radiation is then derived in terms of the Stokes parameters for both high-frequency electromagnetic and gravitational waves. The concept of Stokes parameters is generalized for the most general class of metric theories of gravity, where six (instead of two) independent states of polarization are present.

Diffusion of flexible, charged, nanoscopic molecules in solution: Size and pH dependence for PAMAM dendrimer

NASA Astrophysics Data System (ADS)

Maiti, Prabal K.; Bagchi, Biman

2009-12-01

In order to understand self-diffusion (D) of a charged, flexible, and porous nanoscopic molecule in water, we carry out very long, fully atomistic molecular dynamics simulation of PAMAM dendrimer up to eight generations in explicit salt water under varying pH. We find that while the radius of gyration (Rg) varies as N1/3, the self-diffusion constant (D ) scales, surprisingly, as N-α, with α =0.39 at high pH and 0.5 at neutral pH, indicating a dramatic breakdown of Stokes-Einstein relation for diffusion of charged nanoscopic molecules. The variation in D as a function of radius of gyration demonstrates the importance of treating water and ions explicitly in the diffusion process of a flexible nanoscopic molecule. In agreement with recent experiments, the self-diffusion constant increases with pH, revealing the importance of dielectric friction in the diffusion process. The shape of a dendrimer is found to fluctuate on a nanosecond time scale. We argue that this flexibility (and also the porosity) of the dendrimer may play an important role in determining the mean square displacement of the dendrimer and the breakdown of the Stokes-Einstein relation between diffusion constant and the radius.

Hopping and the Stokes-Einstein relation breakdown in simple glass formers.

PubMed

Charbonneau, Patrick; Jin, Yuliang; Parisi, Giorgio; Zamponi, Francesco

2014-10-21

One of the most actively debated issues in the study of the glass transition is whether a mean-field description is a reasonable starting point for understanding experimental glass formers. Although the mean-field theory of the glass transition--like that of other statistical systems--is exact when the spatial dimension d → ∞, the evolution of systems properties with d may not be smooth. Finite-dimensional effects could dramatically change what happens in physical dimensions,d = 2, 3. For standard phase transitions finite-dimensional effects are typically captured by renormalization group methods, but for glasses the corrections are much more subtle and only partially understood. Here, we investigate hopping between localized cages formed by neighboring particles in a model that allows to cleanly isolate that effect. By bringing together results from replica theory, cavity reconstruction, void percolation, and molecular dynamics, we obtain insights into how hopping induces a breakdown of the Stokes-Einstein relation and modifies the mean-field scenario in experimental systems. Although hopping is found to supersede the dynamical glass transition, it nonetheless leaves a sizable part of the critical regime untouched. By providing a constructive framework for identifying and quantifying the role of hopping, we thus take an important step toward describing dynamic facilitation in the framework of the mean-field theory of glasses.

Generalized Einstein relation for the mutual diffusion coefficient of a binary fluid mixture.

PubMed

Felderhof, B U

2017-08-21

The method employed by Einstein to derive his famous relation between the diffusion coefficient and the friction coefficient of a Brownian particle is used to derive a generalized Einstein relation for the mutual diffusion coefficient of a binary fluid mixture. The expression is compared with the one derived by de Groot and Mazur from irreversible thermodynamics and later by Batchelor for a Brownian suspension. A different result was derived by several other workers in irreversible thermodynamics. For a nearly incompressible solution, the generalized Einstein relation agrees with the expression derived by de Groot and Mazur. The two expressions also agree to first order in solute density. For a Brownian suspension, the result derived from the generalized Smoluchowski equation agrees with both expressions.

Normal versus anomalous self-diffusion in two-dimensional fluids: memory function approach and generalized asymptotic Einstein relation.

PubMed

Shin, Hyun Kyung; Choi, Bongsik; Talkner, Peter; Lee, Eok Kyun

2014-12-07

Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze data obtained from molecular dynamics simulations of a two-dimensional soft disk fluid. We mainly concentrated on medium densities for which we found super-diffusive behavior of a tagged fluid particle. At higher densities a range of normal diffusion can be identified. The motion presumably changes to sub-diffusion for even higher densities.

Normal versus anomalous self-diffusion in two-dimensional fluids: Memory function approach and generalized asymptotic Einstein relation

NASA Astrophysics Data System (ADS)

Shin, Hyun Kyung; Choi, Bongsik; Talkner, Peter; Lee, Eok Kyun

2014-12-01

Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze data obtained from molecular dynamics simulations of a two-dimensional soft disk fluid. We mainly concentrated on medium densities for which we found super-diffusive behavior of a tagged fluid particle. At higher densities a range of normal diffusion can be identified. The motion presumably changes to sub-diffusion for even higher densities.

Active and Passive Microrheology: Theory and Simulation

NASA Astrophysics Data System (ADS)

Zia, Roseanna N.

2018-01-01

Microrheological study of complex fluids traces its roots to the work of the botanist Robert Brown in the early nineteenth century. Indeed, passive microrheology and Brownian motion are one and the same. Once thought to reveal a fundamental life force, the phenomenon was ultimately leveraged by Einstein in proof of the atomic nature of matter ( Haw 2006 ). His work simultaneously paved the way for modern-day passive microrheology by connecting observable particle motion—diffusion—to solvent properties—the viscosity—via the well-known Stokes-Einstein relation. Advances in microscopy techniques in the last two decades have prompted extensions of the original model to generalized forms for passive probing of complex fluids. In the last decade, active microrheology has emerged as a means by which to interrogate the nonequilibrium behavior of complex fluids, in particular, the non-Newtonian rheology of dynamically heterogeneous and microscopically small systems. Here we review theoretical and computational approaches and advances in both passive and active microrheology, with a focus on the extent to which these techniques preserve the connection between single-particle motion and flow properties, as well as the rather surprising recovery of non-Newtonian flow behavior observed in bulk rheology.

Einstein's First Steps Toward General Relativity: Gedanken Experiments and Axiomatics

NASA Astrophysics Data System (ADS)

Miller, A. I.

1999-03-01

Albert Einstein's 1907 Jahrbuch paper is an extraordinary document because it contains his first steps toward generalizing the 1905 relativity theory to include gravitation. Ignoring the apparent experimental disconfirmation of the 1905 relativity theory and his unsuccessful attempts to generalize the mass-energy equivalence, Einstein boldly raises the mass-energy equivalence to an axiom, invokes equality between gravitational and inertial masses, and then postulates the equivalence between a uniform gravitational field and an oppositely directed constant acceleration, the equivalence principle. How did this come about? What is at issue is scientific creativity. This necessitates broadening historical analysis to include aspects of cognitive science such as the role of visual imagery in Einstein's thinking, and the relation between conscious and unconscious modes of thought in problem solving. This method reveals the catalysts that sparked a Gedanken experiment that occurred to Einstein while working on the Jahrbuch paper. A mental model is presented to further explore Einstein's profound scientific discovery.

Einstein and General Relativity: Historical Perspectives.

ERIC Educational Resources Information Center

Chandrasekhar, S.

1979-01-01

This paper presented in the 1978 Oppenheimer Memorial Lecture at Los Alamos Scientific Laboratories on August 17, 1978, discusses Einstein's contributions to physics, in particular, his discovery of the general theory of relativity. (HM)

Einstein and Besso: Not a Partnership of Equals

NASA Astrophysics Data System (ADS)

Janssen, Michel

2005-04-01

In the 1905 special relativity paper Einstein famously acknowledged the help of his friend and colleague Michele Besso. Besso had been an ideal sounding board for Einstein's ideas. During the years that Einstein developed general relativity, Besso was a good deal more than a sounding board. He collaborated with Einstein on calculations of the perihelion motion of Mercury in 1913. His contributions were substantial and would have warranted co-authorship of Einstein's famous paper on Mercury's perihelion of November 1915, in which Besso is not mentioned at all. Besso also alerted Einstein to problems with the early version of general relativity that Einstein had worked out together with Marcel Grossmann. Einstein essentially ignored Besso's warnings. In addition, Besso went out of his way during this period to act as a mediator between a not always appreciative Einstein, living in Berlin with his cousin Elsa who would become his second wife, and his estranged first wife Mileva, living in Zurich with the couple's two young sons. This period is much better documented than the period leading up to the 1905 paper and consequently much more revealing about the nature of the relationship between Einstein and Besso.

Gelation kinetics of gelatin using particle tracking microrheology

NASA Astrophysics Data System (ADS)

Hardcastle, Joseph; Bansil, Rama

2012-02-01

Previous studies with gelatin have observed four distinct stages during the physical gelation process [Normand et al. Macromolecules, 2000, 33, 1063]. In this presentation we report measurements of microrheology in an effort to examine the time evolution of the gel on short length scales and time scales. By tracking latex particles in gelatin solution at different temperatures we can follow the microrheological changes and kinetics of the gelation process. Using the generalized Stokes-Einstein relation viscoelastic properties of these quasi-static gel states the evolution of the storage and loss moduli, G' and G'', are examined as functions of both time and temperature. The data show that both G' and G'' exhibit power law scaling versus frequency with the same exponent. The temperature and concentration dependence of the frequency at which the system crosses over from viscous to elastic behavior will be presented.

EPR before EPR: A 1930 Einstein-Bohr thought Experiment Revisited

ERIC Educational Resources Information Center

Nikolic, Hrvoje

2012-01-01

In 1930, Einstein argued against the consistency of the time-energy uncertainty relation by discussing a thought experiment involving a measurement of the mass of the box which emitted a photon. Bohr seemingly prevailed over Einstein by arguing that Einstein's own general theory of relativity saves the consistency of quantum mechanics. We revisit…

Iontophoretic transport of oligonucleotides across human epidermal membrane: a study of the Nernst-Planck model.

PubMed

Li, S K; Ghanem, A H; Teng, C L; Hardee, G E; Higuchi, W I

2001-07-01

The objective of this study was to investigate the transport behavior of a series of oligonucleotides with human epidermal membrane (HEM) and to examine the applicability of the modified NERNST-PLANCK model to transdermal iontophoresis of these macromolecules. Iontophoretic transport experiments were first carried out in a synthetic model membrane system (Nuclepore membranes) with a four-electrode potentiostat to examine the baseline modified NERNST-PLANCK model. The modified NERNST-PLANCK model derived from the Einstein relation and the Stokes-Einstein equation taken from previous work did not hold for the oligonucleotides. Results obtained in the Nuclepore studies were, however, consistent with predictions of the modified NERNST-PLANCK model using the experimentally determined electromobilities and diffusion coefficients. The electromobilities of the oligonucleotides (determined by capillary electrophoresis) were found to be more than a factor of two smaller than expected from the Einstein relation between electromobilities and diffusion coefficients (the latter determined in diffusion cell experiments). A correlation between these electromobilities and the theoretical electromobilities estimated by considering the effects of counterion binding and the effects of mobility reduction according to colloid theory was also observed. These results suggest that the modified NERNST-PLANCK model predictions are satisfactory only when the electromobilities and the effective molecular size of the oligonucleotides are known and are used directly to predict the iontophoretically enhanced transport. Results with the HEM experiments generally agreed with model predictions based on the experimental electromobilities. The oligonucleotide HEM flux data also suggest the existence of pores with effective pore radii greater than the effective radii estimated in previous studies with small molecular weight model permeants.

What about Albert Einstein? Using Biographies to Promote Students' Scientific Thinking

ERIC Educational Resources Information Center

Fingon, Joan C.; Fingon, Shallon D.

2009-01-01

Who hasn't heard of Einstein? Science educators everywhere are familiar with Einstein's genius and general theory of relativity. Students easily recognize Einstein's image by his white flyaway hair and bushy mustache. It is well known that Einstein was a brilliant physicist and an abstract thinker who often used his creativity and imagination in…

Explicit expressions of self-diffusion coefficient, shear viscosity, and the Stokes-Einstein relation for binary mixtures of Lennard-Jones liquids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ohtori, Norikazu, E-mail: ohtori@chem.sc.niigata-u.ac.jp; Ishii, Yoshiki

Explicit expressions of the self-diffusion coefficient, D{sub i}, and shear viscosity, η{sub sv}, are presented for Lennard-Jones (LJ) binary mixtures in the liquid states along the saturated vapor line. The variables necessary for the expressions were derived from dimensional analysis of the properties: atomic mass, number density, packing fraction, temperature, and the size and energy parameters used in the LJ potential. The unknown dependence of the properties on each variable was determined by molecular dynamics (MD) calculations for an equimolar mixture of Ar and Kr at the temperature of 140 K and density of 1676 kg m{sup −3}. The scalingmore » equations obtained by multiplying all the single-variable dependences can well express D{sub i} and η{sub sv} evaluated by the MD simulation for a whole range of compositions and temperatures without any significant coupling between the variables. The equation for D{sub i} can also explain the dual atomic-mass dependence, i.e., the average-mass and the individual-mass dependence; the latter accounts for the “isotope effect” on D{sub i}. The Stokes-Einstein (SE) relation obtained from these equations is fully consistent with the SE relation for pure LJ liquids and that for infinitely dilute solutions. The main differences from the original SE relation are the presence of dependence on the individual mass and on the individual energy parameter. In addition, the packing-fraction dependence turned out to bridge another gap between the present and original SE relations as well as unifying the SE relation between pure liquids and infinitely dilute solutions.« less

Stokes-Einstein relation of the liquid metal rubidium and its relationship to changes in the microscopic dynamics with increasing temperature

NASA Astrophysics Data System (ADS)

Demmel, F.; Tani, A.

2018-06-01

For liquid rubidium the Stokes-Einstein (SE) relation is well fulfilled near the melting point with an effective hydrodynamic diameter, which agrees well with a value from structural investigations. A wealth of thermodynamic and microscopic data exists for a wide range of temperatures for liquid rubidium and hence it represents a good test bed to challenge the SE relation with rising temperature from an experimental point of view. We performed classical molecular dynamics simulations to complement the existing experimental data using a pseudopotential, which describes perfectly the structure and dynamics of liquid rubidium. The derived SE relation from combining experimental shear viscosity data with simulated diffusion coefficients reveals a weak violation at about 1.3 Tmelting≈400 K. The microscopic relaxation dynamics on nearest neighbor distances from neutron spectroscopy demonstrate distinct changes in the amplitude with rising temperature. The derived average relaxation time for density fluctuations on this length scale shows a non-Arrhenius behavior, with a slope change around 1.5 Tmelting≈450 K. Combining the simulated macroscopic self-diffusion coefficient with that microscopic average relaxation time, a distinct violation of the SE relation in the same temperature range can be demonstrated. One can conclude that the changes in the collective dynamics, a mirror of the correlated movements of the particles, are at the origin for the violation of the SE relation. The changes in the dynamics can be understood as a transition from a more viscous liquid metal to a more fluid-like liquid above the crossover temperature range of 1.3-1.5 Tmelting. The decay of the amplitude of density fluctuations in liquid aluminium, lead, and rubidium demonstrates a remarkable agreement and points to a universal thermal crossover in the dynamics of liquid metals.

Gödel metrics with chronology protection in Horndeski gravities

NASA Astrophysics Data System (ADS)

Geng, Wei-Jian; Li, Shou-Long; Lü, H.; Wei, Hao

2018-05-01

Gödel universe, one of the most interesting exact solutions predicted by General Relativity, describes a homogeneous rotating universe containing naked closed time-like curves (CTCs). It was shown that such CTCs are the consequence of the null energy condition in General Relativity. In this paper, we show that the Gödel-type metrics with chronology protection can emerge in Einstein-Horndeski gravity. We construct such exact solutions also in Einstein-Horndeski-Maxwell and Einstein-Horndeski-Proca theories.

Einstein's 1917 static model of the universe: a centennial review

NASA Astrophysics Data System (ADS)

O'Raifeartaigh, Cormac; O'Keeffe, Michael; Nahm, Werner; Mitton, Simon

2017-08-01

We present a historical review of Einstein's 1917 paper ` Cosmological Considerations in the General Theory of Relativity' to mark the centenary of a key work that set the foundations of modern cosmology. We find that the paper followed as a natural next step after Einstein's development of the general theory of relativity and that the work offers many insights into his thoughts on relativity, astronomy and cosmology. Our review includes a description of the observational and theoretical background to the paper; a paragraph-by-paragraph guided tour of the work; a discussion of Einstein's views of issues such as the relativity of inertia, the curvature of space and the cosmological constant. Particular attention is paid to little-known aspects of the paper such as Einstein's failure to test his model against observation, his failure to consider the stability of the model and a mathematical oversight concerning his interpretation of the role of the cosmological constant. We recall the response of theorists and astronomers to Einstein's cosmology in the context of the alternate models of the universe proposed by Willem de Sitter, Alexander Friedman and Georges Lemaître. Finally, we consider the relevance of the Einstein World in today's `emergent' cosmologies.

High temperature breakdown of the Stokes-Einstein relation in a computer simulated Cu-Zr melt

DOE Office of Scientific and Technical Information (OSTI.GOV)

Han, X. J., E-mail: xjhan@sjtu.edu.cn; Li, J. G., E-mail: lijg@sjtu.edu.cn; Schober, H. R., E-mail: h.schober@fz-juelich.de

Transport properties and the Stokes-Einstein (SE) relation in liquid Cu{sub 8}Zr{sub 3} are studied by molecular dynamics simulation with a modified embedded atom potential. The critical temperature T{sub c} of mode coupling theory (MCT) is derived as 930 K from the self-diffusion coefficient D and viscosity η. The SE relation breaks down around T{sub SE} = 1900 K, which is far above T{sub c}. At temperatures below T{sub SE}, the product of D and η fluctuates around a constant value, similar to the prediction of MCT near T{sub c}. The influence of the microscopic atomic motion on macroscopic properties ismore » investigated by analyzing the time dependent liquid structure and the self-hole filling process. The self-holes for the two components are preferentially filled by atoms of the same component. The self-hole filling dynamics explains the different breakdown behaviors of the SE relation in Zr-rich liquid CuZr{sub 2} compared to Cu-rich Cu{sub 8}Zr{sub 3}. At T{sub SE}, a kink is found in the temperature dependence of both partial and total coordination numbers for the three atomic pair combinations and of the typical time of self-hole filling. This indicates a strong correlation between liquid structure, atomic dynamics, and the breakdown of SE relation. The previously suggested usefulness of the parameter d(D{sub 1}/D{sub 2})/dT to predict T{sub SE} is confirmed. Additionally we propose a viscosity criterion to predict T{sub SE} in the absence of diffusion data.« less

Einstein's Universe.

ERIC Educational Resources Information Center

Carlson, Eric; Wald, Robert

1979-01-01

Presents a guide to be used by students and teachers in conjunction with a television program about Einstein. Provides general information about special and general relativity, and the universe. Includes questions for discussion after each section and a bibliography. (MA)

Einstein for Schools and the General Public

ERIC Educational Resources Information Center

Johansson, K. E.; Kozma, C; Nilsson, Ch

2006-01-01

In April 2005 the World Year of Physics (Einstein Year in the UK and Ireland) was celebrated with an Einstein week in Stockholm House of Science. Seven experiments illustrated Einstein's remarkable work in 1905 on Brownian motion, the photoelectric effect and special relativity. Thirteen school classes with 260 pupils, 30 teachers and 25 members…

Proteins as micro viscosimeters: Brownian motion revisited.

PubMed

Lavalette, Daniel; Hink, Mark A; Tourbez, Martine; Tétreau, Catherine; Visser, Antonie J

2006-08-01

Translational and rotational diffusion coefficients of proteins in solution strongly deviate from the Stokes-Einstein laws when the ambient viscosity is induced by macromolecular co-solutes rather than by a solvent of negligible size as was assumed by A. Einstein one century ago for deriving the laws of Brownian motion and diffusion. Rotational and translational motions experience different micro viscosities and both become a function of the size ratio of protein and macromolecular co-solute. Possible consequences upon fluorescence spectroscopy observations of diffusing proteins within living cells are discussed.

Albert Einstein 1879-1955.

ERIC Educational Resources Information Center

Physics Today, 1979

1979-01-01

Celebrates the centennial of Einstein's birth with an eight-page pictorial biography and two special articles: (1) Einstein the catalyst; and (2) Unitary field theories. His special and general theories of relativity and his contributions to quantum physics and other topics are also presented. (HM)

Gravitation. [Book on general relativity

NASA Technical Reports Server (NTRS)

Misner, C. W.; Thorne, K. S.; Wheeler, J. A.

1973-01-01

This textbook on gravitation physics (Einstein's general relativity or geometrodynamics) is designed for a rigorous full-year course at the graduate level. The material is presented in two parallel tracks in an attempt to divide key physical ideas from more complex enrichment material to be selected at the discretion of the reader or teacher. The full book is intended to provide competence relative to the laws of physics in flat space-time, Einstein's geometric framework for physics, applications with pulsars and neutron stars, cosmology, the Schwarzschild geometry and gravitational collapse, gravitational waves, experimental tests of Einstein's theory, and mathematical concepts of differential geometry.

General relativity at 75: how right was einstein?

PubMed

Will, C M

1990-11-09

The status of experimental tests of general relativity is reviewed on the occasion of its 75th anniversary. Einstein's equivalence principle is well supported by experiments such as the Eötvös experiment, tests of special relativity, and the gravitational redshift experiment. Tests of general relativity have reached high precision, including the light deflection and the perihelion advance of Mercury, proposed by Einstein 75 years ago, and new tests such as the Shapiro time delay and the Nordtvedt effect in lunar motion. Gravitational wave damping has been detected to an accuracy of 1 percent on the basis of measurements of the binary pulsar. The status of the "fifth force" is discussed, along with the frontiers of experimental relativity, including proposals for testing relativistic gravity with advanced technology and spacecraft.

GFP as potential cellular viscosimeter.

PubMed

Visser, Antonie J W G; Westphal, Adrie H; Skakun, Victor V; Borst, Jan Willem

2016-08-18

The molecular dimensions of proteins such as green fluorescent protein (GFP) are large as compared to the ones of solvents like water or glycerol. The microscopic viscosity, which determines the resistance to diffusion of, e.g. GFP, is then the same as that determined from the resistance of the solvent to flow, which is known as macroscopic viscosity. GFP in water/glycerol mixtures senses this macroscopic viscosity, because the translational and rotational diffusion coefficients are proportional to the reciprocal value of the viscosity as predicted by the Stokes-Einstein equations. To test this hypothesis, we have performed time-resolved fluorescence anisotropy (reporting on rotational diffusion) and fluorescence correlation spectroscopy (reporting on translational diffusion) experiments of GFP in water/glycerol mixtures. When the solvent also contains macromolecules of similar or larger dimensions as GFP, the microscopic and macroscopic viscosities can be markedly different and the Stokes-Einstein relations must be adapted. It was established from previous dynamic fluorescence spectroscopy observations of diffusing proteins with dextran polysaccharides as co-solvents (Lavalette et al 2006 Eur. Biophys. J. 35 517-22), that rotation and translation sense a different microscopic viscosity, in which the one arising from rotation is always less than that from translation. A microscopic viscosity parameter is defined that depends on scaling factors between GFP and its immediate environment. The direct consequence is discussed for two reported diffusion coefficients of GFP in living cells.

GFP as potential cellular viscosimeter

NASA Astrophysics Data System (ADS)

Visser, Antonie J. W. G.; Westphal, Adrie H.; Skakun, Victor V.; Borst, Jan Willem

2016-09-01

The molecular dimensions of proteins such as green fluorescent protein (GFP) are large as compared to the ones of solvents like water or glycerol. The microscopic viscosity, which determines the resistance to diffusion of, e.g. GFP, is then the same as that determined from the resistance of the solvent to flow, which is known as macroscopic viscosity. GFP in water/glycerol mixtures senses this macroscopic viscosity, because the translational and rotational diffusion coefficients are proportional to the reciprocal value of the viscosity as predicted by the Stokes-Einstein equations. To test this hypothesis, we have performed time-resolved fluorescence anisotropy (reporting on rotational diffusion) and fluorescence correlation spectroscopy (reporting on translational diffusion) experiments of GFP in water/glycerol mixtures. When the solvent also contains macromolecules of similar or larger dimensions as GFP, the microscopic and macroscopic viscosities can be markedly different and the Stokes-Einstein relations must be adapted. It was established from previous dynamic fluorescence spectroscopy observations of diffusing proteins with dextran polysaccharides as co-solvents (Lavalette et al 2006 Eur. Biophys. J. 35 517-22), that rotation and translation sense a different microscopic viscosity, in which the one arising from rotation is always less than that from translation. A microscopic viscosity parameter is defined that depends on scaling factors between GFP and its immediate environment. The direct consequence is discussed for two reported diffusion coefficients of GFP in living cells.

Optical tracer size differences allow quantitation of active pumping rate versus Stokes-Einstein diffusion in lymphatic transport

NASA Astrophysics Data System (ADS)

DSouza, Alisha V.; Marra, Kayla; Gunn, Jason R.; Samkoe, Kimberley S.; Pogue, Brian W.

2016-10-01

Lymphatic uptake of interstitially administered agents occurs by passive convective-diffusive inflow driven by interstitial concentration and pressure, while the downstream lymphatic transport is facilitated by active propulsive contractions of lymphatic vessel walls. Near-infrared fluorescence imaging in mice was used to measure these central components of lymphatic transport for the first time, using two different-sized molecules-methylene blue (MB) and fluorescence-labeled antibody immunoglobulin G (IgG)-IRDye 680RD. This work confirms the hypothesis that lymphatic passive inflow and active propulsion rates can be separated based upon the relative differences in Stokes-Einstein diffusion coefficient. This coefficient specifically affects the passive-diffusive uptake when the interstitial volume and pressure are constant. Parameters such as mean time-to-peak signal, overall fluorescence signal intensities, and number of active peristaltic pulses, were estimated from temporal imaging data. While the mean time to attain peak signal representative of diffusion-dominated flow in the lymph vessels was 0.6±0.2 min for MB and 8±6 min for IgG, showing a size dependence, the active propulsion rates were 3.4±0.8 pulses/min and 3.3±0.5 pulses/min, respectively, appearing size independent. The propulsion rates for both dyes decreased with clearance from the interstitial injection-site, indicating intrinsic control of the smooth muscles in response to interstitial pressure. This approach to size-comparative agent flow imaging of lymphatic function can enable noninvasive characterization of diseases related to uptake and flow in lymph networks.

Slow relaxation mode in concentrated oil-in-water microemulsions consisting of repulsive droplets

NASA Astrophysics Data System (ADS)

Hattori, Y.; Ushiki, H.; Courbin, L.; Panizza, P.

2007-02-01

The present contribution reports on the observation of two diffusive relaxation modes in a concentrated microemulsion made of repulsive droplets. These two modes can be interpreted in the frame of Weissman’s and Pusey’s theoretical pioneering works. The fast mode is associated to the collective diffusion of droplets whereas the slow one corresponds to the relaxation of droplet concentration fluctuations associated with composition and/or size. We show that (i) repulsive interactions considerably slow down the latter and (ii) a generalized Stokes Einstein relationship between its coefficient of diffusion and the Newtonian viscosity of the solutions, similar to the Walden’s rule for electrolytes, holds for concentrated microemulsion systems made of repulsive droplets.

Fluid/gravity correspondence for massive gravity

NASA Astrophysics Data System (ADS)

Pan, Wen-Jian; Huang, Yong-Chang

2016-11-01

In this paper, we investigate the fluid/gravity correspondence in the framework of massive Einstein gravity. Treating the gravitational mass terms as an effective energy-momentum tensor and utilizing the Petrov-like boundary condition on a timelike hypersurface, we find that the perturbation effects of massive gravity in bulk can be completely governed by the incompressible Navier-Stokes equation living on the cutoff surface under the near horizon and nonrelativistic limits. Furthermore, we have concisely computed the ratio of dynamical viscosity to entropy density for two massive Einstein gravity theories, and found that they still saturate the Kovtun-Son-Starinets (KSS) bound.

Structural relaxation in a binary metallic melt: Molecular dynamics computer simulation of undercooled Al80Ni20

NASA Astrophysics Data System (ADS)

Das, Subir K.; Horbach, Jürgen; Voigtmann, Thomas

2008-08-01

Molecular dynamics computer simulations are performed to study structure and structural relaxation in the glassforming metallic alloy Al80Ni20 . The interactions between the particles are modeled by an effective potential of the embedded atom type. Our model of Al80Ni20 exhibits chemical short-range order (CSRO) that is reflected in a broad prepeak around a wave number of 1.8Å-1 in the partial static structure factor for the Ni-Ni correlations. The CSRO is due to the preference of Ni atoms to have Al rather than Ni atoms as nearest neighbors. By analyzing incoherent and coherent intermediate scattering functions as well as self-diffusion constants and shear viscosity, we discuss how the chemical ordering is reflected in the dynamics of the deeply undercooled melt. The q dependence of the α relaxation time as well as the Debye-Waller factor for the Al-Al correlations show oscillations at the location of the prepeak in the partial static structure factor for the Ni-Ni correlations. The latter feature of the Debye-Waller factor is well reproduced by a calculation in the framework of the mode coupling theory (MCT) of the glass transition, using the partial static structure factors from the simulation as input. We also check the validity of the Stokes-Einstein-Sutherland formula that relates the self-diffusion coefficients with the shear viscosity. We show that it breaks down already far above the mode coupling critical temperature Tc . The failure of the Stokes-Einstein-Sutherland relation is not related to the specific chemical ordering in Al80Ni20 .

Spin and gravitation

NASA Technical Reports Server (NTRS)

Ray, J. R.

1982-01-01

The fundamental variational principle for a perfect fluid in general relativity is extended so that it applies to the metric-torsion Einstein-Cartan theory. Field equations for a perfect fluid in the Einstein-Cartan theory are deduced. In addition, the equations of motion for a fluid with intrinsic spin in general relativity are deduced from a special relativistic variational principle. The theory is a direct extension of the theory of nonspinning fluids in special relativity.

General Relativity and Gravitation

NASA Astrophysics Data System (ADS)

Ashtekar, Abhay; Berger, Beverly; Isenberg, James; MacCallum, Malcolm

2015-07-01

Part I. Einstein's Triumph: 1. 100 years of general relativity George F. R. Ellis; 2. Was Einstein right? Clifford M. Will; 3. Cosmology David Wands, Misao Sasaki, Eiichiro Komatsu, Roy Maartens and Malcolm A. H. MacCallum; 4. Relativistic astrophysics Peter Schneider, Ramesh Narayan, Jeffrey E. McClintock, Peter Mészáros and Martin J. Rees; Part II. New Window on the Universe: 5. Receiving gravitational waves Beverly K. Berger, Karsten Danzmann, Gabriela Gonzalez, Andrea Lommen, Guido Mueller, Albrecht Rüdiger and William Joseph Weber; 6. Sources of gravitational waves. Theory and observations Alessandra Buonanno and B. S. Sathyaprakash; Part III. Gravity is Geometry, After All: 7. Probing strong field gravity through numerical simulations Frans Pretorius, Matthew W. Choptuik and Luis Lehner; 8. The initial value problem of general relativity and its implications Gregory J. Galloway, Pengzi Miao and Richard Schoen; 9. Global behavior of solutions to Einstein's equations Stefanos Aretakis, James Isenberg, Vincent Moncrief and Igor Rodnianski; Part IV. Beyond Einstein: 10. Quantum fields in curved space-times Stefan Hollands and Robert M. Wald; 11. From general relativity to quantum gravity Abhay Ashtekar, Martin Reuter and Carlo Rovelli; 12. Quantum gravity via unification Henriette Elvang and Gary T. Horowitz.

How History Helped Einstein in Special Relativity

NASA Astrophysics Data System (ADS)

Martinez, Alberto

2013-04-01

I will discuss how the German intellectual movement known as ``critical history'' motivated several physicists in the late 1900s to radically analyze the fundamental principles of mechanics, leading eventually to Einstein's special theory of relativity. Eugen Karl Dühring, Johann Bernhard Stallo, Ludwig Lange, and Ernst Mach wrote critical histories of mechanics, some of which emphasized notions of relativity and observation, in opposition to old metaphysical concepts that seemed to infect the foundations of physics. This strand of critical history included the ``genetic method'' of analyzing how concepts develop over time, in our minds, by way of ordinary experiences, which by 1904 was young Albert Einstein's favorite approach for examining fundamental notions. Thus I will discuss how history contributed in Einstein's path to relativity, as well as comment more generally on Einstein's views on history.

Einstein and Rastall theories of gravitation in comparison

NASA Astrophysics Data System (ADS)

Darabi, F.; Moradpour, H.; Licata, I.; Heydarzade, Y.; Corda, C.

2018-01-01

We profit by a recent paper of Visser claiming that Rastall gravity is equivalent to Einstein gravity to compare the two gravitational theories in a general way. Our conclusions are different from Visser's ones. We indeed argue that these two theories are not equivalent. In fact, Rastall theory of gravity is an "open" theory when compared to Einstein general theory of relativity. Thus, it is ready to accept the challenges of observational cosmology and quantum gravity.

Heterogeneous nature of relaxation dynamics of room-temperature ionic liquids (EMIm) 2[Co(NCS) 4] and (BMIm) 2[Co(NCS) 4

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hensel-Bielowka, Stella; Wojnarowska, Zaneta E.; Dzida, Marzena

2015-08-11

Dynamic crossover above T g has been recognized as a characteristic feature of molecular dynamics of liquids approaching glass transition. Experimentally, it is manifested as a change in Vogel Fulcher Tammann dependence or a breakdown of the Stokes Einstein and related relations. In this paper, we report the exception from this rather general pattern of behavior. By means of dielectric, ultrasonic, rheological, and calorimetric methods, dynamics of two good ionic conductors (BMIm) 2[Co(NCS) 4] and (EMIm) 2[Co(NCS) 4] of less common stoichiometry (2:1) was studied in a very broad temperature range. However, none of the mentioned dynamic changes was observedmore » in the entire studied temperature range. On the contrary, the single VFT and the same fractional Walden coefficient were found for conductivity and viscosity changes over 12 decades. Furthermore, ultrasonic studies revealed that the data at temperatures which cover the normal liquid region cannot be fitted by a single exponential decay, and the Cole Cole function should be used instead.« less

Nanorheology of Entangled Polymer Melts

DOE PAGES

Ge, Ting; Grest, Gary S.; Rubinstein, Michael

2018-02-01

In this study, we use molecular simulations to probe the local viscoelasticity of an entangled polymer melt by tracking the motion of embedded nonsticky nanoparticles (NPs). As in conventional microrheology, the generalized Stokes-Einstein relation is employed to extract an effective stress relaxation function G GSE(t) from the mean square displacement of NPs. G GSE(t) for different NP diameters d are compared with the stress relaxation function G(t) of a pure polymer melt. The deviation of G GSE(t) from G(t) reflects the incomplete coupling between NPs and the dynamic modes of the melt. For linear polymers, a plateau in G GSE(t)more » emerges as d exceeds the entanglement mesh size a and approaches the entanglement plateau in G(t) for a pure melt with increasing d. For ring polymers, as d increases towards the spanning size R of ring polymers, G GSE(t) approaches G(t) of the ring melt with no entanglement plateau.« less

Nanorheology of Entangled Polymer Melts

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ge, Ting; Grest, Gary S.; Rubinstein, Michael

In this study, we use molecular simulations to probe the local viscoelasticity of an entangled polymer melt by tracking the motion of embedded nonsticky nanoparticles (NPs). As in conventional microrheology, the generalized Stokes-Einstein relation is employed to extract an effective stress relaxation function G GSE(t) from the mean square displacement of NPs. G GSE(t) for different NP diameters d are compared with the stress relaxation function G(t) of a pure polymer melt. The deviation of G GSE(t) from G(t) reflects the incomplete coupling between NPs and the dynamic modes of the melt. For linear polymers, a plateau in G GSE(t)more » emerges as d exceeds the entanglement mesh size a and approaches the entanglement plateau in G(t) for a pure melt with increasing d. For ring polymers, as d increases towards the spanning size R of ring polymers, G GSE(t) approaches G(t) of the ring melt with no entanglement plateau.« less

Generalization of Einstein's gravitational field equations

NASA Astrophysics Data System (ADS)

Moulin, Frédéric

2017-12-01

The Riemann tensor is the cornerstone of general relativity, but as is well known it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for the first time, following a rigorous mathematical treatment based on the variational principle, that there exists a generalized 4-index gravitational field equation containing the Riemann curvature tensor linearly, and thus the Weyl tensor as well. We show that this equation, written in n dimensions, contains the energy-momentum tensor for matter and that of the gravitational field itself. This new 4-index equation remains completely within the framework of general relativity and emerges as a natural generalization of the familiar 2-index Einstein equation. Due to the presence of the Weyl tensor, we show that this equation contains much more information, which fully justifies the use of a fourth-order theory.

[Photoeffects, Einstein's light quanta and the history of their acceptance].

PubMed

Wiederkehr, Karl Heinrich

2006-01-01

It is generally supposed, that the discovery of the efficacy-quantum by Planck was the impetus to Einstein's hypothesis of lightquanta. With its help Einstein could explain the external light-electrical effect. But even years before Einstein had worked at the photoeffect and already made experiments on it. For that reason the article gives a short survey about the history of the lightelectric effects. Lenard's basical work about the release of the photoelectrons is dealt with in detail, without which Einstein would scarcely have found his lightquanta. Furthermore it is shown how difficult it was for the physicists to give up--at least partially--the traditional view of the undulation-nature of light, and how they searched to explain the great energies of the photoelectrons. On the other side it is set forth how Einstein's formula of lightquanta was gradually confirmed. The tragical development of Einstein's personal relations with Johannes Stark and Philipp Lenard are briefly described. Stark was one of the few who supported Einstein's ideas at the beginning. Only with the Compton-effect, which could only be quantitatively interpreted by means of lightquanta and the special theory of relativity 1923, the way was free for the general acceptance of the lightquanta. Einstein did not agree to the obtained dualism of undulation and corpuscle; he had a different solution in mind about the fusion of the two forms of appearance of light.

Book Review: Book review

NASA Astrophysics Data System (ADS)

Wald, Robert M.

There is no question that the formulation of general relativity was one of the most remarkable episodes in the history of science. As a physicist and researcher in general relativity, the story of the formulation of general relativity that I have heard (and repeated) many times goes basically as follows: In 1907, Einstein obtained his fundamental insight-the "equivalence principle"-that gravitation and inertia are intimately connected; a freely falling observer does not "feel" gravitational force. It then took the genius of Einstein many years of "struggle"-during which he mastered the elements of differential geometry-to formulate a theory that properly incorporated this idea. In November, 1915, he finally succeeded in formulating general relativity.

The Origin of Gravitational Lensing: A Postscript to Einstein's 1936 Science Paper

PubMed

Renn; Sauer; Stachel

1997-01-10

Gravitational lensing, now taken as an important astrophysical consequence of the general theory of relativity, was found even before this theory was formulated but was discarded as a speculative idea without any chance of empirical confirmation. Reconstruction of some of Einstein's research notes dating back to 1912 reveals that he explored the possibility of gravitational lensing 3 years before completing his general theory of relativity. On the basis of preliminary insights into this theory, Einstein had already derived the basic features of the lensing effect. When he finally published the very same results 24 years later, it was only in response to prodding by an amateur scientist.

Comparison of Einstein-Boltzmann solvers for testing general relativity

NASA Astrophysics Data System (ADS)

Bellini, E.; Barreira, A.; Frusciante, N.; Hu, B.; Peirone, S.; Raveri, M.; Zumalacárregui, M.; Avilez-Lopez, A.; Ballardini, M.; Battye, R. A.; Bolliet, B.; Calabrese, E.; Dirian, Y.; Ferreira, P. G.; Finelli, F.; Huang, Z.; Ivanov, M. M.; Lesgourgues, J.; Li, B.; Lima, N. A.; Pace, F.; Paoletti, D.; Sawicki, I.; Silvestri, A.; Skordis, C.; Umiltà, C.; Vernizzi, F.

2018-01-01

We compare Einstein-Boltzmann solvers that include modifications to general relativity and find that, for a wide range of models and parameters, they agree to a high level of precision. We look at three general purpose codes that primarily model general scalar-tensor theories, three codes that model Jordan-Brans-Dicke (JBD) gravity, a code that models f (R ) gravity, a code that models covariant Galileons, a code that models Hořava-Lifschitz gravity, and two codes that model nonlocal models of gravity. Comparing predictions of the angular power spectrum of the cosmic microwave background and the power spectrum of dark matter for a suite of different models, we find agreement at the subpercent level. This means that this suite of Einstein-Boltzmann solvers is now sufficiently accurate for precision constraints on cosmological and gravitational parameters.

Microscopic theory for dynamics in entangled polymer nanocomposites

NASA Astrophysics Data System (ADS)

Yamamoto, Umi

New microscopic theories for describing dynamics in polymer nanocomposites are developed and applied. The problem is addressed from two distinct perspectives and using two different theoretical approaches. The first half of this dissertation studies the long-time and intermediate-time dynamics of nanoparticles in entangled and unentangled polymer melts for dilute particle concentrations. Using a combination of mode-coupling, Brownian motion, and polymer physics ideas, the nanoparticle long-time diffusion coefficients is formulated in terms of multiple length-scales, packing microstructures, and spatially-resolved polymer density fluctuation dynamics. The key motional mechanism is described via the parallel relaxation of the force exerted on the particle controlled by collective polymer constraint-release and the particle self-motion. A sharp but smooth crossover from the hydrodynamic to the non-hydrodynamic regime is predicted based on the Stokes-Einstein violation ratio as a function of all the system variables. Quantitative predictions are made for the recovery of the Stokes-Einstein law, and the diffusivity in the crossover regime agrees surprisingly well with large-scale molecular dynamics simulations for all particle sizes and chain lengths studied. The approach is also extended to address intermediate-time anomalous transport of a single nanoparticle and two-particle relative diffusion. The second half of this dissertation focuses on developing a novel dynamical theory for a liquid of infinitely-thin rods in the presence of hard spherical obstacles, aiming at a technical and conceptual extension of the existing paradigm for entangled polymer dynamics. As a fundamental theoretical development, the two-component generalization of a first-principles dynamic meanfield approach is presented. The theory enforces inter-needle topological uncrossability and needlesphere impenetrability in a unified manner, leading to a generalized theory of entanglements that includes the sphere excluded volume effect. Coupled self-consistent equations for the generalized diffusion tensors are constructed, and the expressions for the transverse localization lengths and the long-time diffusion coefficients are derived. In the static sphere limit, we find the effective tube diameter is generally reduced as a function of a single confinement parameter that quantifies the number of particles penetrating into the pure-polymer tube. A preliminary extension to treat flexible chain melts has also been achieved, and shown to agree reasonably well with simulations. The anisotropic needle diffusion constants are rich functions of the length-scale ratios, needle concentration and particle volume fraction. We show that the steric blocking of the longitudinal motion causes a literal and simultaneous localization of the two diffusion channels, and entangled needles can diffuse via a modified reptation dynamics over a window of polymer concentration but the compression of the tube and the blocking of the reptation motion must be accounted for. Generalization to treat mobile spheres is also possible and fully formulated.

The Einstein tower : an intertexture of dynamic construction, relativity theory and astronomy

NASA Astrophysics Data System (ADS)

Hentschel, Klaus; Hentschel, Ann M.

This book focuses on the `Einstein Tower', an architecturally historic observatory built in Potsdam in 1920 to allow the German astronomer Erwin Finlay Freundlich to attempt to verify experimentally Einstein's general theory of relativity. Freundlich, who was the first German astronomer to show a genuine interest in Einstein's theory, managed to interest his architect friend Erich Mendelsohn in designing this unique building. To develop a full historical picture, the book interweaves several descriptive levels: the biography of Freundlich; the social context in which he interacted with teachers, co-workers, students, his patrons (including Einstein), and scientific opponents; the cognitive aspects of his attempts to verify Einstein's theory; the political milieu within the Berlin scientific research community; and a cross-national comparison of astrophysics. This is an interesting account of this unconventional tale in the history of science.

The Einstein/CFA stellar survey - Overview of the data and interpretation of results

NASA Technical Reports Server (NTRS)

Vaiana, G. S.

1981-01-01

Results are presented from an extensive survey of stellar X-ray emission, using the Einstein Observatory. Over 140 stars have been detected to date, throughout the H-R diagram, thus showing that soft X-ray emission is the norm rather than the exception for stars in general. This finding is strongly at odds with pre-Einstein expectations based on standard acoustic theories of coronal heating. Typical examples of stellar X-ray detections and an overview of the survey data are presented. In combination with recent results from solar X-ray observations, the new Einstein data argue for the general applicability of magnetic field-related coronal heating mechanisms.

Dynamic heterogeneity in crossover spin facilitated model of supercooled liquid and fractional Stokes-Einstein relation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Choi, Seo-Woo; Kim, Soree; Jung, YounJoon, E-mail: yjjung@snu.ac.kr

Kinetically constrained models have gained much interest as models that assign the origins of interesting dynamic properties of supercooled liquids to dynamical facilitation mechanisms that have been revealed in many experiments and numerical simulations. In this work, we investigate the dynamic heterogeneity in the fragile-to-strong liquid via Monte Carlo method using the model that linearly interpolates between the strong liquid-like behavior and the fragile liquid-like behavior by an asymmetry parameter b. When the asymmetry parameter is sufficiently small, smooth fragile-to-strong transition is observed both in the relaxation time and the diffusion constant. Using these physical quantities, we investigate fractional Stokes-Einsteinmore » relations observed in this model. When b is fixed, the system shows constant power law exponent under the temperature change, and the exponent has the value between that of the Frederickson-Andersen model and the East model. Furthermore, we investigate the dynamic length scale of our systems and also find the crossover relation between the relaxation time. We ascribe the competition between energetically favored symmetric relaxation mechanism and entropically favored asymmetric relaxation mechanism to the fragile-to-strong crossover behavior.« less

The Spacetime Between Einstein and Kaluza-Klein: Further Explorations

NASA Astrophysics Data System (ADS)

Vuille, Chris

2017-01-01

Tensor multinomials can be used to create a generalization of Einstein's general relativity that in a mathematical sense falls between Einstein's original theory in four dimensions and the Kaluza-Klein theory in five dimensions. In the extended theory there are only four physical dimensions, but the tensor multinomials are expanded operators that can accommodate other forces of nature. The equivalent Ricci tensor of this geometry yields vacuum general relativity and electromagnetism, as well as a Klein-Gordon-like quantum scalar field. With a generalization of the stress-energy tensor, an exact solution for a plane-symmetric dust can be found where the scalar portion of the field drives early universe inflation, levels off for a period, then causes a later continued universal acceleration, a possible geometric mechanism for the inflaton or dark energy. Some new explorations of the equations, the problems, and possibilities will be presented and discussed.

Einstein: The Gourmet of Creativity.

ERIC Educational Resources Information Center

Greenberg, Joel

1979-01-01

Reports a psychiatrist's analysis of Einstein's personal account of how he developed the theory of relativity. The psychiatrist cites Janusian thinking, actively conceiving two or more opposite concepts simultaneously, as a characteristic of much creative thought in general. (MA)

Einstein's Jury -The Race to Test Relativity

NASA Astrophysics Data System (ADS)

Crelinsten, Jeffrey

2006-12-01

It is common belief that Einstein’s general theory of relativity won worldwide acceptance after British astronomers announced in November 1919 that the sun’s gravitational field bends starlight by an amount predicted by Einstein. This paper demonstrates that the case for Einstein was not settled until much later and that there was considerable confusion and debate about relativity during this period. Most astronomers considered Einstein’s general theory too metaphysical and abstruse, and many tried to find more conventional explanations of the astronomical observations. Two American announcements before the British results appeared had been contrary to Einstein’s prediction. They came from Lick and Mt. Wilson observatories, which enjoyed international reputations as two of the most advanced astrophysical research establishments in the world. Astronomers at these renowned institutions were instrumental in swaying the court of scientific opinion during the decade of the 1920s, which saw numerous attempts to measure light-bending, as well as solar line displacements and even ether-drift. How astronomers approached the “Einstein problem” in these early years before and after the First World War, and how the public reacted to what they reported, helped to shape attitudes we hold today about Einstein and his ideas.

Einstein Meets Hilbert: At the Crossroads of Physics and Mathematics

NASA Astrophysics Data System (ADS)

Rowe, David E.

One of the most famous episodes in the early history of general relativity involves the ``race'' in November 1915 between Albert Einstein and David Hilbert to uncover the ``correct'' form for the ten gravitational field equations. In light of recent archival findings, however, this story now has become a topic of renewed interest and controversy among historians of physics and mathematics. Drawing on recent studies and newly found sources, the present essay takes up this familiar tale from a new perspective, one that has seldom received due attention in the standard literature, namely, the mathematical issues at the heart of Einstein's theory. Told from this angle, the leading actors are Einstein's collaborator Marcel Grossmann, his critic Tullio Levi-Civita, his competitor David Hilbert, and several other mathematicians, many of them connected with Hilbert's Göttingen colleagues such as Hermann Weyl, Felix Klein, and Emmy Noether. As Einstein was the first to admit, Göttingen was far more important than Berlin as an active center for research in general relativity. Any account which, like this one, tries to understand both the actions and motives of the leading players must confront the problem of interpreting the rather sparse documentary evidence available. The interpretation offered herein, whatever its merits, aims first and foremost to show how mathematical issues deeply permeated the early history of general relativity.

Diffusion Rates of Organic Molecules in Secondary Organic Aerosol Particle

NASA Astrophysics Data System (ADS)

Bertram, A. K.; Chenyakin, Y.; Song, M.; Grayson, J. W.; Ullmann, D.; Evoy, E.; Renbaum-Wolff, L.; Liu, P.; Zhang, Y.; Kamal, S.; Martin, S. T.

2016-12-01

Information on the diffusion rates of organic molecules in secondary organic aerosol (SOA) particles are needed when predicting their size distribution, growth rates, photochemistry and heterogeneous chemistry. We have used two approaches to determine diffusion rates of organic molecules in SOA particles and proxies of SOA. In the first approach, we measured viscosities and then predicted diffusion rates using the Stokes-Einstein relation. In the second approach, we measured diffusion rates directly using a technique referred to as fluorescence recovery after photobleaching. Results from these measurements, including diffusion coefficients as a function of water activity, will be presented and the implications discussed.

Ballistic and diffusive dynamics in a two-dimensional ideal gas of macroscopic chaotic Faraday waves.

PubMed

Welch, Kyle J; Hastings-Hauss, Isaac; Parthasarathy, Raghuveer; Corwin, Eric I

2014-04-01

We have constructed a macroscopic driven system of chaotic Faraday waves whose statistical mechanics, we find, are surprisingly simple, mimicking those of a thermal gas. We use real-time tracking of a single floating probe, energy equipartition, and the Stokes-Einstein relation to define and measure a pseudotemperature and diffusion constant and then self-consistently determine a coefficient of viscous friction for a test particle in this pseudothermal gas. Because of its simplicity, this system can serve as a model for direct experimental investigation of nonequilibrium statistical mechanics, much as the ideal gas epitomizes equilibrium statistical mechanics.

The creativity of Einstein and astronomy

NASA Technical Reports Server (NTRS)

Zeldovich, Y. B.

1980-01-01

A discussion of Einstein's scientific achievements for the 100th anniversary of his birth is presented. His works dealing with thermodynamics are described, along with his quantum theory of radiation. Most of the article discusses his general theory of relativity.

Dutch museum marks Einstein anniversary

NASA Astrophysics Data System (ADS)

van Calmthout, Matijn

2016-01-01

A new painting of Albert Einstein's field equation from his 1915 general theory of relativity was unveiled in a ceremony in November 2015 by the Dutch physicist Robbert Dijkgraaf, who is director of the Princeton Institute for Advanced Study in the US.

Gravity Probe B: Examining Einstein's Spacetime with Gyroscopes. An Educator's Guide with Activities in Space Science.

ERIC Educational Resources Information Center

Range, Shannon K'doah; Mullins, Jennifer

This teaching guide introduces a relativity gyroscope experiment aiming to test two unverified predictions of Albert Einstein's general theory of relativity. An introduction to the theory includes the following sections: (1) "Spacetime, Curved Spacetime, and Frame-Dragging"; (2) "'Seeing' Spacetime with Gyroscopes"; (3)…

BOOK REVIEW: A Student's Guide to Einstein's Major Papers A Student's Guide to Einstein's Major Papers

NASA Astrophysics Data System (ADS)

Janssen, Michel

2013-12-01

The core of this volume is formed by four chapters (2-5) with detailed reconstructions of the arguments and derivations in four of Einstein's most important papers, the three main papers of his annus mirabilis 1905 (on the light quantum, Brownian motion, and special relativity) and his first systematic exposition of general relativity of 1916. The derivations are given in sufficient detail and in sufficiently modernized notation (without any serious distortion of the originals) for an undergraduate physics major to read and understand them with far less effort than it would take him or her to understand (English translations of) Einstein's original papers. Each of these four papers is accompanied by a detailed introduction, which covers the conceptual development of the relevant field prior to Einstein's contribution to it and corrects some of the myths surrounding these papers that still have not been fully eradicated among physicists. (One quibble: though Kennedy correctly points out that the goal of the light quantum paper was not to explain the photoelectric effect, it is also not quite right to say that 'it was written to explain the Wien region of blackbody radiation' (p. xv). Einstein used this explanatory feat as the central argument for his light quantum hypothesis.) These four chapters then are the most valuable part of the volume. They could be used, independently of one another, but preferably in conjunction with Einstein's original texts, in courses on quantum mechanics, statistical mechanics, electrodynamics, and general relativity, respectively, to add a historical component to such courses. As a historian of science embedded in a physics department who is regularly called upon to give guest lectures in such courses on the history of their subjects, I can highly recommend the volume for this purpose. However, I would not adopt this volume as (one of) the central text(s) for a course on the history of modern physics. For one thing, chapter 1, which in just 26 pages (not counting six pages of notes and references) covers everything from Copernicus, Galileo, Kepler and Newton to Maxwell and Lorentz to Einstein's early biography to a cardboard version of Popper versus Kuhn, is too superficial to be useful for such a course. To a lesser extent, this is also true for chapter 6, which compresses the development of quantum theory after Einstein's 1905 paper into 20 pages (plus seven pages of notes and references) and for chapter 7, a brief epilogue. However, this is not my main worry. One could easily supplement or even replace the bookends of the volume with other richer sources and use this volume mainly for its excellent detailed commentaries on some Einstein classics in the four chapters in between. My more serious reservation about the use of the volume as a whole in a history of physics course, ironically, comes from the exact same feature that made me whole-heartedly recommend its core chapters for physics courses. This is especially true for the chapters on special and general relativity. How useful is it for a student to go through, in as much detail as this volume provides, the Lorentz transformation of Maxwell's equations in vector form? I can see how a student in an E&M class (with a section on special relativity) might benefit from this exercise. The clumsiness of the calculations in vector form by Lorentz and Einstein could help a student encountering Maxwell's equations in tensor form for the first time appreciate the advantages of the latter formalism. Similarly, it would be useful for a student in a GR class to go through the basics of tensor calculus in the old-fashioned but not inelegant mathematical introduction of Einstein's 1916 review article on general relativity. This could reinforce mastery of material that a student in a GR class will have to learn anyway (though Einstein's presentation of the mathematics of both special and general relativity in The Meaning of Relativity would seem to be more suitable for these purposes). It is not so clear what benefit a student in a history of physics course rather than a E&M course or a GR course would derive from the exhaustive coverage of the papers on special and general relativity in this volume. In the case of the history of special relativity, it would seem to make sense to leave out the details of the Lorentz transformation of Maxwell's equations to make room for a discussion, even if only qualitatively, of Minkowski's four-dimensional formalism and Minkowski diagrams. In the case of the history of general relativity, coverage of tensor calculus could profitably be curtailed to make room for discussion of how Einstein found his field equations or how GR failed to make all motion relative. Chapter 3 on Brownian motion also contains its share of detailed calculations that may be useful for students in a class on Stat Mech but not for those in a class on history of physics. Chapter 2 on the light quantum paper does not suffer from this problem. However, whereas the other three papers covered in detail in the volume can serve as representative of Einstein's broader efforts in those fields, the light quantum paper is only the first in a series of remarkable contributions that Einstein made to early quantum theory. Several of these contributions (specific heat, wave-particle duality, stimulated emission, Bose--Einstein statistics) are covered very briefly in chapter 6. I would have liked to see a presentation of Einstein's 1917 derivation of the Planck law for the spectral distribution of black-body radiation with the famous A and B coefficients as detailed and as easy to follow as many less important derivations in the chapters on relativity and Brownian motion. This derivation is much easier yet much more illuminating than, say, the original proofs of the Lorentz invariance of Maxwell's equations. I hope the author will consider such changes in emphasis for a second edition, for his reconstructions and commentaries certainly do open up these four classic Einstein papers to interested undergraduates in physics and other disciplines in ways that the scholarly literature on Einstein does not.

A Staged Reading of the Play: TRANSCENDENCE: Relativity and Its Discontents by Robert Marc Friedman

NASA Astrophysics Data System (ADS)

Friedman, Robert Marc

2015-04-01

TRANSCENDENCE explores aspects of Einstein's life and his general theory of relativity at the time of the theory's creation and initial reception. While being faithful to historical scholarship, the play creates its own theatrical reality aiming to engage emotions and intellect. Those who strive for transcendence must nevertheless also confront the harsh realities of living in specific time-bound social contexts. Universal constants that anchor physical theory in an objective reality, as Einstein believed, do not readily have equivalents in notions of identity, duty, loyalty, and excellence. In November 1915 after toiling for years in Zurich, Prague, and now Berlin, Einstein achieved his general theory of relativity. When in 1919 British astronomers announced evidence for the bending of starlight by the sun as Einstein had predicted, he soon surprisingly found himself an international celebrity. Expectations arose that he would be called to Stockholm. But the Nobel Committee for Physics refused to acknowledge ``speculations'' such Einstein's. The dismissal of relativity entailed principled and biased opposition, and not simply mistakes in evaluation. Several committee members agreed that Einstein must not receive a Prize. Join us for a dramatic staged reading of TRANSCENDENCE, a play by the science historian Robert Marc Friedman (http://www.hf.uio.no/iakh/english/people/aca/robertfr/index.html) and directed by James Glossman, Lecturer in Directing and Shakespeare, Johns Hopkins University. After the performance, the playwright, director and actors will be available for a talk-back audience discussion.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Takeshita, Kenji

A mathematical model to predict the extraction behavior of metal ion between a polymer gel and an aqueous solution was proposed. It consists of the Flory-Huggins formula for evaluating thermodynamically the physico-chemical properties of polymer gel, the modified Stokes-Einstein equation to evaluate the mass transfer rate of metal ion into polymer gel and the equation to evaluate the extraction equilibrium. The extraction of lanthanide elements, Nd(III), Sm(III) and Gd(III), from an aqueous solution containing nitrate ion was carried out by the use of SDB (styrene-divinylbenzene copolymer) gel swollen with a bidentate organophosphorus compound, CMP (dihexyl-N,N-diethylcarbamoylmethylpohosphonate). The binary extraction and themore » effect of the crosslinking degree of SDB gel on the extraction rate were examined. These experimental results were in agreement with the predictions calculated by the proposed model. It was confirmed that the extraction behavior of lanthanide ions into the SDB gel was predicted accurately, when the physico-chemical properties of SDB gel, such as the affinity between SDB and CMP ({chi}) and the crosslinking degree ({nu}{sub e}), and a coefficient defined in the modified Stokes-Einstein equation (K{sub 0}) were known. This model is available as a tool to design an extraction chromatographic process using polymer gel.« less

Diffusivity Measurements of Volatile Organics in Levitated Viscous Aerosol Particles

NASA Astrophysics Data System (ADS)

Bastelberger, Sandra; Krieger, Ulrich; Luo, Beiping; Peter, Thomas

2017-04-01

Field measurements indicating that atmospheric secondary aerosol (SOA) particles can be present in a highly viscous, glassy state have spurred numerous studies addressing low water diffusivities in glassy aerosols, focusing on kinetic limitations to hygroscopic growth and the plasticizing effect of water. Less is known about diffusion limitations of organic molecules and oxidants in viscous matrices and how these might affect atmospheric chemistry and gas-particle phase partitioning of complex mixtures with constituents of different volatility. Often viscosity data has been used to infer diffusivity via the Stokes- Einstein relationship even though strong deviations from this relationship have been observed for matrices of high viscosity. In this study, we provide a quantitative estimate for the diffusivity of a volatile organic in a viscous matrix. Evaporation of single particles generated from an aqueous solution of sucrose and a small quantity of volatile tetraethylene glycol (PEG-4) is investigated in an electrodynamic balance at controlled relative humidity (RH) and temperature conditions, thereby varying the viscosity of the sucrose matrix. The evaporative loss of tetraethylene glycol as determined by Mie resonance spectroscopy is used in conjunction with a diffusion model to retrieve translational diffusion coefficients of tetraethylene glycol. The evaporation of PEG-4 shows a pronounced RH and temperature dependence and is severely depressed for RH 30% corresponding to diffusivities < 10-14 cm2/s at temperatures as high as 15 °C, implying that atmospheric volatile organic compounds (VOC) can be subject to severe diffusion limitations in glassy SOA. Comparison of the experimentally derived diffusivities with viscosity estimates for the ternary system reveals a breakdown of the Stokes-Einstein relationship.

Quintessence background for 5D Einstein-Gauss-Bonnet black holes

NASA Astrophysics Data System (ADS)

Ghosh, Sushant G.; Amir, Muhammed; Maharaj, Sunil D.

2017-08-01

As we know that the Lovelock theory is an extension of the general relativity to the higher-dimensions, in this theory the first- and the second-order terms correspond to general relativity and the Einstein-Gauss-Bonnet gravity, respectively. We obtain a 5D black hole solution in Einstein-Gauss-Bonnet gravity surrounded by the quintessence matter, and we also analyze their thermodynamical properties. Owing to the quintessence corrected black hole, the thermodynamic quantities have also been corrected except for the black hole entropy, and a phase transition is achievable. The phase transition for the thermodynamic stability is characterized by a discontinuity in the specific heat at r=r_C, with the stable (unstable) branch for r < (>) r_C.

Changes in concepts of time from Aristotle to Einstein

NASA Astrophysics Data System (ADS)

Sachs, Mendel

1996-03-01

The meaning of time and motion is discussed, at first tracing conceptual changes from Aristotle to Galileo/Newton to Einstein. Different views of ‘time’ in 20th century physics are then examined, with primary focus on the revolutionary changes that came with the theory of general relativity. Implications of its new view in all domains of physics are discussed — from elementary particles to cosmology. The special role of Hamilton's quaternion calculus in equations of motion in general relativity is shown.

On the hydrogen-bond network and the non-Arrhenius transport properties of water

NASA Astrophysics Data System (ADS)

Galamba, N.

2017-01-01

We study the structural and dynamic transformations of SPC/E water with temperature, through molecular dynamics (MD), and discuss the non-Arrhenius behavior of the transport properties and orientational dynamics, and the magnitude of the breakdown of the Stokes-Einstein (SE) and the Stokes-Einstein-Debye (SED) relations, in the light of these transformations. Our results show that deviations from Arrhenius behavior of the self-diffusion at low temperatures cannot be exclusively explained by the reduction of water defects (interstitial waters) and the increase of the local tetrahedrality, thus, suggesting the importance of the slowdown of collective rearrangements. Interestingly we find that at high temperatures (T  ⩾  340 K) water defects lead to a slight increase of the tetrahedrality and a decrease of the self-diffusion, opposite to water at low temperatures. The relative magnitude of the breakdown of the SE and the SED relations is found to be in accord with recent experiments (Dehaoui et al 2015 Proc. Natl Acad. Sci. USA 112 12020) resolving the discrepancy with previous MD results. Further, we show that SPC/E hydrogen-bond (HB) lifetimes deviate from Arrhenious behaviour at low temperatures in contrast with some previous MD studies. This deviation is nevertheless much smaller than that observed for the orientational dynamics and the transport properties of water, consistent with the relaxation times measured by several experimental methods. The HB acceptor exchange dynamics defined here by the acceptor switch and reform (librational dynamics) frequencies exhibit similar Arrhenius deviations, thus explaining to some extent the non-Arrhenius behavior of the transport properties and of the orientational dynamics of water. Our results also show that the fraction of HB switches through a bifurcated pathway follow a power law with the temperature decrease. Thus, at low temperatures HB acceptor switches are less frequent but occur on a faster time scale consistent with the temperature dependence of the ratio of the rotational relaxation times for the different Legendre polynomial ranks.

On the hydrogen-bond network and the non-Arrhenius transport properties of water.

PubMed

Galamba, N

2017-01-11

We study the structural and dynamic transformations of SPC/E water with temperature, through molecular dynamics (MD), and discuss the non-Arrhenius behavior of the transport properties and orientational dynamics, and the magnitude of the breakdown of the Stokes-Einstein (SE) and the Stokes-Einstein-Debye (SED) relations, in the light of these transformations. Our results show that deviations from Arrhenius behavior of the self-diffusion at low temperatures cannot be exclusively explained by the reduction of water defects (interstitial waters) and the increase of the local tetrahedrality, thus, suggesting the importance of the slowdown of collective rearrangements. Interestingly we find that at high temperatures (T  ⩾  340 K) water defects lead to a slight increase of the tetrahedrality and a decrease of the self-diffusion, opposite to water at low temperatures. The relative magnitude of the breakdown of the SE and the SED relations is found to be in accord with recent experiments (Dehaoui et al 2015 Proc. Natl Acad. Sci. USA 112 12020) resolving the discrepancy with previous MD results. Further, we show that SPC/E hydrogen-bond (HB) lifetimes deviate from Arrhenious behaviour at low temperatures in contrast with some previous MD studies. This deviation is nevertheless much smaller than that observed for the orientational dynamics and the transport properties of water, consistent with the relaxation times measured by several experimental methods. The HB acceptor exchange dynamics defined here by the acceptor switch and reform (librational dynamics) frequencies exhibit similar Arrhenius deviations, thus explaining to some extent the non-Arrhenius behavior of the transport properties and of the orientational dynamics of water. Our results also show that the fraction of HB switches through a bifurcated pathway follow a power law with the temperature decrease. Thus, at low temperatures HB acceptor switches are less frequent but occur on a faster time scale consistent with the temperature dependence of the ratio of the rotational relaxation times for the different Legendre polynomial ranks.

Fluctuation, dissipation, and a non-equilibrium ``equation of state'' via nonlinear microrheology of hydrodynamically interacting colloids

NASA Astrophysics Data System (ADS)

Chu, Henry; Zia, Roseanna

2014-11-01

In our recently developed non-equilibrium Stokes-Einstein relation for microrheology, we showed that, in the absence of hydrodynamic interactions, the stress in a suspension is given by a balance between fluctuation and dissipation. Here we generalize our theory to develop a simple analytical relation connecting diffusive fluctuation, viscous dissipation and suspension stress in systems of hydrodynamically interacting colloids. In active microrheology, a Brownian probe is driven through a complex medium. The strength of probe forcing compared to the entropic restoring force defines a Peclet number, Pe. In the absence of hydrodynamics, normal stress differences scale as Pe4 and Pe for weak and strong probe forcing, respectively. But as hydrodynamics become important, interparticle forces give way to lubrication interactions and the normal stresses scale as Pe2 and Peδln(Pe), where 0.773 <= δ <= 1 as hydrodynamics vary from strong to weak. The new phenomenological theory is shown to agree with standard micromechanical definitions of the stress. A connection is made between the stress and an effective temperature of the medium, prompting the interpretation of the particle stress as the energy density, and the expression for osmotic pressure as a ``non-equilibrium equation of state.''

Freud's superpotential in general relativity and in Einstein-Cartan theory

NASA Astrophysics Data System (ADS)

Böhmer, Christian G.; Hehl, Friedrich W.

2018-02-01

The identification of a suitable gravitational energy in theories of gravity has a long history, and it is well known that a unique answer cannot be given. In the first part of this paper we present a streamlined version of the derivation of Freud's superpotential in general relativity. It is found if we once integrate the gravitational field equation by parts. This allows us to extend these results directly to the Einstein-Cartan theory. Interestingly, Freud's original expression, first stated in 1939, remains valid even when considering gravitational theories in Riemann-Cartan or, more generally, in metric-affine spacetimes.

The dynamic crossover in water does not require bulk water.

PubMed

Turton, David A; Corsaro, Carmelo; Martin, David F; Mallamace, Francesco; Wynne, Klaas

2012-06-14

Many of the anomalous properties of water may be explained by invoking a second critical point that terminates the coexistence line between the low- and high-density amorphous states in the liquid. Direct experimental evidence of this point, and the associated polyamorphic liquid-liquid transition, is elusive as it is necessary for liquid water to be cooled below its homogeneous-nucleation temperature. To avoid crystallization, water in the eutectic LiCl solution has been studied but then it is generally considered that "bulk" water cannot be present. However, recent computational and experimental studies observe cooperative hydration in which case it is possible that sufficient hydrogen-bonded water is present for the essential characteristics of water to be preserved. For femtosecond optical Kerr-effect and nuclear magnetic resonance measurements, we observe in each case a fractional Stokes-Einstein relation with evidence of the dynamic crossover appearing near 220 K and 250 K respectively. Spectra obtained in the glass state also confirm the complex nature of the hydrogen-bonding modes reported for neat room-temperature water and support predictions of anomalous diffusion due to "worm-hole" structure.

Viscoelasticity of Depletion-Induced Emulsion Gels

NASA Astrophysics Data System (ADS)

Meller, Amit; Stavans, Joel; Gisler, Thomas; Weitz, David A.

1997-03-01

The presence of non-adsorbing polymer in an oil-in-water emulsion results in a depletion attraction between the emulsion droplets, causing a phase separation into an droplet-rich phase and a polymer-rich phase largely devoid of emulsion droplets. At high enough droplet concentration, however, this phase separation is kinetically arrested to a gel-like state where large (diameter>50 μm) clusters of droplets are weakly connected via ramifications, leading to a measurable elastic modulus. We measure the mean-square displacement <Δ r ^2 (t)> of a droplet of size a inside a cluster using diffusing wave spectroscopy (DWS); by means of a generalized Stokes-Einstein relation we obtain frequency dependent storage and loss moduli G'(ω) and G''(ω), respectively. G'(ω) reaches a plateau at frequencies between 1 rad/s and 100 rad/s; this plateau modulus is found to scale with the hard-sphere energy density k_BT/a^3; within the clusters the droplets are densely packed, yet remain undeformed, the droplet volume fraction being determined by the osmotic pressure exerted by the polymer.

The Foundations of Einstein's Theory of Gravitation

NASA Astrophysics Data System (ADS)

Freundlich, Erwin; Brose, Translated by Henry L.; Einstein, Preface by Albert; Turner, Introduction by H. H.

2011-06-01

Introduction; 1. The special theory of relativity as a stepping-stone to the general theory of relativity; 2. Two fundamental postulates in the mathematical formulation of physical laws; 3. Concerning the fulfilment of the two postulates; 4. The difficulties in the principles of classical mechanics; 5. Einstein's theory of gravitation; 6. The verification of the new theory by actual experience; Appendix; Index.

Efficient Scheme for Perfect Collective Einstein-Podolsky-Rosen Steering

PubMed Central

Wang, M.; Gong, Q. H.; Ficek, Z.; He, Q. Y.

2015-01-01

A practical scheme for the demonstration of perfect one-sided device-independent quantum secret sharing is proposed. The scheme involves a three-mode optomechanical system in which a pair of independent cavity modes is driven by short laser pulses and interact with a movable mirror. We demonstrate that by tuning the laser frequency to the blue (anti-Stokes) sideband of the average frequency of the cavity modes, the modes become mutually coherent and then may collectively steer the mirror mode to a perfect Einstein-Podolsky-Rosen state. The scheme is shown to be experimentally feasible, it is robust against the frequency difference between the modes, mechanical thermal noise and damping, and coupling strengths of the cavity modes to the mirror. PMID:26212901

A Classical Based Derivation of Time Dilation Providing First Order Accuracy to Schwarzschild's Solution of Einstein's Field Equations

NASA Astrophysics Data System (ADS)

Austin, Rickey W.

In Einstein's theory of Special Relativity (SR), one method to derive relativistic kinetic energy is via applying the classical work-energy theorem to relativistic momentum. This approach starts with a classical based work-energy theorem and applies SR's momentum to the derivation. One outcome of this derivation is relativistic kinetic energy. From this derivation, it is rather straight forward to form a kinetic energy based time dilation function. In the derivation of General Relativity a common approach is to bypass classical laws as a starting point. Instead a rigorous development of differential geometry and Riemannian space is constructed, from which classical based laws are derived. This is in contrast to SR's approach of starting with classical laws and applying the consequences of the universal speed of light by all observers. A possible method to derive time dilation due to Newtonian gravitational potential energy (NGPE) is to apply SR's approach to deriving relativistic kinetic energy. It will be shown this method gives a first order accuracy compared to Schwarzschild's metric. The SR's kinetic energy and the newly derived NGPE derivation are combined to form a Riemannian metric based on these two energies. A geodesic is derived and calculations compared to Schwarzschild's geodesic for an orbiting test mass about a central, non-rotating, non-charged massive body. The new metric results in high accuracy calculations when compared to Einsteins General Relativity's prediction. The new method provides a candidate approach for starting with classical laws and deriving General Relativity effects. This approach mimics SR's method of starting with classical mechanics when deriving relativistic equations. As a compliment to introducing General Relativity, it provides a plausible scaffolding method from classical physics when teaching introductory General Relativity. A straight forward path from classical laws to General Relativity will be derived. This derivation provides a minimum first order accuracy to Schwarzschild's solution to Einstein's field equations.

BOOK REVIEW: Partial Differential Equations in General Relativity

NASA Astrophysics Data System (ADS)

Halburd, Rodney G.

2008-11-01

Although many books on general relativity contain an overview of the relevant background material from differential geometry, very little attention is usually paid to background material from the theory of differential equations. This is understandable in a first course on relativity but it often limits the kinds of problems that can be studied rigorously. Einstein's field equations lie at the heart of general relativity. They are a system of partial differential equations (PDEs) relating the curvature of spacetime to properties of matter. A central part of most problems in general relativity is to extract information about solutions of these equations. Most standard texts achieve this by studying exact solutions or numerical and analytical approximations. In the book under review, Alan Rendall emphasises the role of rigorous qualitative methods in general relativity. There has long been a need for such a book, giving a broad overview of the relevant background from the theory of partial differential equations, and not just from differential geometry. It should be noted that the book also covers the basic theory of ordinary differential equations. Although there are many good books on the rigorous theory of PDEs, methods related to the Einstein equations deserve special attention, not only because of the complexity and importance of these equations, but because these equations do not fit into any of the standard classes of equations (elliptic, parabolic, hyperbolic) that one typically encounters in a course on PDEs. Even specifying exactly what ones means by a Cauchy problem in general relativity requires considerable care. The main problem here is that the manifold on which the solution is defined is determined by the solution itself. This means that one does not simply define data on a submanifold. Rendall's book gives a good overview of applications and results from the qualitative theory of PDEs to general relativity. It would be impossible to give detailed proofs of the main results in a self-contained book of reasonable length. Instead, the author concentrates on providing key definitions together with their motivations and explaining the main results, tools and difficulties for each topic. There is a section at the end of each chapter which points the reader to appropriate literature for further details. In this way, Rendall manages to describe the central issues concerning many subjects. Each of the twelve chapters (except for one on functional analysis) contains an important application to general relativity. For example, the chapter on ODEs discusses Bianchi spacetimes and the Einstein constraint equations are discussed in the chapter on elliptic equations. In the chapter on hyperbolic equations, the Einstein dust system is considered in the context of Leray hyperbolicity and Gowdy spacetimes are analysed in the section on Fuchsian methods. The book concludes with four chapters purely on applications to general relativity, namely The Cauchy problem for the Einstein equations, Global results, The Einstein-Vlasov system and The Einstein-scalar field systems. On reading this book, someone with a basic understanding of relativity could rapidly develop a picture, painted in broad brush strokes, of the main problems and tools in the area. It would be particularly useful for someone, such as a graduate student, just entering the field, or for someone who wants a general idea of the main issues. For those who want to go further, a lot more reading will be necessary but the author has sign-posted appropriate entry points to the literature throughout the book. Ultimately, this is a very technical subject and this book can only provide an overview. I believe that Alan Rendall's book is a valuable contribution to the field of mathematical relativity.

Einstein's creative thinking and the general theory of relativity: a documented report.

PubMed

Rothenberg, A

1979-01-01

A document written by Albert Einstein has recently come to light in which the eminent scientist described the actual sequence of his thoughts leading to the development of the general theory of relativity. The key creative thought was an instance of a type of creative cognition the author has previously designated "Janusian thinking," Janusian thinking consists of actively conceiving two or more opposite or antithetical concepts, ideas, or images simultaneously. This form of high-level secondary process cognition has been found to operate widely in art, science, and other fields.

Pure field theories and MACSYMA algorithms

NASA Technical Reports Server (NTRS)

Ament, W. S.

1977-01-01

A pure field theory attempts to describe physical phenomena through singularity-free solutions of field equations resulting from an action principle. The physics goes into forming the action principle and interpreting specific results. Algorithms for the intervening mathematical steps are sketched. Vacuum general relativity is a pure field theory, serving as model and providing checks for generalizations. The fields of general relativity are the 10 components of a symmetric Riemannian metric tensor; those of the Einstein-Straus generalization are the 16 components of a nonsymmetric. Algebraic properties are exploited in top level MACSYMA commands toward performing some of the algorithms of that generalization. The light cone for the theory as left by Einstein and Straus is found and simplifications of that theory are discussed.

Multilocality and fusion rules on the generalized structure functions in two-dimensional and three-dimensional Navier-Stokes turbulence.

PubMed

Gkioulekas, Eleftherios

2016-09-01

Using the fusion-rules hypothesis for three-dimensional and two-dimensional Navier-Stokes turbulence, we generalize a previous nonperturbative locality proof to multiple applications of the nonlinear interactions operator on generalized structure functions of velocity differences. We call this generalization of nonperturbative locality to multiple applications of the nonlinear interactions operator "multilocality." The resulting cross terms pose a new challenge requiring a new argument and the introduction of a new fusion rule that takes advantage of rotational symmetry. Our main result is that the fusion-rules hypothesis implies both locality and multilocality in both the IR and UV limits for the downscale energy cascade of three-dimensional Navier-Stokes turbulence and the downscale enstrophy cascade and inverse energy cascade of two-dimensional Navier-Stokes turbulence. We stress that these claims relate to nonperturbative locality of generalized structure functions on all orders and not the term-by-term perturbative locality of diagrammatic theories or closure models that involve only two-point correlation and response functions.

Einstein's conversion from his static to an expanding universe

NASA Astrophysics Data System (ADS)

Nussbaumer, Harry

2014-02-01

In 1917 Einstein initiated modern cosmology by postulating, based on general relativity, a homogenous, static, spatially curved universe. To counteract gravitational contraction he introduced the cosmological constant. In 1922 Alexander Friedman showed that Albert Einstein's fundamental equations also allow dynamical worlds, and in 1927 Georges Lemaître, backed by observational evidence, concluded that our universe was expanding. Einstein impetuously rejected Friedman's as well as Lemaître's findings. However, in 1931 he retracted his former static model in favour of a dynamic solution. This investigation follows Einstein on his hesitating path from a static to the expanding universe. Contrary to an often advocated belief the primary motive for his switch was not observational evidence, but the realisation that his static model was unstable.

Measuring the viscosity of whole bovine lens using a fiber optic oxygen sensing system

PubMed Central

Thao, Mai T.; Perez, Daniel; Dillon, James

2014-01-01

Purpose To obtain a better understanding of oxygen and nutrient transport within the lens, the viscosity of whole lenses was investigated using a fiber optic oxygen sensor (optode). The diffusion coefficient of oxygen was calculated using the Stokes-Einstein equation at the slip boundary condition. Methods The optode was used to measure the oxygen decay signal in samples consisting of different glycerol/water solutions with known viscosities. The oxygen decay signal was fitted to a double exponential decay rate equation, and the lifetimes (tau) were calculated. It was determined that the tau-viscosity relationship is linear, which served as the standard curve. The same procedure was applied to fresh bovine lenses, and the unknown viscosity of the bovine lens was calculated from the tau-viscosity relationship. Results The average viscosity in a whole bovine lens was determined to be 5.74±0.88 cP by our method. Using the Stokes-Einstein equation at the slip boundary condition, the diffusion coefficient for oxygen was calculated to be 8.2 × 10−6 cm2/s. Conclusions These data indicate a higher resistance to flow for oxygen and nutrients in the lens than what is currently assumed in the literature. Overall, this study allows a better understanding of oxygen transport within the lens. PMID:24505211

A novel biological 'twin-father' temporal paradox of General Relativity in a Gödel universe - Where reproductive biology meets theoretical physics.

PubMed

Ashrafian, Hutan

2018-03-01

Several temporal paradoxes exist in physics. These include General Relativity's grandfather and ontological paradoxes and Special Relativity's Langevin-Einstein twin-paradox. General relativity paradoxes can exist due to a Gödel universe that follows Gödel's closed timelike curves solution to Einstein's field equations. A novel biological temporal paradox of General Relativity is proposed based on reproductive biology's phenomenon of heteropaternal fecundation. Herein, dizygotic twins from two different fathers are the result of concomitant fertilization during one menstrual cycle. In this case an Oedipus-like individual exposed to a Gödel closed timelike curve would sire a child during his maternal fertilization cycle. As a consequence of heteropaternal superfecundation, he would father his own dizygotic twin and would therefore generate a new class of autofraternal superfecundation, and by doing so creating a 'twin-father' temporal paradox. Copyright © 2017 Elsevier Ltd. All rights reserved.

Incompressible limit of the degenerate quantum compressible Navier-Stokes equations with general initial data

NASA Astrophysics Data System (ADS)

Kwon, Young-Sam; Li, Fucai

2018-03-01

In this paper we study the incompressible limit of the degenerate quantum compressible Navier-Stokes equations in a periodic domain T3 and the whole space R3 with general initial data. In the periodic case, by applying the refined relative entropy method and carrying out the detailed analysis on the oscillations of velocity, we prove rigorously that the gradient part of the weak solutions (velocity) of the degenerate quantum compressible Navier-Stokes equations converge to the strong solution of the incompressible Navier-Stokes equations. Our results improve considerably the ones obtained by Yang, Ju and Yang [25] where only the well-prepared initial data case is considered. While for the whole space case, thanks to the Strichartz's estimates of linear wave equations, we can obtain the convergence of the weak solutions of the degenerate quantum compressible Navier-Stokes equations to the strong solution of the incompressible Navier-Stokes/Euler equations with a linear damping term. Moreover, the convergence rates are also given.

General Relativity and Energy

ERIC Educational Resources Information Center

Jackson, A. T.

1973-01-01

Reviews theoretical and experimental fundamentals of Einstein's theory of general relativity. Indicates that recent development of the theory of the continually expanding universe may lead to revision of the space-time continuum of the finite and unbounded universe. (CC)

A review of the contributions of Albert Einstein to earth sciences--in commemoration of the World Year of Physics.

PubMed

Martínez-Frías, Jesús; Hochberg, David; Rull, Fernando

2006-02-01

The World Year of Physics (2005) is an international celebration to commemorate the 100th anniversary of Einstein's "Annus Mirabilis." The United Nations has officially declared 2005 as the International Year of Physics. However, the impact of Einstein's ideas was not restricted to physics. Among numerous other disciplines, Einstein also made significant and specific contributions to Earth Sciences. His geosciences-related letters, comments, and scientific articles are dispersed, not easily accessible, and are poorly known. The present review attempts to integrate them as a tribute to Einstein in commemoration of this centenary. These contributions can be classified into three basic areas: geodynamics, geological (planetary) catastrophism, and fluvial geomorphology. Regarding geodynamics, Einstein essentially supported Hapgood's very controversial theory called Earth Crust Displacement. With respect to geological (planetary) catastrophism, it is shown how the ideas of Einstein about Velikovsky's proposals evolved from 1946 to 1955. Finally, in relation to fluvial geodynamics, the review incorporates the elegant work in which Einstein explains the formation of meandering rivers. A general analysis of his contributions is also carried out from today's perspective. Given the interdisciplinarity and implications of Einstein's achievements to multiple fields of knowledge, we propose that the year 2005 serve, rather than to confine his universal figure within a specific scientific area, to broaden it for a better appreciation of this brilliant scientist in all of his dimensions.

Discrete adjoint of fractional step Navier-Stokes solver in generalized coordinates

NASA Astrophysics Data System (ADS)

Wang, Mengze; Mons, Vincent; Zaki, Tamer

2017-11-01

Optimization and control in transitional and turbulent flows require evaluation of gradients of the flow state with respect to the problem parameters. Using adjoint approaches, these high-dimensional gradients can be evaluated with a similar computational cost as the forward Navier-Stokes simulations. The adjoint algorithm can be obtained by discretizing the continuous adjoint Navier-Stokes equations or by deriving the adjoint to the discretized Navier-Stokes equations directly. The latter algorithm is necessary when the forward-adjoint relations must be satisfied to machine precision. In this work, our forward model is the fractional step solution to the Navier-Stokes equations in generalized coordinates, proposed by Rosenfeld, Kwak & Vinokur. We derive the corresponding discrete adjoint equations. We also demonstrate the accuracy of the combined forward-adjoint model, and its application to unsteady wall-bounded flows. This work has been partially funded by the Office of Naval Research (Grant N00014-16-1-2542).

Long-time dynamics of Rouse-Zimm polymers in dilute solutions with hydrodynamic memory.

PubMed

Lisy, V; Tothova, J; Zatovsky, A V

2004-12-01

The dynamics of flexible polymers in dilute solutions is studied taking into account the hydrodynamic memory, as a consequence of fluid inertia. As distinct from the Rouse-Zimm (RZ) theory, the Boussinesq friction force acts on the monomers (beads) instead of the Stokes force, and the motion of the solvent is governed by the nonstationary Navier-Stokes equations. The obtained generalized RZ equation is solved approximately using the preaveraging of the Oseen tensor. It is shown that the time correlation functions describing the polymer motion essentially differ from those in the RZ model. The mean-square displacement (MSD) of the polymer coil is at short times approximately t(2) (instead of approximately t). At long times the MSD contains additional (to the Einstein term) contributions, the leading of which is approximately t. The relaxation of the internal normal modes of the polymer differs from the traditional exponential decay. It is displayed in the long-time tails of their correlation functions, the longest lived being approximately t(-3/2) in the Rouse limit and t(-5/2) in the Zimm case, when the hydrodynamic interaction is strong. It is discussed that the found peculiarities, in particular, an effectively slower diffusion of the polymer coil, should be observable in dynamic scattering experiments. (c) 2004 American Institute of Physics

Energy distributions of Bianchi type-VI h Universe in general relativity and teleparallel gravity

NASA Astrophysics Data System (ADS)

Özkurt, Ş.; eref; Aygün, Sezg&idot; n.

2017-04-01

In this paper, we have investigated the energy and momentum density distributions for the inhomogeneous generalizations of homogeneous Bianchi type-VI h metric with Einstein, Bergmann-Thomson, Landau-Lifshitz, Papapetrou, Tolman and Møller prescriptions in general relativity (GR) and teleparallel gravity (TG). We have found exactly the same results for Einstein, Bergmann-Thomson and Landau-Lifshitz energy-momentum distributions in Bianchi type-VI h metric for different gravitation theories. The energy-momentum distributions of the Bianchi type- VI h metric are found to be zero for h = -1 in GR and TG. However, our results agree with Tripathy et al, Tryon, Rosen and Aygün et al.

Curved spaces before Einstein: Karl Schwarzschild's cosmological speculations and the beginnings of relativistic cosmology (German Title: Gekrümmte Universen vor Einstein: Karl Schwarzschilds kosmologische Spekulationen und die Anfänge der relativistischen Kosmologie)

NASA Astrophysics Data System (ADS)

Schemmel, Matthias

In contrast to most of his collegues in astronomy and physics, the German astronomer Karl Schwarzschild immediately recognized the significance of general relativity for physics and astronomy, and played a pioneering role in its early development. In this contribution, it is argued that the clue for understanding Schwarzschild's exceptional reaction to general relativity lies in the study of his prerelativistic work. Long before the rise of general relativity, Schwarzschild occupied himself with foundational problems on the borderline of physics, astronomy, and mathematics that, from today's perspective, belong to the field of problems of that theory. In this contribution, the example of Schwarzschild's early speculations about the non-Euclidean nature of physical space on cosmological scales is presented and their reflection in his reception of general relativity is discussed.

Einstein-Gauss-Bonnet theory of gravity: The Gauss-Bonnet-Katz boundary term

NASA Astrophysics Data System (ADS)

Deruelle, Nathalie; Merino, Nelson; Olea, Rodrigo

2018-05-01

We propose a boundary term to the Einstein-Gauss-Bonnet action for gravity, which uses the Chern-Weil theorem plus a dimensional continuation process, such that the extremization of the full action yields the equations of motion when Dirichlet boundary conditions are imposed. When translated into tensorial language, this boundary term is the generalization to this theory of the Katz boundary term and vector for general relativity. The boundary term constructed in this paper allows to deal with a general background and is not equivalent to the Gibbons-Hawking-Myers boundary term. However, we show that they coincide if one replaces the background of the Katz procedure by a product manifold. As a first application we show that this Einstein Gauss-Bonnet Katz action yields, without any extra ingredients, the expected mass of the Boulware-Deser black hole.

Averaging problem in general relativity, macroscopic gravity and using Einstein's equations in cosmology.

NASA Astrophysics Data System (ADS)

Zalaletdinov, R. M.

1998-04-01

The averaging problem in general relativity is briefly discussed. A new setting of the problem as that of macroscopic description of gravitation is proposed. A covariant space-time averaging procedure is described. The structure of the geometry of macroscopic space-time, which follows from averaging Cartan's structure equations, is described and the correlation tensors present in the theory are discussed. The macroscopic field equations (averaged Einstein's equations) derived in the framework of the approach are presented and their structure is analysed. The correspondence principle for macroscopic gravity is formulated and a definition of the stress-energy tensor for the macroscopic gravitational field is proposed. It is shown that the physical meaning of using Einstein's equations with a hydrodynamic stress-energy tensor in looking for cosmological models means neglecting all gravitational field correlations. The system of macroscopic gravity equations to be solved when the correlations are taken into consideration is given and described.

Probe diffusion of labeled polymers inside polyacrylic acid solutions: A polyelectrolyte effect

NASA Astrophysics Data System (ADS)

Mishra, Banani; Mithra, K.; Khandai, Santripti; Jena, Sidhartha S.

2018-05-01

Probe diffusion of fluorescently labeled Dextran 40 inside polyelectrolyte solution of polyacrylic acid (PAA) was investigated using Fluorescence Recovery After Photobleaching technique. The crowding and interaction effects on probe diffusion were controlled by tuning background polymer and added external electrolyte concentration. For all the salt concentration, an overall decrease in diffusion coefficient is observed with rise in polymer concentration. The diffusion coefficient decreases with decrease in salt concentration whereas the solution viscosity increases, indicating a competition between viscous drag and electrostatic interaction. A large positive deviation from the ideal Stokes-Einstein relation is observed for high polymer and low salt concentration, which reduces markedly with addition of salt confirming polyelectrolyte effects, plays a major role in deciding the probe diffusion.

Einstein versus the Simple Pendulum Formula: Does Gravity Slow All Clocks?

ERIC Educational Resources Information Center

Puri, Avinash

2015-01-01

According to the Newtonian formula for a simple pendulum, the period of a pendulum is inversely proportional to the square root of "g", the gravitational field strength. Einstein's theory of general relativity leads to the result that time slows down where gravity is intense. The two claims look contradictory and can muddle student and…

Schwinger's Approach to Einstein's Gravity

NASA Astrophysics Data System (ADS)

Milton, Kim

2012-05-01

Albert Einstein was one of Julian Schwinger's heroes, and Schwinger was greatly honored when he received the first Einstein Prize (together with Kurt Godel) for his work on quantum electrodynamics. Schwinger contributed greatly to the development of a quantum version of gravitational theory, and his work led directly to the important work of (his students) Arnowitt, Deser, and DeWitt on the subject. Later in the 1960's and 1970's Schwinger developed a new formulation of quantum field theory, which he dubbed Source Theory, in an attempt to get closer contact to phenomena. In this formulation, he revisited gravity, and in books and papers showed how Einstein's theory of General Relativity emerged naturally from one physical assumption: that the carrier of the gravitational force is a massless, helicity-2 particle, the graviton. (There has been a minor dispute whether gravitational theory can be considered as the massless limit of a massive spin-2 theory; Schwinger believed that was the case, while Van Dam and Veltman concluded the opposite.) In the process, he showed how all of the tests of General Relativity could be explained simply, without using the full machinery of the theory and without the extraneous concept of curved space, including such effects as geodetic precession and the Lense-Thirring effect. (These effects have now been verified by the Gravity Probe B experiment.) This did not mean that he did not accept Einstein's equations, and in his book and full article on the subject, he showed how those emerge essentially uniquely from the assumption of the graviton. So to speak of Schwinger versus Einstein is misleading, although it is true that Schwinger saw no necessity to talk of curved spacetime. In this talk I will lay out Schwinger's approach, and the connection to Einstein's theory.

Competing effects of particle and medium inertia on particle diffusion in viscoelastic materials, and their ramifications for passive microrheology.

PubMed

Indei, Tsutomu; Schieber, Jay D; Córdoba, Andrés

2012-04-01

We analyze the appropriate form for the generalized Stokes-Einstein relation (GSER) for viscoelastic solids and fluids when bead inertia and medium inertia are taken into account, which we call the inertial GSER. It was previously shown for Maxwell fluids that the Basset (or Boussinesq) force arising from medium inertia can act purely dissipatively at high frequencies, where elasticity of the medium is dominant. In order to elucidate the cause of this counterintuitive result, we consider Brownian motion in a purely elastic solid where ordinary Stokes-type dissipation is not possible. The fluctuation-dissipation theorem requires the presence of a dissipative mechanism for the particle to experience fluctuating Brownian forces in a purely elastic solid. We show that the mechanism for such dissipation arises from the radiation of elastic waves toward the system boundaries. The frictional force associated with this mechanism is the Basset force, and it exists only when medium inertia is taken into consideration in the analysis of such a system. We consider first a one-dimensional harmonic lattice where all terms in the generalized Langevin equation--i.e., the elastic term, the memory kernel, and Brownian forces-can be found analytically from projection-operator methods. We show that the dissipation is purely from radiation of elastic waves. A similar analysis is made on a particle in a continuum, three-dimensional purely elastic solid, where the memory kernel is determined from continuum mechanics. Again, dissipation arises only from radiation of elastic shear waves toward infinite boundaries when medium inertia is taken into account. If the medium is a viscoelastic solid, Stokes-type dissipation is possible in addition to radiational dissipation so that the wave decays at the penetration depth. Inertial motion of the bead couples with the elasticity of the viscoelastic material, resulting in a possible resonant oscillation of the mean-square displacement (MSD) of the bead. On the other hand, medium inertia (the Basset force) tends to attenuate the oscillations by the dissipation mechanism described above. Thus competition between bead inertia and medium inertia determines whether or not the MSD oscillates. We find that, if the medium density is larger than 4/7 of the bead density, the Basset damping will suppress oscillations in the MSD; this criterion is sufficient but not necessary to present oscillations.

Covariant Formulation of Fluid Dynamics and Estakhr's Material Geodesic Equation, far down the Rabbit hole

NASA Astrophysics Data System (ADS)

Estakhr, Ahmad Reza

2013-11-01

``When i meet God, I am going to ask him two questions, why relativity and why turbulence. A. Einstein'' You probably will not need to ask these questions of God, I've already answered both of them. Uμ = γ (c , u (r --> , t)) denotes four-velocity field. Jμ = ρUμ denotes four-current mass density. Estakhr's Material-Geodesic equation is developed analogy of Navier Stokes equation and Einstein Geodesic equation. DJμ/Dτ =dJμ/Dτ +ΓαβμJαUβ =JνΩμν +∂νTμν +ΓαβμJαUβ Covariant formulation of fluid dynamics, describe the motion of fluid substances. The local existence and uniqueness theorem for geodesics states that geodesics on a smooth manifold with an affine connection exist, and are unique. EMG equation is also applicable in different branches of physics, it all depend on what you mean by 4-current density, if you mean 4-current electron number density then it is plasma physics, if you mean 4-current electron charge density then it is DJμ/Dτ =JνFμν +∂νTμν +ΓαβμJαUβ electromagnetism.

Induced matter brane gravity and Einstein static universe

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heydarzade, Y.; Darabi, F., E-mail: heydarzade@azaruniv.edu, E-mail: f.darabi@azaruniv.edu

We investigate stability of the Einstein static universe against the scalar, vector and tensor perturbations in the context of induced matter brane gravity. It is shown that in the framework of this model, the Einstein static universe has a positive spatial curvature. In contrast to the classical general relativity, it is found that a stable Einstein static universe against the scalar perturbations does exist provided that the variation of time dependent geometrical equation of state parameter is proportional to the minus of the variation of the scale factor, δ ω{sub g}(t) = −Cδ a(t). We obtain neutral stability against the vector perturbations, and themore » stability against the tensor perturbations is guaranteed due to the positivity of the spatial curvature of the Einstein static universe in induced matter brane gravity.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mohapi, N.; Hees, A.; Larena, J., E-mail: n.mohapi@gmail.com, E-mail: a.hees@ru.ac.za, E-mail: j.larena@ru.ac.za

The Einstein Equivalence Principle is a fundamental principle of the theory of General Relativity. While this principle has been thoroughly tested with standard matter, the question of its validity in the Dark sector remains open. In this paper, we consider a general tensor-scalar theory that allows to test the equivalence principle in the Dark sector by introducing two different conformal couplings to standard matter and to Dark matter. We constrain these couplings by considering galactic observations of strong lensing and of velocity dispersion. Our analysis shows that, in the case of a violation of the Einstein Equivalence Principle, data favourmore » violations through coupling strengths that are of opposite signs for ordinary and Dark matter. At the same time, our analysis does not show any significant deviations from General Relativity.« less

Stability of stationary-axisymmetric black holes in vacuum general relativity to axisymmetric electromagnetic perturbations

NASA Astrophysics Data System (ADS)

Prabhu, Kartik; Wald, Robert M.

2018-01-01

We consider arbitrary stationary and axisymmetric black holes in general relativity in (d +1) dimensions (with d ≥slant 3 ) that satisfy the vacuum Einstein equation and have a non-degenerate horizon. We prove that the canonical energy of axisymmetric electromagnetic perturbations is positive definite. This establishes that all vacuum black holes are stable to axisymmetric electromagnetic perturbations. Our results also hold for asymptotically de Sitter black holes that satisfy the vacuum Einstein equation with a positive cosmological constant. Our results also apply to extremal black holes provided that the initial perturbation vanishes in a neighborhood of the horizon.

Mesoscale Particle-Based Model of Electrophoresis

DOE PAGES

Giera, Brian; Zepeda-Ruiz, Luis A.; Pascall, Andrew J.; ...

2015-07-31

Here, we develop and evaluate a semi-empirical particle-based model of electrophoresis using extensive mesoscale simulations. We parameterize the model using only measurable quantities from a broad set of colloidal suspensions with properties that span the experimentally relevant regime. With sufficient sampling, simulated diffusivities and electrophoretic velocities match predictions of the ubiquitous Stokes-Einstein and Henry equations, respectively. This agreement holds for non-polar and aqueous solvents or ionic liquid colloidal suspensions under a wide range of applied electric fields.

Mesoscale Particle-Based Model of Electrophoresis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Giera, Brian; Zepeda-Ruiz, Luis A.; Pascall, Andrew J.

Here, we develop and evaluate a semi-empirical particle-based model of electrophoresis using extensive mesoscale simulations. We parameterize the model using only measurable quantities from a broad set of colloidal suspensions with properties that span the experimentally relevant regime. With sufficient sampling, simulated diffusivities and electrophoretic velocities match predictions of the ubiquitous Stokes-Einstein and Henry equations, respectively. This agreement holds for non-polar and aqueous solvents or ionic liquid colloidal suspensions under a wide range of applied electric fields.

The relativity revolution from the perspective of historical epistemology.

PubMed

Renn, Jürgen

2004-12-01

This essay analyzes Einstein's relativity revolution as part of a long-term development of knowledge in which the knowledge system of classical physics was reorganized in a process of reflection, described here as a "Copernican process." This process led in 1905 to the introduction of fundamentally new concepts of space, time, matter, and radiation. On the basis of an extensive historical reconstruction, the heuristics of Einstein's creation of the general theory of relativity, completing the relativity revolution, is interpreted as a further transformation of the knowledge of classical physics, starting from conceiving gravitation as a borderline problem between field theory and mechanics. The essay thus provides an answer to the puzzle of how Einstein was able to create a theory capable of accounting for a wide range of phenomena that were discovered only much later.

Spinning fluids in general relativity. II - Self-consistent formulation

NASA Technical Reports Server (NTRS)

Ray, John R.; Smalley, Larry, L.; Krisch, Jean P.

1987-01-01

Methods used earlier to derive the equations of motion for a spinning fluid in the Einstein-Cartan theory are specialized to the case of general relativity. The main idea is to include the spin as a thermodynamic variable in the theory.

Gravitational consequences of modern field theories

NASA Technical Reports Server (NTRS)

Horowitz, Gary T.

1989-01-01

Some gravitational consequences of certain extensions of Einstein's general theory of relativity are discussed. These theories are not alternative theories of gravity in the usual sense. It is assumed that general relativity is the appropriate description of all gravitational phenomena which were observed to date.

Critical remarks on Bruno Thuring's polemic against Einstein.

NASA Astrophysics Data System (ADS)

Kerschbaum, F.; Lackner, K.; Posch, T.

2005-08-01

Bruno Thüring (1905-1989) was among those scientists who joined the campaign against Einstein's Theories of Relativity which was undertaken in the name of so-called "German Physics". Thüring served as director of Vienna's University Observatory between 1940-45; hence, we present biographical information on his scientific and administrative activities in Vienna, partly based on interviews with time-witnesses. It is one of Thüring's basic convictions that Einstein's work cannot be understood without an analysis of the developments of physics and philosophy in the 19th century. While this is true generally, Thüring's account of these developments is rather superficial. For example, Thüring considers Kant's idea of the a priori status of geometry as a wholly sufficient epistemological foundation of mechanics, while both post-Kantian idealism and positivism were a mere backdrop to the development of knowledge - a view which can hardly stand critical examination. Concerning the impact of Einstein's theories on physics, Thüring argues that the principles of special and general relativity be nothing else but arbitrary decisions (as opposed to real insights). Hence these principles would never be verified or falsified by any experiment. The Michelson-Moreley experiment, e.g., would not prove the principles of special relativity. Thüring considers Einstein's interpretation of this experiment as premature and as an arbitrary judgement on a very particular and subaltern phenomenon which would not justify the conclusion that the velocity of the Earth with respect to the luminiferous aether be immeasurable by just any experimental technique.

The Concept of General Relativity is not Related to Reality

NASA Astrophysics Data System (ADS)

Kotas, Ronald

2015-04-01

The concept of general relativity is not related to reality. It is not real or factual Science. GR cannot account for objects falling to earth or for the weight of objects sitting on the earth. The Cavendish demonstration showing the attraction between two masses at right angles to earth's gravity, is not explained by GR. No one can prove the existence of ``space fabric.'' The concept of ``space time'' effects causing gravitational attraction between masses is wrong. Conservation law of energy - momentum does not exist in GR. LIGO fails in detecting ``gravity waves'' because there is no ``space fabric'' to transmit them. The Gravity B Probe data manipulated to show some effects, is not proof of ``space fabric.'' It is Nuclear Quantum Gravitation that provides clear definitive explanation of Gravity and Gravitation. It is harmonious with Newtonian and Quantum Mechanics, and Scientific Logic. Nuclear Quantum Gravitation has 10 clear, Scientific proofs and 21 more good indications. With this theory the Physical Forces are Unified. See: OBSCURANTISM ON EINSTEIN GRAVITATION? http://www.santilli-foundation.org/inconsistencies-gravitation.php and Einstein's Theory of Relativity versus Classical Mechanics, by Paul Marmet http://www.newtonphysics.on.ca/einstein/

Casimir effect in the rainbow Einstein's universe

NASA Astrophysics Data System (ADS)

Bezerra, V. B.; Mota, H. F.; Muniz, C. R.

2017-10-01

In the present paper we investigate the effects caused by the modification of the dispersion relation obtained by solving the Klein-Gordon equation in the closed Einstein's universe in the context of rainbow's gravity models. Thus, we analyse how the quantum vacuum fluctuations of the scalar field are modified when compared with the results obtained in the usual General Relativity scenario. The regularization, and consequently the renormalization, of the vacuum energy is performed adopting the Epstein-Hurwitz and Riemann's zeta functions.

Einstein's physical strategy, energy conservation, symmetries, and stability: "But Grossmann & I believed that the conservation laws were not satisfied"

NASA Astrophysics Data System (ADS)

Pitts, J. Brian

2016-05-01

Recent work on the history of General Relativity by Renn et al. shows that Einstein found his field equations partly by a physical strategy including the Newtonian limit, the electromagnetic analogy, and energy conservation. Such themes are similar to those later used by particle physicists. How do Einstein's physical strategy and the particle physics derivations compare? What energy-momentum complex(es) did he use and why? Did Einstein tie conservation to symmetries, and if so, to which? How did his work relate to emerging knowledge (1911-1914) of the canonical energy-momentum tensor and its translation-induced conservation? After initially using energy-momentum tensors hand-crafted from the gravitational field equations, Einstein used an identity from his assumed linear coordinate covariance xμ‧ = Mνμ xν to relate it to the canonical tensor. Usually he avoided using matter Euler-Lagrange equations and so was not well positioned to use or reinvent the Herglotz-Mie-Born understanding that the canonical tensor was conserved due to translation symmetries, a result with roots in Lagrange, Hamilton and Jacobi. Whereas Mie and Born were concerned about the canonical tensor's asymmetry, Einstein did not need to worry because his Entwurf Lagrangian is modeled not so much on Maxwell's theory (which avoids negative-energies but gets an asymmetric canonical tensor as a result) as on a scalar theory (the Newtonian limit). Einstein's theory thus has a symmetric canonical energy-momentum tensor. But as a result, it also has 3 negative-energy field degrees of freedom (later called "ghosts" in particle physics). Thus the Entwurf theory fails a 1920s-1930s a priori particle physics stability test with antecedents in Lagrange's and Dirichlet's stability work; one might anticipate possible gravitational instability. This critique of the Entwurf theory can be compared with Einstein's 1915 critique of his Entwurf theory for not admitting rotating coordinates and not getting Mercury's perihelion right. One can live with absolute rotation but cannot live with instability. Particle physics also can be useful in the historiography of gravity and space-time, both in assessing the growth of objective knowledge and in suggesting novel lines of inquiry to see whether and how Einstein faced the substantially mathematical issues later encountered in particle physics. This topic can be a useful case study in the history of science on recently reconsidered questions of presentism, whiggism and the like. Future work will show how the history of General Relativity, especially Noether's work, sheds light on particle physics.

Non-local Effects of Conformal Anomaly

NASA Astrophysics Data System (ADS)

Meissner, Krzysztof A.; Nicolai, Hermann

2018-03-01

It is shown that the nonlocal anomalous effective actions corresponding to the quantum breaking of the conformal symmetry can lead to observable modifications of Einstein's equations. The fact that Einstein's general relativity is in perfect agreement with all observations including cosmological or recently observed gravitational waves imposes strong restrictions on the field content of possible extensions of Einstein's theory: all viable theories should have vanishing conformal anomalies. It is shown that a complete cancellation of conformal anomalies in D=4 for both the C^2 invariant and the Euler (Gauss-Bonnet) invariant can only be achieved for N-extended supergravity multiplets with N ≥ 5.

The Einstein-Vlasov System/Kinetic Theory.

PubMed

Andréasson, Håkan

2011-01-01

The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on non-relativistic and special relativistic physics, i.e., to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. This paper gives introductions to kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental to a good comprehension of kinetic theory in general relativity.

Solutions to horava gravity.

PubMed

Lü, H; Mei, Jianwei; Pope, C N

2009-08-28

Recently Horava proposed a nonrelativistic renormalizable theory of gravitation, which reduces to Einstein's general relativity at large distances, and that may provide a candidate for a UV completion of Einstein's theory. In this Letter, we derive the full set of equations of motion, and then we obtain spherically symmetric solutions and discuss their properties. We also obtain solutions for the Friedmann-Lemaître-Robertson-Walker cosmological metric.

Origin of Stability in Particle Sedimentation

NASA Technical Reports Server (NTRS)

Segre, Philip N.

2003-01-01

Particle Image Velocimetry (PIV) is used to study the slow settling motions of spheres in suspensions ranging from dilute to highly concentrated, 0.0001 less than phi less than 0.50. During sedimentation, particle velocity fluctuations are found to be organized into regions of characteristic size xi approximately 11 a phi (exp -1/3). A simple model, based upon buoyant mass fluctuations DELTAm given by random density fluctuations in a region of size xi, accurately predicts the magnitudes of the velocity fluctuations DELTAV. We also find a new universal relation for particle diffusion during sedimentation. It can be written in a Stokes-Einstein form as Dapproximately(DELTAmxi)/(6pietaxi), where the effective temperature DELTAmgxi is the gravitational potential energy of density fluctuations. In addition related experiments examining inertial effects and transient states, that are aimed at uncovering the origin of the new lengthscale xi, will also be given.

Thermophysical properties of liquid Ni around the melting temperature from molecular dynamics simulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rozas, R. E.; Department of Physics, University of Bío-Bío, Av. Collao 1202, P.O. Box 5C, Concepción; Demiraǧ, A. D.

Thermophysical properties of liquid nickel (Ni) around the melting temperature are investigated by means of classical molecular dynamics (MD) simulation, using three different embedded atom method potentials to model the interactions between the Ni atoms. Melting temperature, enthalpy, static structure factor, self-diffusion coefficient, shear viscosity, and thermal diffusivity are compared to recent experimental results. Using ab initio MD simulation, we also determine the static structure factor and the mean-squared displacement at the experimental melting point. For most of the properties, excellent agreement is found between experiment and simulation, provided the comparison relative to the corresponding melting temperature. We discuss themore » validity of the Hansen-Verlet criterion for the static structure factor as well as the Stokes-Einstein relation between self-diffusion coefficient and shear viscosity. The thermal diffusivity is extracted from the autocorrelation function of a wavenumber-dependent temperature fluctuation variable.« less

Probing Students' Ideas of the Principle of Equivalence

ERIC Educational Resources Information Center

Bandyopadhyay, Atanu; Kumar, Arvind

2011-01-01

The principle of equivalence was the first vital clue to Einstein in his extension of special relativity to general relativity, the modern theory of gravitation. In this paper we investigate in some detail students' understanding of this principle in a variety of contexts, when they are undergoing an introductory course on general relativity. The…

Bose-Einstein condensation in microgravity.

PubMed

van Zoest, T; Gaaloul, N; Singh, Y; Ahlers, H; Herr, W; Seidel, S T; Ertmer, W; Rasel, E; Eckart, M; Kajari, E; Arnold, S; Nandi, G; Schleich, W P; Walser, R; Vogel, A; Sengstock, K; Bongs, K; Lewoczko-Adamczyk, W; Schiemangk, M; Schuldt, T; Peters, A; Könemann, T; Müntinga, H; Lämmerzahl, C; Dittus, H; Steinmetz, T; Hänsch, T W; Reichel, J

2010-06-18

Albert Einstein's insight that it is impossible to distinguish a local experiment in a "freely falling elevator" from one in free space led to the development of the theory of general relativity. The wave nature of matter manifests itself in a striking way in Bose-Einstein condensates, where millions of atoms lose their identity and can be described by a single macroscopic wave function. We combine these two topics and report the preparation and observation of a Bose-Einstein condensate during free fall in a 146-meter-tall evacuated drop tower. During the expansion over 1 second, the atoms form a giant coherent matter wave that is delocalized on a millimeter scale, which represents a promising source for matter-wave interferometry to test the universality of free fall with quantum matter.

On the invariant mass conjecture in general relativity

NASA Astrophysics Data System (ADS)

Chruściel, Piotr T.

1988-06-01

An asymptotic symmetries theorem is proved under certain hypotheses on the behaviour of the metric at spatial infinity. This implies that the Einstein-von Freud-ADM mass can be invariantly assigned to an asymptotically flat four dimensional end of an asymptotically empty solution of Einstein equations if the metric is a no-radiation metric or if the end is defined in terms of a collection of boost-type domains.

The Adolescence of Relativity: Einstein, Minkowski, and the Philosophy of Space and Time

NASA Astrophysics Data System (ADS)

Dieks, Dennis

An often repeated account of the genesis of special relativity tells us that relativity theory was to a considerable extent the fruit of an operationalist philosophy of science. Indeed, Einstein's 1905 paper stresses the importance of rods and clocks for giving concrete physical content to spatial and temporal notions. I argue, however, that it would be a mistake to read too much into this. Einstein's operationalist remarks should be seen as serving rhetoric purposes rather than as attempts to promulgate a particular philosophical position - in fact, Einstein never came close to operationalism in any of his philosophical writings. By focussing on what could actually be measured with rods and clocks Einstein shed doubt on the empirical status of a number of pre-relativistic concepts, with the intention to persuade his readers that the applicability of these concepts was not obvious. This rhetoric manoeuvre has not always been rightly appreciated in the philosophy of physics. Thus, the influence of operationalist misinterpretations, according to which associated operations strictly define what a concept means, can still be felt in present-day discussions about the conventionality of simultaneity.The standard story continues by pointing out that Minkowski in 1908 supplanted Einstein's approach with a realist spacetime account that has no room for a foundational role of rods and clocks: relativity theory became a description of a four-dimensional "absolute world." As it turns out, however, it is not at all clear that Minkowski was proposing a substantivalist position with respect to spacetime. On the contrary, it seems that from a philosophical point of view Minkowski's general position was not very unlike the one in the back of Einstein's mind. However, in Minkowski's formulation of special relativity it becomes more explicit that the content of spatiotemporal concepts relates to considerations about the form of physical laws. If accepted, this position has important consequences for the discussion about the conventionality of simultaneity.

A centennial gift from Einstein

NASA Astrophysics Data System (ADS)

Oswalt, T. D.

2017-06-01

The 1919 detection of the apparent displacement of background stars near the edge of the eclipsed Sun's disk provided one of the first convincing proofs of Einstein's theory of general relativity (1, 2). Almost 100 years later, Sahu et al. report on page 1046 of this issue the first measurement of the gravitational deflection of starlight by a star other than the Sun (3). Using the superior angular resolution of the Hubble Space Telescope (HST), they measured shifts in the apparent position of a distant background star as a nearby dense stellar remnant called a white dwarf passed almost in front of it in 2014. Because of the relative distances involved, the deflections they observed were about 1000 times smaller than those seen in 1919, but also in agreement with general relativity theory.

Approximate Stokes Drift Profiles and their use in Ocean Modelling

NASA Astrophysics Data System (ADS)

Breivik, O.; Biblot, J.; Janssen, P. A. E. M.

2016-02-01

Deep-water approximations to the Stokes drift velocity profile are explored as alternatives to the monochromatic profile. The alternative profiles investigated rely on the same two quantities required for the monochromatic profile, viz the Stokes transport and the surface Stokes drift velocity. Comparisons with parametric spectra and profiles under wave spectra from the ERA-Interim reanalysis and buoy observations reveal much better agreement than the monochromatic profile even for complex sea states. That the profiles give a closer match and a more correct shear has implications for ocean circulation models since the Coriolis-Stokes force depends on the magnitude and direction of the Stokes drift profile and Langmuir turbulence parameterizations depend sensitively on the shear of the profile. The NEMO general circulation ocean model was recently extended to incorporate the Stokes-Coriolis force along with two other wave-related effects. I will show some results from the coupled atmosphere-wave-ocean ensemble forecast system of ECMWF where these wave effects are now included in the ocean model component.

Regular black holes in Einstein-Gauss-Bonnet gravity

NASA Astrophysics Data System (ADS)

Ghosh, Sushant G.; Singh, Dharm Veer; Maharaj, Sunil D.

2018-05-01

Einstein-Gauss-Bonnet theory, a natural generalization of general relativity to a higher dimension, admits a static spherically symmetric black hole which was obtained by Boulware and Deser. This black hole is similar to its general relativity counterpart with a curvature singularity at r =0 . We present an exact 5D regular black hole metric, with parameter (k >0 ), that interpolates between the Boulware-Deser black hole (k =0 ) and the Wiltshire charged black hole (r ≫k ). Owing to the appearance of the exponential correction factor (e-k /r2), responsible for regularizing the metric, the thermodynamical quantities are modified, and it is demonstrated that the Hawking-Page phase transition is achievable. The heat capacity diverges at a critical radius r =rC, where incidentally the temperature is maximum. Thus, we have a regular black hole with Cauchy and event horizons, and evaporation leads to a thermodynamically stable double-horizon black hole remnant with vanishing temperature. The entropy does not satisfy the usual exact horizon area result of general relativity.

The collected papers of Albert Einstein. Volume 2. The Swiss years: Writings, 1900-1909

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stachel, J.; Cassidy, D.C.; Renn, J.

1989-01-01

This second volume of the papers of Albert Einstein chronologically presents published articles, unpublished papers, research and lecture notes, reviews, and patent applications for the period 1900-1909 during which time Einstein had a two-year period of short-term employment and a permanent position at the Swiss Patent Office in Bern. There are 62 published documents reproduced. The writings of this period deal with seven general themes: molecular forces, the foundation of statistical physics, the quantum hypothesis, determining molecular dimensions, Brownian movement, the theory of relativity, and the electrodynamics of moving media. The book also presents all available letters written by Einsteinmore » along with all significant letters sent to him and many important third-party letters written about him. The editors have added substantial introduction and a set of eight editorial notes that place Einstein's writings within their immediate scientific context. Footnotes to Einstein texts designed to illuminate the sources of scientific problems that Einstein confronted and the ideas and techniques with which he addressed them have been added by the editors. A comprehensive index to Einstein's early writings is provided.« less

A family of solutions to the Einstein-Maxwell system of equations describing relativistic charged fluid spheres

NASA Astrophysics Data System (ADS)

Komathiraj, K.; Sharma, Ranjan

2018-05-01

In this paper, we present a formalism to generate a family of interior solutions to the Einstein-Maxwell system of equations for a spherically symmetric relativistic charged fluid sphere matched to the exterior Reissner-Nordström space-time. By reducing the Einstein-Maxwell system to a recurrence relation with variable rational coefficients, we show that it is possible to obtain closed-form solutions for a specific range of model parameters. A large class of solutions obtained previously are shown to be contained in our general class of solutions. We also analyse the physical viability of our new class of solutions.

Quantum computational complexity, Einstein's equations and accelerated expansion of the Universe

NASA Astrophysics Data System (ADS)

Ge, Xian-Hui; Wang, Bin

2018-02-01

We study the relation between quantum computational complexity and general relativity. The quantum computational complexity is proposed to be quantified by the shortest length of geodesic quantum curves. We examine the complexity/volume duality in a geodesic causal ball in the framework of Fermi normal coordinates and derive the full non-linear Einstein equation. Using insights from the complexity/action duality, we argue that the accelerated expansion of the universe could be driven by the quantum complexity and free from coincidence and fine-tunning problems.

"Einstein's Playground": An Interactive Planetarium Show on Special Relativity

ERIC Educational Resources Information Center

Sherin, Zachary; Tan, Philip; Fairweather, Heather; Kortemeyer, Gerd

2017-01-01

The understanding of many aspects of astronomy is closely linked with relativity and the finite speed of light, yet relativity is generally not discussed in great detail during planetarium shows for the general public. One reason may be the difficulty to visualize these phenomena in a way that is appropriate for planetariums; another may be their…

Covariant Formulation of Fluid Dynamics and Estakhr's Material Geodesic Equation, far down the Rabbit hole

NASA Astrophysics Data System (ADS)

Estakhr, Ahmad Reza

2012-07-01

``When i meet God, I am going to ask him two questions, why relativity and why turbulence. A. Einstein'' You probably will not need to ask these questions of God, I've already answered both of them. U^{μ}=γ (c,u({r}, t)) denotes four-velocity field. J^ {μ}=ρ U^{μ} denotes four-current mass density. Estakhr's Material-Geodesic equation is developed analogy of Navier Stokes equation and Einstein Geodesic equation. {DJ^ {μ}}/{Dτ}={dJ^{μ}}/{D τ}+Γ^{μ}_{α β}J^{α}U^{β}=J_ {ν}Ω^{μν}+npartial_ {ν}T^{μν}+Γ^{μ} _{αβ}J^{α}U^{β} Covariant formulation of fluid dynamics, describe the motion of fluid substances. The local existence and uniqueness theorem for geodesics states that geodesics on a smooth manifold with an affine connection exist, and are unique. EMG equation is also applicable in different branches of physics, it all depend on what you mean by 4-current density, if you mean 4-current electron number density then it is plasma physics, if you mean 4-current electron charge density then it is {DJ^ {μ}}/{Dτ}=J_{ν}F^{μν} +partial_{ν}T^{μν}+ Γ^{μ}_{αβ}J^ {α}U^{β} electromagnetism.

Diffusive motion with nonlinear friction: apparently Brownian.

PubMed

Goohpattader, Partho S; Chaudhury, Manoj K

2010-07-14

We study the diffusive motion of a small object placed on a solid support using an inertial tribometer. With an external bias and a Gaussian noise, the object slides accompanied with a fluctuation of displacement that exhibits unique characteristics at different powers of the noise. While it exhibits a fluidlike motion at high powers, a stick-slip motion occurs at a low power. Below a critical power, no motion is observed. The signature of a nonlinear friction is evident in this type of stochastic motion both in the reduced mobility in comparison to that governed by a linear kinematic (Stokes-Einstein-like) friction and in the non-Gaussian probability distribution of the displacement fluctuation. As the power of the noise increases, the effect of the nonlinearity appears to play a lesser role, so that the displacement fluctuation becomes more Gaussian. When the distribution is exponential, it also exhibits an asymmetry with its skewness increasing with the applied bias. A new finding of this study is that the stochastic velocities of the object are so poorly correlated that its diffusivity is much lower than either the linear or the nonlinear friction cases studied by de Gennes [J. Stat. Phys. 119, 953 (2005)]. The mobilities at different powers of the noise together with the estimated variances of velocity fluctuations follow an Einstein-like relation.

Dark matter as a ghost free conformal extension of Einstein theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barvinsky, A.O., E-mail: barvin@td.lpi.ru

We discuss ghost free models of the recently suggested mimetic dark matter theory. This theory is shown to be a conformal extension of Einstein general relativity. Dark matter originates from gauging out its local Weyl invariance as an extra degree of freedom which describes a potential flow of the pressureless perfect fluid. For a positive energy density of this fluid the theory is free of ghost instabilities, which gives strong preference to stable configurations with a positive scalar curvature and trace of the matter stress tensor. Instabilities caused by caustics of the geodesic flow, inherent in this model, serve asmore » a motivation for an alternative conformal extension of Einstein theory, based on the generalized Proca vector field. A potential part of this field modifies the inflationary stage in cosmology, whereas its rotational part at the post inflationary epoch might simulate rotating flows of dark matter.« less

BV-BFV approach to general relativity: Einstein-Hilbert action

NASA Astrophysics Data System (ADS)

Cattaneo, Alberto S.; Schiavina, Michele

2016-02-01

The present paper shows that general relativity in the Arnowitt-Deser-Misner formalism admits a BV-BFV formulation. More precisely, for any d + 1 ≠ 2 (pseudo-) Riemannian manifold M with space-like or time-like boundary components, the BV data on the bulk induces compatible BFV data on the boundary. As a byproduct, the usual canonical formulation of general relativity is recovered in a straightforward way.

Einstein and a century of time

NASA Astrophysics Data System (ADS)

Raine, D. J.

2005-09-01

In a world overabundant in information, a subject is defined by its iconography. Physics is the falling apple, the planetary atom, the laser, the mushroom cloud and the image of the later Einstein - images that represent, respectively, gravity, atomic theory, quantum theory, mass-energy and the scientist who had a hand in all four. It is therefore appropriate that World Year of Physics is called Einstein Year in the UK. Of course one can argue that progress in science depends on the contributions of many people; that there are other geniuses in physics, even some colourful personalities. Nevertheless there are fundamental reasons why Einstein's early achievements stand out even in their company. When at last the thought came to him that 'time itself was suspect', Einstein had found a new insight into the nature of the physical universe. It is this: that the universal properties of material objects tell us about the nature of space and time, and it is through these properties, not philosophical logic or common sense, that we discover the structure of spacetime. The later Einstein turned this successful formula on its head and sought to use the properties of spacetime to define those of material objects, thereby seeking to abolish matter entirely in favour of geometry. Before I introduce this special feature of European Journal of Physics I will say a few words about what is not here. Like all great geniuses Einstein can be seen as the climax of what went before him and the initiation of what was to follow. Looking back we can see the influence of Mach's positivism, according to which the role of science is to relate observations to other observations; hence only observations can tell us what is 'real'. But Einstein also grew up with the family electromechanical businesses, which testifies to the reality of the Maxwellian electromagnetic fields: thus only theory can tell us what is real! As is well known, Einstein himself refused to accept the full consequences of this pivotal insight into the role of theory when it came to quantum mechanics. Much has been written about this and we do not add to it in this collection. Quantum theory is a consistent description of nature whatever Einstein may think of 'god' for making it so. Many of us would side with Einstein in hoping it will yet turn out not to be a complete description. This will not happen, as Einstein hoped throughout his later work, from a return to classical field theory. But quantum behaviour is a universal property of matter and may therefore be expected, according to Einstein's way of thought, to have a geometrical origin. The advent of non-commutative quantum geometries may turn out to be a step in this direction. My own introduction to Einstein's physics was through what has come to be known as Mach's principle. My research supervisor, Dennis Sciama, in what he always claimed was probably Einstein's last significant scientific conversation, talked with him on this subject, during which Einstein explained that he had abandoned the idea of Mach's principle. This principle had been a guiding thought in the development of general relativity, but superfluous to its final exposition. It can be interpreted variously as the determination of the local compass of inertia by the distant stars, the non-rotation of the Universe or, more restrictedly, as requiring a critical density universe (to generate the right amount of inertia). This last formulation amounts to Gρτ2 approx 1, where ρ is the density of the Universe at time τ. This appears to be a classical expression, which would probably be sufficient to relegate Mach's principle to mere historical interest along with the classical unified field theories. It is also usually considered to be accounted for by inflation, which drives the Universe to Ω=1. However, we can also think of the expression as saying that the Universe has a Planck mass in a Planck volume at the Planck time: G=(hc / G)1/2(c3 / Gh)3/2(Gh / c5)=1. This suggests that Mach's principle may yet have a surprising role in expressing the fact that the Universe contains sufficient matter to exist as a classical system: that is, that it contains sufficient material degrees of freedom to allow quantum decoherence to occur. It would at least be a nice irony if Mach's principle turned out to be a necessary quantum condition for the existence of a classical universe! Coming now to the papers in this special feature, these include several that treat historical aspects of relativity. Brown offers us a novel insight into Einstein's ambivalence about the status of special relativity in providing a mechanism for the contraction hypothesis. Trainer looks at the way in which Einstein presented a brief account of relativity in a lecture that he gave in Glasgow in 1933. Galvangno and Giribet look at Einstein's approach to the representation of particles within general relativity, or variants thereof, while Battimelli provides an account of attempts at unification of electromagnetism and relativity from the point of view of the origin of mass. In their contribution, Guerra and de Abreu look again at the relationship between the constancy of the speed of light and the nature of time that was central to Einstein's thinking. Next we come to a group of papers that look at educational issues. Einstein's equation E = mc2 is now iconic even if general knowledge quizzes that ask what the c stands for miss the entire point of the equation! Thomas starts from the way in which perceptions of relativity still focus on this equation as the essential ingredient of nuclear power and the need to disabuse even students of physics of this notion. He also looks at how we can in fact demonstrate the significance of the equation to a lay audience. I have added a short note on friction, another topic that confuses teachers and students alike, that throws up problems to which the solutions are contained in Einstein's Brownian motion paper. The Open University in the UK has been teaching relativity to distance-learners for forty years; Lambourne writes about the experience that has been gained. Finally, I have always been intrigued by the opprobrium that Einstein seems to attract from crank authors. I no longer regularly receive such nonsense to referee, I assume because the internet is now awash with 'publication' opportunities for anti-Einstein articles. I do believe however that the work of these authors throws light on the way science works and I have tried to illustrate this thesis briefly in the final paper of this collection.

Optical coherence tomography speckle decorrelation for detecting cell death

NASA Astrophysics Data System (ADS)

Farhat, Golnaz; Mariampillai, Adrian; Yang, Victor X. D.; Czarnota, Gregory J.; Kolios, Michael C.

2011-03-01

We present a dynamic light scattering technique applied to optical coherence tomography (OCT) for detecting changes in intracellular motion caused by cellular reorganization during apoptosis. We have validated our method by measuring Brownian motion in microsphere suspensions and comparing the measured values to those derived based on particle diffusion calculated using the Einstein-Stokes equation. Autocorrelations of OCT signal intensities acquired from acute myeloid leukemia cells as a function of treatment time demonstrated a significant drop in the decorrelation time after 24 hours of cisplatin treatment. This corresponded with nuclear fragmentation and irregular cell shape observed in histological sections. A similar analysis conducted with multicellular tumor spheroids indicated a shorter decorrelation time in the spheroid core relative to its edges. The spheroid core corresponded to a region exhibiting signs of cell death in histological sections and increased backscatter intensity in OCT images.

Application of Microrheology in Food Science.

PubMed

Yang, Nan; Lv, Ruihe; Jia, Junji; Nishinari, Katsuyoshi; Fang, Yapeng

2017-02-28

Microrheology provides a technique to probe the local viscoelastic properties and dynamics of soft materials at the microscopic level by observing the motion of tracer particles embedded within them. It is divided into passive and active microrheology according to the force exerted on the embedded particles. Particles are driven by thermal fluctuations in passive microrheology, and the linear viscoelasticity of samples can be obtained on the basis of the generalized Stokes-Einstein equation. In active microrheology, tracer particles are controlled by external forces, and measurements can be extended to the nonlinear regime. Microrheology techniques have many advantages such as the need for only small sample amounts and a wider measurable frequency range. In particular, microrheology is able to examine the spatial heterogeneity of samples at the microlevel, which is not possible using traditional rheology. Therefore, microrheology has considerable potential for studying the local mechanical properties and dynamics of soft matter, particularly complex fluids, including solutions, dispersions, and other colloidal systems. Food products such as emulsions, foams, or gels are complex fluids with multiple ingredients and phases. Their macroscopic properties, such as stability and texture, are closely related to the structure and mechanical properties at the microlevel. In this article, the basic principles and methods of microrheology are reviewed, and the latest developments and achievements of microrheology in the field of food science are presented.

General Relativity and Gravitation

NASA Astrophysics Data System (ADS)

Ehlers, J.; Murdin, P.

2000-11-01

The General Theory of Relativity (GR), created by Albert Einstein between 1907 and 1915, is a theory both of gravitation and of spacetime structure. It is based on the assumption that matter, via its energy-momentum, interacts with the metric of spacetime, which is considered (in contrast to Newtonian physics and SPECIAL RELATIVITY) as a dynamical field having degrees of freedom of its own (GRAVI...

What is general relativity?

NASA Astrophysics Data System (ADS)

Coley, Alan A.; Wiltshire, David L.

2017-05-01

General relativity is a set of physical and geometric principles, which lead to a set of (Einstein) field equations that determine the gravitational field and to the geodesic equations that describe light propagation and the motion of particles on the background. But open questions remain, including: what is the scale on which matter and geometry are dynamically coupled in the Einstein equations? Are the field equations valid on small and large scales? What is the largest scale on which matter can be coarse grained while following a geodesic of a solution to Einstein’s equations? We address these questions. If the field equations are causal evolution equations, whose average on cosmological scales is not an exact solution of the Einstein equations, then some simplifying physical principle is required to explain the statistical homogeneity of the late epoch Universe. Such a principle may have its origin in the dynamical coupling between matter and geometry at the quantum level in the early Universe. This possibility is hinted at by diverse approaches to quantum gravity which find a dynamical reduction to two effective dimensions at high energies on one hand, and by cosmological observations which are beginning to strongly restrict the class of viable inflationary phenomenologies on the other. We suggest that the foundational principles of general relativity will play a central role in reformulating the theory of spacetime structure to meet the challenges of cosmology in the 21st century.

Shear Melting of a Colloidal Glass

NASA Astrophysics Data System (ADS)

Eisenmann, Christoph; Kim, Chanjoong; Mattsson, Johan; Weitz, David A.

2010-01-01

We use confocal microscopy to explore shear melting of colloidal glasses, which occurs at strains of ˜0.08, coinciding with a strongly non-Gaussian step size distribution. For larger strains, the particle mean square displacement increases linearly with strain and the step size distribution becomes Gaussian. The effective diffusion coefficient varies approximately linearly with shear rate, consistent with a modified Stokes-Einstein relationship in which thermal energy is replaced by shear energy and the length scale is set by the size of cooperatively moving regions consisting of ˜3 particles.

On Einstein's Path, essays in honor of Engelbert Schucking

NASA Astrophysics Data System (ADS)

Harvey, Alex

This collection of essays in honor of Engelbert Schucking spans the gamut of research in general relativity and presents a lively and personal account of current work in the field. Contributions include: E.L. Schucking: Jordan, Pauli, Politics, Brecht... and a Variable Gravitational Constant J.L. Anderson: Thomson Scattering in an Expanding Universe A. Ashtekar & T.A. Schilling: Geometrical Formulation of Quantum Mechanics J. Baugh, D.R. Finkelstein, H. Saller, and Zhong Tang: General Covariance is Bose-Einstein Statistics S.L. Bazanski: The Split and Propagation of Light Rays in Relativity L. Bel: How to Define a Unique Vacuum in Cosmology P.G. Bergmann: EIH Theory and Noether's Theorem W.B. Bonnor: The Static Cylinder in General Relativity C.H. Brahns: Gravity and the Tenacious Scalar Field D. Brill: The Cavendish Experiment in General Relativity Y. Choquet-Bruhat: Wave Maps in General Relativity T. Damour: General Relativty and Experiment J. Ehlers: Some Developments in Newtonian Cosmology G.F.R. Ellis & H. van Elst: Deviation of Geodesics in FLRW Spacetime Geometries S. Frittelli & E.T. Newman: Poincar Pseudo-symmetries in Asymptotically Flat Spacetimes E.N. Glass: Taub Numbers and Asymptotic Invariants J.N. Goldberg: Second Class Constraints F.W. Hehl, A. Macias, E.W. Mielke, & Yu.N. Obukhov: On the Structure of the Energy-momentum and the Spin Currents in Dirac's Electron

Exact general relativistic disks with magnetic fields

NASA Astrophysics Data System (ADS)

Letelier, Patricio S.

1999-11-01

The well-known ``displace, cut, and reflect'' method used to generate cold disks from given solutions of Einstein equations is extended to solutions of Einstein-Maxwell equations. Four exact solutions of the these last equations are used to construct models of hot disks with surface density, azimuthal pressure, and azimuthal current. The solutions are closely related to Kerr, Taub-NUT, Lynden-Bell-Pinault, and to a one-soliton solution. We find that the presence of the magnetic field can change in a nontrivial way the different properties of the disks. In particular, the pure general relativistic instability studied by Bic̆ák, Lynden-Bell, and Katz [Phys. Rev. D 47, 4334 (1993)] can be enhanced or cured by different distributions of currents inside the disk. These currents, outside the disk, generate a variety of axial symmetric magnetic fields. As far as we know these are the first models of hot disks studied in the context of general relativity.

Rotating black holes in dilatonic Einstein-Gauss-Bonnet theory.

PubMed

Kleihaus, Burkhard; Kunz, Jutta; Radu, Eugen

2011-04-15

We construct generalizations of the Kerr black holes by including higher-curvature corrections in the form of the Gauss-Bonnet density coupled to the dilaton. We show that the domain of existence of these Einstein-Gauss-Bonnet-dilaton (EGBD) black holes is bounded by the Kerr black holes, the critical EGBD black holes, and the singular extremal EGBD solutions. The angular momentum of the EGBD black holes can exceed the Kerr bound. The EGBD black holes satisfy a generalized Smarr relation. We also compare their innermost stable circular orbits with those of the Kerr black holes and show the existence of differences which might be observable in astrophysical systems.

Dynamic wormhole solutions in Einstein-Cartan gravity

NASA Astrophysics Data System (ADS)

Mehdizadeh, Mohammad Reza; Ziaie, Amir Hadi

2017-12-01

In the present work, we investigate evolving wormhole configurations described by a constant redshift function in Einstein-Cartan theory. The matter content consists of a Weyssenhoff fluid along with an anisotropic matter which together generalize the anisotropic energy momentum tensor in general relativity in order to include the effects of intrinsic angular momentum (spin) of particles. Using a generalized Friedmann-Robertson-Walker spacetime, we derive analytical evolving wormhole geometries by assuming a particular equation of state for energy density and pressure profiles. We introduce exact asymptotically flat and anti-de Sitter spacetimes that admit traversable wormholes and respect energy conditions throughout the spacetime. The rate of expansion of these evolving wormholes is determined only by the Friedmann equation in the presence of spin effects.

The particle problem in classical gravity: a historical note on 1941

NASA Astrophysics Data System (ADS)

Galvagno, Mariano; Giribet, Gastón

2005-11-01

This historical note is mainly based on a relatively unknown paper published by Albert Einstein in Revista de la Universidad Nacional de Tucumán in 1941. Taking the ideas of this work as a leitmotiv, we review the discussions about the particle problem in the theory of gravitation within the historical context by means of the study of seminal works on the subject. The revision shows how the digressions regarding the structure of matter and the concise problem of finding regular solutions of the pure field equations turned out to be intrinsically unified in the beginning of the programme towards a final theory of fields. The paper mentioned (Einstein 1941a Rev. Univ. Nac. Tucumán A 2 11) represents the basis of the one written by Einstein in collaboration with Wolfgang Pauli in 1943, in which, following analogous lines, the proof of the non-existence of regular particle-type solutions was generalized to the case of cylindrical geometries in Kaluza-Klein theory (Einstein and Pauli 1943 Ann. Math. 44 131). Besides, other generalizations were subsequently presented. The (non-)existence of such solutions in classical unified field theory was undoubtedly an important criterion leading Einstein's investigations. This aspect was investigated with expertness by Jeroen van Dongen in a recent work, though restricting the scope to the particular case of Kaluza-Klein theory (van Dongen 2002 Stud. Hist. Phil. Mod. Phys. 33 185). Here, we discuss the particle problem within a more general context, presenting in this way a complement to previous reviews.

Approximate Stokes Drift Profiles and their use in Ocean Modelling

NASA Astrophysics Data System (ADS)

Breivik, Oyvind; Bidlot, Jea-Raymond; Janssen, Peter A. E. M.; Mogensen, Kristian

2016-04-01

Deep-water approximations to the Stokes drift velocity profile are explored as alternatives to the monochromatic profile. The alternative profiles investigated rely on the same two quantities required for the monochromatic profile, viz the Stokes transport and the surface Stokes drift velocity. Comparisons against parametric spectra and profiles under wave spectra from the ERA-Interim reanalysis and buoy observations reveal much better agreement than the monochromatic profile even for complex sea states. That the profiles give a closer match and a more correct shear has implications for ocean circulation models since the Coriolis-Stokes force depends on the magnitude and direction of the Stokes drift profile and Langmuir turbulence parameterizations depend sensitively on the shear of the profile. Of the two Stokes drift profiles explored here, the profile based on the Phillips spectrum is by far the best. In particular, the shear near the surface is almost identical to that influenced by the f-5 tail of spectral wave models. The NEMO general circulation ocean model was recently extended to incorporate the Stokes-Coriolis force along with two other wave-related effects. The ECWMF coupled atmosphere-wave-ocean ensemble forecast system now includes these wave effects in the ocean model component (NEMO).

Merging Black Holes, Gravitational Waves, and Numerical Relativity

NASA Technical Reports Server (NTRS)

Centrella, Joan M.

2009-01-01

The final merger of two black holes will emit more energy than all the stars in the observable universe combined. This energy will come in the form of gravitational waves, which are a key prediction of Einstein's general relativity and a new tool for exploring the universe. Observing these mergers with gravitational wave detectors, such as the ground-based LIGO and the space-based LISA, requires knowledge of the radiation waveforms. Since these mergers take place in regions of extreme gravity, we need to solve Einstein's equations of general relativity on a computer. For more than 30 years, scientists have tried to compute black hole mergers using the methods of numerical relativity. The resulting computer codes were long plagued by instabilities, causing them to crash well before the black holes in the binary could complete even a single orbit. Within the past few years, however, this situation has changed dramatically, with a series of remarkable breakthroughs. This talk will focus on new simulations that are revealing the dynamics and w aefo rms of binary black hole mergers, and their applications in gravitational wave detection, testing general relativity, and astrophysics.

Generalized geometry and non-symmetric metric gravity

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Khoo, Fech Scen; Schupp, Peter; Vysoký, Jan

2016-04-01

Generalized geometry provides the framework for a systematic approach to non-symmetric metric gravity theory and naturally leads to an Einstein-Kalb-Ramond gravity theory with totally anti-symmetric contortion. The approach is related to the study of the low-energy effective closed string gravity actions.

The science, technology and mission design for the Laser Astrometric test of relativity

NASA Technical Reports Server (NTRS)

Turyshev, Slava G.

2006-01-01

The Laser Astrometric Test of Relativity (LATOR) is a Michelson-Morley-type experiment designed to test the Einstein's general theory of relativity in the most intense gravitational environment available in the solar system - the close proximity to the Sun.

A confirmation of the general relativistic prediction of the Lense-Thirring effect.

PubMed

Ciufolini, I; Pavlis, E C

2004-10-21

An important early prediction of Einstein's general relativity was the advance of the perihelion of Mercury's orbit, whose measurement provided one of the classical tests of Einstein's theory. The advance of the orbital point-of-closest-approach also applies to a binary pulsar system and to an Earth-orbiting satellite. General relativity also predicts that the rotation of a body like Earth will drag the local inertial frames of reference around it, which will affect the orbit of a satellite. This Lense-Thirring effect has hitherto not been detected with high accuracy, but its detection with an error of about 1 per cent is the main goal of Gravity Probe B--an ongoing space mission using orbiting gyroscopes. Here we report a measurement of the Lense-Thirring effect on two Earth satellites: it is 99 +/- 5 per cent of the value predicted by general relativity; the uncertainty of this measurement includes all known random and systematic errors, but we allow for a total +/- 10 per cent uncertainty to include underestimated and unknown sources of error.

q-deformed Einstein's model to describe specific heat of solid

NASA Astrophysics Data System (ADS)

Guha, Atanu; Das, Prasanta Kumar

2018-04-01

Realistic phenomena can be described more appropriately using generalized canonical ensemble, with proper parameter sets involved. We have generalized the Einstein's theory for specific heat of solid in Tsallis statistics, where the temperature fluctuation is introduced into the theory via the fluctuation parameter q. At low temperature the Einstein's curve of the specific heat in the nonextensive Tsallis scenario exactly lies on the experimental data points. Consequently this q-modified Einstein's curve is found to be overlapping with the one predicted by Debye. Considering only the temperature fluctuation effect(even without considering more than one mode of vibration is being triggered) we found that the CV vs T curve is as good as obtained by considering the different modes of vibration as suggested by Debye. Generalizing the Einstein's theory in Tsallis statistics we found that a unique value of the Einstein temperature θE along with a temperature dependent deformation parameter q(T) , can well describe the phenomena of specific heat of solid i.e. the theory is equivalent to Debye's theory with a temperature dependent θD.

S2 like Star Orbits near the Galactic Center in Rn and Yukawa Gravity

NASA Astrophysics Data System (ADS)

Borka, Dusko; Jovanović, Predrag; Jovanović Vesna Borka; Zakharov, Alexander F.

2015-01-01

In this chapter we investigate the possibility to provide theoretical explanation for the observed deviations of S2 star orbit around the Galactic Center using gravitational potentials derived from extended gravity models, but in absence of dark matter. Extended Theories of Gravity are alternative theories of gravitational interaction developed from the exact starting points investigated first by Einstein and Hilbert and aimed from one side to extend the positive results of General Relativity and, on the other hand, to cure its shortcomings. One of the aims of these theories is to explain galactic and extragalactic dynamics without introduction of dark matter. They are based on straightforward generalizations of the Einstein theory where the gravitational action (the Hilbert-Einstein action) is assumed to be linear in the Ricci curvature scalar R. The f(R) gravity is a type of modified gravity which generalizes Einstein's General Relativity, i.e. the simplest case is just the General Relativity. It is actually a family of models, each one defined by a different function of the Ricci scalar. Here, we consider Rn (power-law fourth-order theories of gravity) and Yukawa-like modified gravities in the weak field limit and discuss the constrains on these theories. For that purpose we simulate the orbit of S2 star around the Galactic Center in Rn and Yukawa-like gravity potentials and compare it with New Technology Telescope/Very Large Telescope (NTT/VLT) as well as by Keck telescope observations. Our simulations result in strong constraints on the range of gravity interaction and showed that both Rn and Yukawa gravity could satisfactorily explain the observed orbits of S2 star. However, we concluded that parameters of Rn and Yukawa gravity theories must be very close to those corresponding to the Newtonian limit of the theory. Besides, in contrast to Newtonian gravity, these two modified theories induce orbital precession, even in the case of point-like central mass. The approach we are proposing seems to be sufficiently reliable to constrain the modified gravity models from stellar orbits around Galactic Center.

Black hole dynamics in Einstein-Maxwell-dilaton theory

NASA Astrophysics Data System (ADS)

Hirschmann, Eric W.; Lehner, Luis; Liebling, Steven L.; Palenzuela, Carlos

2018-03-01

We consider the properties and dynamics of black holes within a family of alternative theories of gravity, namely Einstein-Maxwell-dilaton theory. We analyze the dynamical evolution of individual black holes as well as the merger of binary black hole systems. We do this for a wide range of parameter values for the family of Einstein-Maxwell-dilaton theories, investigating, in the process, the stability of these black holes. We examine radiative degrees of freedom, explore the impact of the scalar field on the dynamics of merger, and compare with other scalar-tensor theories. We argue that the dilaton can largely be discounted in understanding merging binary systems and that the end states essentially interpolate between charged and uncharged, rotating black holes. For the relatively small charge values considered here, we conclude that these black hole systems will be difficult to distinguish from their analogs within General Relativity.

Taming the nonlinearity of the Einstein equation.

PubMed

Harte, Abraham I

2014-12-31

Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein's equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate all such nonlinearities beyond a particular order: Both Landau-Lifshitz and tetrad formulations of Einstein's equation are obtained that involve only finite products of the unknowns and their derivatives. Considerable additional simplifications arise in physically interesting cases where metrics become approximately Kerr or, e.g., plane waves, suggesting that the variables described here can be used to efficiently reformulate perturbation theory in a variety of contexts. In all cases, these variables are shown to have simple geometrical interpretations that directly relate the local causal structure associated with the metric of interest to the causal structure associated with a prescribed background. A new method to search for exact solutions is outlined as well.

General Motors sued for 'denigrating' Einstein's image

NASA Astrophysics Data System (ADS)

Gwynne, Peter

2010-07-01

The US car giant General Motors (GM) has played down the consequences of a lawsuit against it for using the likeness of Albert Einstein in an advertisement for its Terrain sports utility vehicle (SUV).

Towards thermodynamics of universal horizons in Einstein-æther theory.

PubMed

Berglund, Per; Bhattacharyya, Jishnu; Mattingly, David

2013-02-15

Holography grew out of black hole thermodynamics, which relies on the causal structure and general covariance of general relativity. In Einstein-æther theory, a generally covariant theory with a dynamical timelike unit vector, every solution breaks local Lorentz invariance, thereby grossly modifying the causal structure of gravity. However, there are still absolute causal boundaries, called "universal horizons," which are not Killing horizons yet obey a first law of black hole mechanics and must have an entropy if they do not violate a generalized second law. We couple a scalar field to the timelike vector and show via the tunneling approach that the universal horizon radiates as a blackbody at a fixed temperature, even if the scalar field equations also violate local Lorentz invariance. This suggests that the class of holographic theories may be much broader than currently assumed.

Why was Relativity Accepted?

NASA Astrophysics Data System (ADS)

Brush, S. G.

Historians of science have published many studies of the reception of Einstein's special and general theories of relativity. Based on a review of these studies, and my own research on the role of the light-bending prediction in the reception of general relativity, I discuss the role of three kinds of reasons for accepting relativity (1) empirical predictions and explanations; (2) social-psychological factors; and (3) aesthetic-mathematical factors. According to the historical studies, acceptance was a three-stage process. First, a few leading scientists adopted the special theory for aesthetic-mathematical reasons. In the second stage, their enthusiastic advocacy persuaded other scientists to work on the theory and apply it to problems currently of interest in atomic physics. The special theory was accepted by many German physicists by 1910 and had begun to attract some interest in other countries. In the third stage, the confirmation of Einstein's light-bending prediction attracted much public attention and forced all physicists to take the general theory of relativity seriously. In addition to light-bending, the explanation of the advance of Mercury's perihelion was considered strong evidence by theoretical physicists. The American astronomers who conducted successful tests of general relativity became defenders of the theory. There is little evidence that relativity was `socially constructed' but its initial acceptance was facilitated by the prestige and resources of its advocates.

The Einstein-Vlasov System/Kinetic Theory.

PubMed

Andréasson, Håkan

2005-01-01

The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on nonrelativistic and special relativistic physics, i.e. to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. The Vlasov equation describes matter phenomenologically, and it should be stressed that most of the theorems presented in this article are not presently known for other such matter models (i.e. fluid models). This paper gives introductions to kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental to good comprehension of kinetic theory in general relativity.

The Einstein-Vlasov System/Kinetic Theory.

PubMed

Andréasson, Håkan

2002-01-01

The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on nonrelativistic and special relativistic physics, i.e. to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. The Vlasov equation describes matter phenomenologically, and it should be stressed that most of the theorems presented in this article are not presently known for other such matter models (i.e. fluid models). This paper gives introductions to kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental to good comprehension of kinetic theory in general relativity.

BOOK REVIEW: Once Upon Einstein

NASA Astrophysics Data System (ADS)

Giannetto, E.

2007-07-01

Thibault Damour is a theoretical physicist, and a member of the French Academy of Sciences. This book is the translation, by Eric Novak, of the original French Si Einstein m'etait conté (Le Cherche Midi, 2005). It is neither a book of theoretical physics nor a biography of Einstein. It is not a book of history nor philosophy of science. In Damour's words it was written to encourage the reader to share with Einstein `those times when he understood some part of the hidden order of the universe'. It is a relatively short book, written in a very fluent style, but it deals with all the major problems and achievements of Einstein's works. Starting from special relativity, it continues with general relativity, quantum theories, unified field theory and a brief overview of the actual research related to Einstein's legacy. It is essentially a popular science book with some related exploration in history and philosophy to interpret physical theories. The most important problem discussed by Damour is the nature of time. On this subject, there is a very interesting short paragraph (pp 33--35) dedicated to the reception of the relativity idea by the great writer Marcel Proust and its counterpart within À la Recherche du Temps Perdu. A correct discussion of the implications of a relativistic time should imply the distinction of the different possible interpretations of this concept. Damour seems to conclude that only one interpretation is possible: `time does not exist', flowing of time is an illusion. One has to know that Einstein's ideas on time were related to Spinoza's perspective of a knowledge sub specie aeternitatis. However, other interpretations are possible and are related to the idea of time as an actuality. Damour speaks about the controversy between Einstein and Bergson, but Bergson is considered as a philosopher who did not understand relativity. This philosophical problem of relativistic time is indeed related to a historical problem briefly discussed by Damour (pp 17--21, 48--52 and related endnotes): had Henri Poincaré constructed a special relativistic dynamics before Einstein? There is a long debate on this subject in the literature. Damour's answer is negative and his conclusions seem related to the conservation of a myth of Einstein, that is, the rise of special relativity is considered as a creatio ex nihilo within Einstein's mind and Einstein is considered as the only genius able to conceive the relativity of time. Poincaré's texts are undervalued and misunderstood by Damour's cutting quotations from their context. Damour never quotes La Science et l'Hypothèse (1902): we know it was read by Einstein and here Poincaré first (within chapters already published as separate papers in 1900) stated the relativity of time and of simultaneity. Damour never quotes Poincaré's paper published on 5 June 1905, La dynamique de l'èlectron, which presents the first relativistic dynamics, invariant by Lorentz transformations. Poincaré's (July 1905) introduction of a quadrimensional space-time is considered by Damour only a mathematical artifice (p 51) and Damour never said that Minkowski took this idea from Poincaré! Poincaré's interpretation of relativistic time implies that it is not an illusion but a complex net of different real flows related to different processes. Poincaré and Einstein had different conceptions of Nature at the root of special relativity: respectively an electromagnetic conception (Poincaré) and a semi-mechanist one (Einstein). Thus, the (philosophical) meaning of relativity can be very different from the one presented by Damour. Furthermore, Damour accepts Kantian philosophy as a key to understanding relativity and quantum theories. This perspective seems to me very anachronistic and based on a misunderstanding: an interpretation of 20th century physical theories (relativity and quantum physics) is given within the framework of an 18th century philosophical perspective, created to give a foundation to Newton's theory. Relativity and quantum physics imply a breakdown of Kantian philosophy (see, for instance, G Bachelard's La Philosophie du Non). Relativity of space and time was considered possible only by overcoming the epistemological obstacle of Kantian idealistic foundation of Euclidean geometry and of Newton's absolute space and time. Relativity and quantum theories turn up not only the hierarchy between mathematics and physics, but also between epistemology (and logic) and physics: quantum physics implies not only a new conception of an indeterminate and unpredictable Nature, but a quantum logic too, that is, it implies a change in our way of thinking and knowing. When will the revolutionary impact of 20th century physics be reduced (by physicists themselves) to an already given philosophical framework?

Relativity in Transylvania and Patusan: Finding the roots of Einstein's theories of relativity in "Dracula" and "Lord Jim"

NASA Astrophysics Data System (ADS)

Tatum, Brian Shane

This thesis investigates the similarities in the study of time and space in literature and science during the modern period. Specifically, it focuses on the portrayal of time and space within Bram Stoker's Dracula (1897) and Joseph Conrad's Lord Jim (1899-1900), and compares the ideas presented with those later scientifically formulated by Albert Einstein in his special and general theories of relativity (1905-1915). Although both novels precede Einstein's theories, they reveal advanced complex ideas of time and space very similar to those later argued by the iconic physicist. These ideas follow a linear progression including a sense of temporal dissonance, the search for a communal sense of the present, the awareness and expansion of the individual's sense of the present, and the effect of mass on surrounding space. This approach enhances readings of Dracula and Lord Jim, illuminating the fascination with highly refined notions of time and space within modern European culture.

A modification of Einstein-Schrödinger theory that contains both general relativity and electrodynamics

NASA Astrophysics Data System (ADS)

Shifflett, J. A.

2008-08-01

We modify the Einstein-Schrödinger theory to include a cosmological constant Λ z which multiplies the symmetric metric, and we show how the theory can be easily coupled to additional fields. The cosmological constant Λ z is assumed to be nearly cancelled by Schrödinger’s cosmological constant Λ b which multiplies the nonsymmetric fundamental tensor, such that the total Λ = Λ z + Λ b matches measurement. The resulting theory becomes exactly Einstein-Maxwell theory in the limit as | Λ z | → ∞. For | Λ z | ~ 1/(Planck length)2 the field equations match the ordinary Einstein and Maxwell equations except for extra terms which are < 10-16 of the usual terms for worst-case field strengths and rates-of-change accessible to measurement. Additional fields can be included in the Lagrangian, and these fields may couple to the symmetric metric and the electromagnetic vector potential, just as in Einstein-Maxwell theory. The ordinary Lorentz force equation is obtained by taking the divergence of the Einstein equations when sources are included. The Einstein-Infeld-Hoffmann (EIH) equations of motion match the equations of motion for Einstein-Maxwell theory to Newtonian/Coulombian order, which proves the existence of a Lorentz force without requiring sources. This fixes a problem of the original Einstein-Schrödinger theory, which failed to predict a Lorentz force. An exact charged solution matches the Reissner-Nordström solution except for additional terms which are ~10-66 of the usual terms for worst-case radii accessible to measurement. An exact electromagnetic plane-wave solution is identical to its counterpart in Einstein-Maxwell theory.

Einstein contra Aristotle: The sound from the heavens

NASA Astrophysics Data System (ADS)

Neves, J. C. S.

2017-09-01

In "On the Heavens" Aristotle criticizes the Pythagorean point of view which claims the existence of a cosmic music and a cosmic sound. According to the Pythagorean argument, there exists a cosmic music produced by stars and planets. These celestial bodies generate sound in its movements, and the music appears due to the cosmic harmony. For Aristotle, there is no sound produced by celestial bodies. Then, there is no music as well. However, recently, LIGO (Laser Interferometer Gravitational-Waves Observatory) has detected the gravitational waves predicted by Einstein. In some sense, a sound originated from black holes has been heard. That is, Einstein or the General Relativity and LIGO appear to be with the Pythagoreanism and against the master of the Lyceum.

Quantum information and general relativity

NASA Astrophysics Data System (ADS)

Peres, A.

2004-11-01

The Einstein-Podolsky-Rosen paradox (1935) is reexamined in the light of Shannon's information theory (1948). The EPR argument did not take into account that the observers' information was localized, like any other physical object. General relativity introduces new problems: there are horizons which act as on-way membranes for the propagation of quantum information, in particular black holes which act like sinks.

Dark Energy, or Worse

ScienceCinema

Carroll, Sean

2018-01-09

General relativity is inconsistent with cosmological observations unless we invoke components of dark matter and dark energy that dominate the universe. While it seems likely that these exotic substances really do exist, the alternative is worth considering: that Einstein's general relativity breaks down on cosmological scales. I will discuss models of modified gravity, tests in the solar system and elsewhere, and consequences for cosmology.

The dynamical crossover phenomenon in bulk water, confined water and protein hydration water.

PubMed

Mallamace, Francesco; Corsaro, Carmelo; Baglioni, Piero; Fratini, Emiliano; Chen, Sow-Hsin

2012-02-15

We discuss a phenomenon regarding water that was until recently a subject of scientific controversy, i.e. the dynamical crossover from fragile-to-strong glass-forming material, for both bulk and protein hydration water. Such a crossover is characterized by a temperature T(L) at which significant dynamical changes occur, such as violation of the Stokes-Einstein relation and changes of behaviour of homologous transport parameters such as the density relaxation time and the viscosity. In this respect we will consider carefully the dynamic properties of water-protein systems. More precisely, we will study proteins and their hydration water as far as bulk and confined water. In order to clarify the controversy we will discuss in a comparative way many previous and new experimental data that have emerged using different techniques and molecular dynamic simulation (MD). We point out the reasons for the different dynamical findings from the use of different experimental techniques.

Nano-viscosity of supercooled liquid measured by fluorescence correlation spectroscopy: Pressure and temperature dependence and the density scaling

NASA Astrophysics Data System (ADS)

Meier, G.; Gapinski, J.; Ratajczyk, M.; Lettinga, M. P.; Hirtz, K.; Banachowicz, E.; Patkowski, A.

2018-03-01

The Stokes-Einstein relation allows us to calculate apparent viscosity experienced by tracers in complex media on the basis of measured self-diffusion coefficients. Such defined nano-viscosity values can be obtained through single particle techniques, like fluorescence correlation spectroscopy (FCS) and particle tracking (PT). In order to perform such measurements, as functions of pressure and temperature, a new sample cell was designed and is described in this work. We show that this cell in combination with a long working distance objective of the confocal microscope can be used for successful FCS, PT, and confocal imaging experiments in broad pressure (0.1-100 MPa) and temperature ranges. The temperature and pressure dependent nano-viscosity of a van der Waals liquid obtained from the translational diffusion coefficient measured in this cell by means of FCS obeys the same scaling as the rotational relaxation and macro-viscosity of the system.

Neutron stars in Horndeski gravity

NASA Astrophysics Data System (ADS)

Maselli, Andrea; Silva, Hector O.; Minamitsuji, Masato; Berti, Emanuele

2016-06-01

Horndeski's theory of gravity is the most general scalar-tensor theory with a single scalar whose equations of motion contain at most second-order derivatives. A subsector of Horndeski's theory known as "Fab Four" gravity allows for dynamical self-tuning of the quantum vacuum energy, and therefore it has received particular attention in cosmology as a possible alternative to the Λ CDM model. Here we study compact stars in Fab Four gravity, which includes as special cases general relativity ("George"), Einstein-dilaton-Gauss-Bonnet gravity ("Ringo"), theories with a nonminimal coupling with the Einstein tensor ("John"), and theories involving the double-dual of the Riemann tensor ("Paul"). We generalize and extend previous results in theories of the John class and were not able to find realistic compact stars in theories involving the Paul class.

Gravitation Theory: Empirical Status from Solar System Experiments: All observations to date are consistent with Einstein's general relativity theory of gravity.

PubMed

Nordtvedt, K L

1972-12-15

I have reviewed the historical and contemporary experiments that guide us in choosing a post-Newtonian, relativistic gravitational theory. The foundation experiments essentially constrain gravitation theory to be a metric theory in which matter couples solely to one gravitational field, the metric field, although other cosmological gravitational fields may exist. The metric field for any metric theory can be specified (for the solar system, for our present purposes) by a series of potential terms with several parameters. A variety of experiments specify (or put limits on) the numerical values of the seven parameters in the post-Newtonian metric field, and other such experiments have been planned. The empirical results, to date, yield values of the parameters that are consistent with the predictions of Einstein's general relativity.

Relativistic GLONASS and geodesy

NASA Astrophysics Data System (ADS)

Mazurova, E. M.; Kopeikin, S. M.; Karpik, A. P.

2016-12-01

GNSS technology is playing a major role in applications to civil, industrial and scientific areas. Nowadays, there are two fully functional GNSS: American GPS and Russian GLONASS. Their data processing algorithms have been historically based on the Newtonian theory of space and time with only a few relativistic effects taken into account as small corrections preventing the system from degradation on a fairly long time. Continuously growing accuracy of geodetic measurements and atomic clocks suggests reconsidering the overall approach to the GNSS theoretical model based on the Einstein theory of general relativity. This is essentially more challenging but fundamentally consistent theoretical approach to relativistic space geodesy. In this paper, we overview the basic principles of the relativistic GNSS model and explain the advantages of such a system for GLONASS and other positioning systems. Keywords: relativistic GLONASS, Einstein theory of general relativity.

Bardeen regular black hole with an electric source

NASA Astrophysics Data System (ADS)

Rodrigues, Manuel E.; Silva, Marcos V. de S.

2018-06-01

If some energy conditions on the stress-energy tensor are violated, is possible construct regular black holes in General Relativity and in alternative theories of gravity. This type of solution has horizons but does not present singularities. The first regular black hole was presented by Bardeen and can be obtained from Einstein equations in the presence of an electromagnetic field. E. Ayon-Beato and A. Garcia reinterpreted the Bardeen metric as a magnetic solution of General Relativity coupled to a nonlinear electrodynamics. In this work, we show that the Bardeen model may also be interpreted as a solution of Einstein equations in the presence of an electric source, whose electric field does not behave as a Coulomb field. We analyzed the asymptotic forms of the Lagrangian for the electric case and also analyzed the energy conditions.

Exact quantization of Einstein-Rosen waves coupled to massless scalar matter.

PubMed

Barbero G, J Fernando; Garay, Iñaki; Villaseñor, Eduardo J S

2005-07-29

We show in this Letter that gravity coupled to a massless scalar field with full cylindrical symmetry can be exactly quantized by an extension of the techniques used in the quantization of Einstein-Rosen waves. This system provides a useful test bed to discuss a number of issues in quantum general relativity, such as the emergence of the classical metric, microcausality, and large quantum gravity effects. It may also provide an appropriate framework to study gravitational critical phenomena from a quantum point of view, issues related to black hole evaporation, and the consistent definition of test fields and particles in quantum gravity.

Stochastic quantization of (λϕ4)d scalar theory: Generalized Langevin equation with memory kernel

NASA Astrophysics Data System (ADS)

Menezes, G.; Svaiter, N. F.

2007-02-01

The method of stochastic quantization for a scalar field theory is reviewed. A brief survey for the case of self-interacting scalar field, implementing the stochastic perturbation theory up to the one-loop level, is presented. Then, it is introduced a colored random noise in the Einstein's relations, a common prescription employed by one of the stochastic regularizations, to control the ultraviolet divergences of the theory. This formalism is extended to the case where a Langevin equation with a memory kernel is used. It is shown that, maintaining the Einstein's relations with a colored noise, there is convergence to a non-regularized theory.

Self-Diffusion and Heteroassociation in an Acetone-Chloroform Mixture at 298 K

NASA Astrophysics Data System (ADS)

Golubev, V. A.; Gurina, D. L.; Kumeev, R. S.

2018-01-01

The self-diffusion coefficients of acetone and chloroform in a binary acetone-chloroform mixture at 298 K are determined via pulsed field gradient NMR spectroscopy. It is estimated that the hydrodynamic radii of the mixture's components, calculated using the Stokes-Einstein equation, grow as the concentrations of the components fall. It is shown that such behavior of hydrodynamic radii is due to acetone-chloroform heteroassociation. The hydrodynamic radii of monomers and heteroassociates in a 1: 1 ratio are determined along with the constant of heteroassociation, using the proposed model of an associated solution.

New variables for classical and quantum gravity

NASA Technical Reports Server (NTRS)

Ashtekar, Abhay

1986-01-01

A Hamiltonian formulation of general relativity based on certain spinorial variables is introduced. These variables simplify the constraints of general relativity considerably and enable one to imbed the constraint surface in the phase space of Einstein's theory into that of Yang-Mills theory. The imbedding suggests new ways of attacking a number of problems in both classical and quantum gravity. Some illustrative applications are discussed.

Finding Horndeski theories with Einstein gravity limits

DOE Office of Scientific and Technical Information (OSTI.GOV)

McManus, Ryan; Lombriser, Lucas; Peñarrubia, Jorge, E-mail: ryanm@roe.ac.uk, E-mail: llo@roe.ac.uk, E-mail: jorpega@roe.ac.uk

The Horndeski action is the most general scalar-tensor theory with at most second-order derivatives in the equations of motion, thus evading Ostrogradsky instabilities and making it of interest when modifying gravity at large scales. To pass local tests of gravity, these modifications predominantly rely on nonlinear screening mechanisms that recover Einstein's Theory of General Relativity in regions of high density. We derive a set of conditions on the four free functions of the Horndeski action that examine whether a specific model embedded in the action possesses an Einstein gravity limit or not. For this purpose, we develop a new andmore » surprisingly simple scaling method that identifies dominant terms in the equations of motion by considering formal limits of the couplings that enter through the new terms in the modified action. This enables us to find regimes where nonlinear terms dominate and Einstein's field equations are recovered to leading order. Together with an efficient approximation of the scalar field profile, one can then further evaluate whether these limits can be attributed to a genuine screening effect. For illustration, we apply the analysis to both a cubic galileon and a chameleon model as well as to Brans-Dicke theory. Finally, we emphasise that the scaling method also provides a natural approach for performing post-Newtonian expansions in screened regimes.« less

Outer boundary as arrested history in general relativity

NASA Astrophysics Data System (ADS)

Lau, Stephen R.

2002-06-01

We present explicit outer boundary conditions for the canonical variables of general relativity. The conditions are associated with the causal evolution of a finite Cauchy domain, a so-called quasilocal boost, and they suggest a consistent scheme for modelling such an evolution numerically. The scheme involves a continuous boost in the spacetime orthogonal complement ⊥Tp(B) of the tangent space Tp(B) belonging to each point p on the system boundary B. We show how the boost rate may be computed numerically via equations similar to those appearing in canonical investigations of black-hole thermodynamics (although here holding at an outer two-surface rather than the bifurcate two-surface of a Killing horizon). We demonstrate the numerical scheme on a model example, the quasilocal boost of a spherical three-ball in Minkowski spacetime. Developing our general formalism with recent hyperbolic formulations of the Einstein equations in mind, we use Anderson and York's 'Einstein-Christoffel' hyperbolic system as the evolution equations for our numerical simulation of the model.

Instationary Generalized Stokes Equations in Partially Periodic Domains

NASA Astrophysics Data System (ADS)

Sauer, Jonas

2018-06-01

We consider an instationary generalized Stokes system with nonhomogeneous divergence data under a periodic condition in only some directions. The problem is set in the whole space, the half space or in (after an identification of the periodic directions with a torus) bounded domains with sufficiently regular boundary. We show unique solvability for all times in Muckenhoupt weighted Lebesgue spaces. The divergence condition is dealt with by analyzing the associated reduced Stokes system and in particular by showing maximal regularity of the partially periodic reduced Stokes operator.

Relating structure and flow of soft colloids

NASA Astrophysics Data System (ADS)

Kundu, S. K.; Gupta, S.; Stellbrink, J.; Willner, L.; Richter, D.

2013-11-01

To relate the complex macroscopic flow of soft colloids to details of its microscopic equilibrium and non-equilibrium structure is still one big challenge in soft matter science. We investigated several well-defined colloidal model systems like star polymers or diblock copolymer micelles by linear/non-linear rheology, static/dynamic light scattering (SLS/DLS) and small angle neutron scattering (SANS). In addition, in-situ SANS experiments during shear (Rheo-SANS) revealed directly shear induced structural changes on a microscopic level. Varying the molecular architecture of the individual colloidal particle as well as particle-particle interactions and covering at the same time a broad concentration range from the very dilute to highly concentrated, glassy regime, we could separate contributions from intra- and inter-particle softness. Both can be precisely "tuned" by varying systematically the functionality, 6 ≤ f≤ 64, for star polymers or aggregation number, 30 ≤ N agg ≤ 1000 for diblock copolymer micelles, as well as the degree of polymerization of the individual polymer arm 100 ≤ D p ≤ 3000. In dilute solutions, the characteristic shear rate at which deformation of the soft colloid is observed can be related to the Zimm time of the polymeric corona. In concentrated solutions, we validated a generalized Stokes-Einstein approach to describe the increase in macroscopic viscosity and mesoscopic self diffusion coefficient on approaching the glassy regime. Both can be explained in terms of an ultra-soft interaction potential. Moreover, non-equilibrium structure factors are obtained by Rheo-SANS. All experimental results are in excellent quantitative agreement with recent theoretical predictions.

Antigravity Acts on Photons

NASA Astrophysics Data System (ADS)

Brynjolfsson, Ari

2002-04-01

Einstein's general theory of relativity assumes that photons don't change frequency as they move from Sun to Earth. This assumption is correct in classical physics. All experiments proving the general relativity are in the domain of classical physics. This include the tests by Pound et al. of the gravitational redshift of 14.4 keV photons; the rocket experiments by Vessot et al.; the Galileo solar redshift experiments by Krisher et al.; the gravitational deflection of light experiments by Riveros and Vucetich; and delay of echoes of radar signals passing close to Sun as observed by Shapiro et al. Bohr's correspondence principle assures that quantum mechanical theory of general relativity agrees with Einstein's classical theory when frequency and gravitational field gradient approach zero, or when photons cannot interact with the gravitational field. When we treat photons as quantum mechanical particles; we find that gravitational force on photons is reversed (antigravity). This modified theory contradicts the equivalence principle, but is consistent with all experiments. Solar lines and distant stars are redshifted in accordance with author's plasma redshift theory. These changes result in a beautiful consistent cosmology.

Cerebral cortex astroglia and the brain of a genius: A propos of A. Einstein's

PubMed Central

Colombo, Jorge A.; Reisin, Hernán D.; Miguel-Hidalgo, José J.; Rajkowska, Grazyna

2010-01-01

The glial fibrillary acidic protein immunoreactive astroglial layout of the cerebral cortex from Albert Einstein and other four age-matched human cases lacking any known neurological disease was analyzed using quantification of geometrical features mathematically defined. Several parameters (parallelism, relative depth, tortuosity) describing the primate-specific interlaminar glial processes did not show individually distinctive characteristics in any of the samples analyzed. However, A. Einstein's astrocytic processes showed larger sizes and higher numbers of interlaminar terminal masses, reaching sizes of 15 μm in diameter. These bulbous endings are of unknown significance and they have been described occurring in Alzheimer's disease. These observations are placed in the context of the general discussion regarding the proposal – by other authors – that structural, postmortem characteristics of the aged brain of Albert Einstein may serve as markers of his cognitive performance, a proposal to which the authors of this paper do not subscribe, and argue against. PMID:16675021

Inevitable inflation in Einstein-Cartan theory with improved energy-momentum tensor with spin

NASA Technical Reports Server (NTRS)

Fennelly, A. J.; Bradas, James C.; Smalley, Larry L.

1988-01-01

Generalized, or power-law, inflation is shown to necessarily exist for a simple, anisotropic, (Bianchi Type-1) cosmology in the Einstein-Cartan gravitational theory with the Ray-Smalley improved energy momentum tensor with spin. Formal solution of the EC field equations with the fluid equations of motion explicitly shows inflation caused by the RS spin angular kinetic energy density. Shear is not effective in preventing inflation in the ECRS model. The relation between fluid vorticity, torsion, reference axis rotation, and shear ellipsoid precession shows through clearly.

Schwarzschild Solution: A Historical Perspective

NASA Astrophysics Data System (ADS)

Bartusiak, Marcia

2016-03-01

While eighteenth-century Newtonians had imagined a precursor to the black hole, the modern version has its roots in the first full solution to Einstein's equations of general relativity, derived by the German astronomer Karl Schwarzschild on a World War I battlefront just weeks after Einstein introduced his completed theory in November 1915. This talk will demonstrate how Schwarzschild's solution is linked to the black hole and how it took more than half a century for the physics community to accept that such a bizarre celestial object could exist in the universe.

Nonsingular solutions and instabilities in Einstein-scalar-Gauss-Bonnet cosmology

NASA Astrophysics Data System (ADS)

Sberna, Laura; Pani, Paolo

2017-12-01

It is generically believed that higher-order curvature corrections to the Einstein-Hilbert action might cure the curvature singularities that plague general relativity. Here we consider Einstein-scalar-Gauss-Bonnet gravity, the only four-dimensional, ghost-free theory with quadratic curvature terms. For any choice of the coupling function and of the scalar potential, we show that the theory does not allow for bouncing solutions in the flat and open Friedmann universe. For the case of a closed universe, using a reverse-engineering method, we explicitly provide a bouncing solution which is nevertheless linearly unstable in the scalar gravitational sector. Moreover, we show that the expanding, singularity-free, early-time cosmologies allowed in the theory are unstable. These results rely only on analyticity and finiteness of cosmological variables at early times.

Twistor-strings and gravity tree amplitudes

NASA Astrophysics Data System (ADS)

Adamo, Tim; Mason, Lionel

2013-04-01

Recently we discussed how Einstein supergravity tree amplitudes might be obtained from the original Witten and Berkovits twistor-string theory when external conformal gravitons are restricted to be Einstein gravitons. Here we obtain a more systematic understanding of the relationship between conformal and Einstein gravity amplitudes in that twistor-string theory. We show that although it does not in general yield Einstein amplitudes, we can nevertheless obtain some partial twistor-string interpretation of the remarkable formulae recently been found by Hodges and generalized to all tree amplitudes by Cachazo and Skinner. The Hodges matrix and its higher degree generalizations encode the world sheet correlators of the twistor string. These matrices control both Einstein amplitudes and those of the conformal gravity arising from the Witten and Berkovits twistor-string. Amplitudes in the latter case arise from products of the diagonal elements of the generalized Hodges matrices and reduced determinants give the former. The reduced determinants arise if the contractions in the worldsheet correlator are restricted to form connected trees at MHV. The (generalized) Hodges matrices arise as weighted Laplacian matrices for the graph of possible contractions in the correlators and the reduced determinants of these weighted Laplacian matrices give the sum of the connected tree contributions by an extension of the matrix-tree theorem.

The Redshifts in Relativity

ERIC Educational Resources Information Center

Singh, Satya Pal; Singh, Apoorva; Hareet, Prabhav

2011-01-01

The progress of modern cosmology took off in 1917 when A. Einstein published his paper on general theory of relativity extending his work of special theory of relativity (1905). In 1922 Alexander Friedmann constructed a mathematical model for expanding Universe that had a big bang in remote past. The experimental evidences could come in 1929 by…

String Theory Methods for Condensed Matter Physics

NASA Astrophysics Data System (ADS)

Nastase, Horatiu

2017-09-01

Preface; Acknowledgments; Introduction; Part I. Condensed Matter Models and Problems: 1. Lightning review of statistical mechanics, thermodynamics, phases and phase transitions; 2. Magnetism in solids; 3. Electrons in solids: Fermi gas vs. Fermi liquid; 4. Bosonic quasi-particles: phonons and plasmons; 5. Spin-charge separation in 1+1 dimensional solids: spinons and holons; 6. The Ising model and the Heisenberg spin chain; 7. Spin chains and integrable systems; 8. The thermodynamic Bethe ansatz; 9. Conformal field theories and quantum phase transitions; 10. Classical vs. quantum Hall effect; 11. Superconductivity: Landau-Ginzburg, London and BCS; 12. Topology and statistics: Berry and Chern-Simons, anyons and nonabelions; 13. Insulators; 14. The Kondo effect and the Kondo problem; 15. Hydrodynamics and transport properties: from Boltzmann to Navier-Stokes; Part II. Elements of General Relativity and String Theory: 16. The Einstein equation and the Schwarzschild solution; 17. The Reissner-Nordstrom and Kerr-Newman solutions and thermodynamic properties of black holes; 18. Extra dimensions and Kaluza-Klein; 19. Electromagnetism and gravity in various dimensions. Consistent truncations; 20. Gravity plus matter: black holes and p-branes in various dimensions; 21. Weak/strong coupling dualities in 1+1, 2+1, 3+1 and d+1 dimensions; 22. The relativistic point particle and the relativistic string; 23. Lightcone strings and quantization; 24. D-branes and gauge fields; 25. Electromagnetic fields on D-branes. Supersymmetry and N = 4 SYM. T-duality of closed strings; 26. Dualities and M theory; 27. The AdS/CFT correspondence: definition and motivation; Part III. Applying String Theory to Condensed Matter Problems: 28. The pp wave correspondence: string Hamiltonian from N = 4 SYM; 29. Spin chains from N = 4 SYM; 30. The Bethe ansatz: Bethe strings from classical strings in AdS; 31. Integrability and AdS/CFT; 32. AdS/CFT phenomenology: Lifshitz, Galilean and Schrodinger symmetries and their gravity duals; 33. Finite temperature and black holes; 34. Hot plasma equilibrium thermodynamics: entropy, charge density and chemical potential of strongly coupled theories; 35. Spectral functions and transport properties; 36. Dynamic and nonequilibrium properties of plasmas: electric transport, Langevin diffusion and thermalization via black hole quasi-normal modes; 37. The holographic superconductor; 38. The fluid-gravity correspondence: conformal relativistic fluids from black hole horizons; 39. Nonrelativistic fluids: from Einstein to Navier-Stokes and back; Part IV. Advanced Applications: 40. Fermi gas and liquid in AdS/CFT; 41. Quantum Hall effect from string theory; 42. Quantum critical systems and AdS/CFT; 43. Particle-vortex duality and ABJM vs. AdS4 X CP3 duality; 44. Topology and non-standard statistics from AdS/CFT; 45. DBI scalar model for QGP/black hole hydro- and thermo-dynamics; 46. Holographic entanglement entropy in condensed matter; 47. Holographic insulators; 48. Holographic strange metals and the Kondo problem; References; Index.

The rotational motion of an earth orbiting gyroscope according to the Einstein theory of general relativity

NASA Technical Reports Server (NTRS)

Hoots, F. R.; Fitzpatrick, P. M.

1979-01-01

The classical Poisson equations of rotational motion are used to study the attitude motions of an earth orbiting, rapidly spinning gyroscope perturbed by the effects of general relativity (Einstein theory). The center of mass of the gyroscope is assumed to move about a rotating oblate earth in an evolving elliptic orbit which includes all first-order oblateness effects produced by the earth. A method of averaging is used to obtain a transformation of variables, for the nonresonance case, which significantly simplifies the Poisson differential equations of motion of the gyroscope. Long-term solutions are obtained by an exact analytical integration of the simplified transformed equations. These solutions may be used to predict both the orientation of the gyroscope and the motion of its rotational angular momentum vector as viewed from its center of mass. The results are valid for all eccentricities and all inclinations not near the critical inclination.

Tikekar superdense stars in electric fields

NASA Astrophysics Data System (ADS)

Komathiraj, K.; Maharaj, S. D.

2007-04-01

We present exact solutions to the Einstein-Maxwell system of equations with a specified form of the electric field intensity by assuming that the hypersurface {t=constant} are spheroidal. The solution of the Einstein-Maxwell system is reduced to a recurrence relation with variable rational coefficients which can be solved in general using mathematical induction. New classes of solutions of linearly independent functions are obtained by restricting the spheroidal parameter K and the electric field intensity parameter α. Consequently, it is possible to find exact solutions in terms of elementary functions, namely, polynomials and algebraic functions. Our result contains models found previously including the superdense Tikekar neutron star model [J. Math. Phys. 31, 2454 (1990)] when K=-7 and α=0. Our class of charged spheroidal models generalize the uncharged isotropic Maharaj and Leach solutions [J. Math. Phys. 37, 430 (1996)]. In particular, we find an explicit relationship directly relating the spheroidal parameter K to the electromagnetic field.

Republication of: Geometrodynamics in the null case. Exact solutions of the field equations of the general theory of relativity III

NASA Astrophysics Data System (ADS)

Jordan, Pascual; Kundt, Wolfgang

2014-03-01

This is an English translation of a paper by Pascual Jordan and Wolfgang Kundt, first published in 1961 in the proceedings of the Academy of Sciences and Literature in Mainz (Germany). The original paper was part 3 of a five-part series of articles containing the first summary of knowledge about exact solutions of Einstein's equations found until then. (Parts 1, 2 and 4 of the series have already been reprinted, part 5 will be printed as a Golden Oldie in near future.) This third paper shows how solutions of the Einstein-Maxwell equations with null Maxwell field can be incorporated into the scheme of geometrodynamics. It has been selected by the Editors of General Relativity and Gravitation for republication in the Golden Oldies series of the journal. The republication is accompanied by an editorial note written by Charles Misner.

Mass Function of Galaxy Clusters in Relativistic Inhomogeneous Cosmology

NASA Astrophysics Data System (ADS)

Ostrowski, Jan J.; Buchert, Thomas; Roukema, Boudewijn F.

The current cosmological model (ΛCDM) with the underlying FLRW metric relies on the assumption of local isotropy, hence homogeneity of the Universe. Difficulties arise when one attempts to justify this model as an average description of the Universe from first principles of general relativity, since in general, the Einstein tensor built from the averaged metric is not equal to the averaged stress-energy tensor. In this context, the discrepancy between these quantities is called "cosmological backreaction" and has been the subject of scientific debate among cosmologists and relativists for more than 20 years. Here we present one of the methods to tackle this problem, i.e. averaging the scalar parts of the Einstein equations, together with its application, the cosmological mass function of galaxy clusters.

The NASA Beyond Einstein Program

NASA Technical Reports Server (NTRS)

White, Nicholas E.

2006-01-01

Einstein's legacy is incomplete, his theory of General relativity raises -- but cannot answer --three profound questions: What powered the big bang? What happens to space, time, and matter at the edge of a black hole? and What is the mysterious dark energy pulling the Universe apart? The Beyond Einstein program within NASA's Office of Space Science aims to answer these questions, employing a series of missions linked by powerful new technologies and complementary approaches towards shared science goals. The Beyond Einstein program has three linked elements which advance science and technology towards two visions; to detect directly gravitational wave signals from the earliest possible moments of the BIg Bang, and to image the event horizon of a black hole. The central element is a pair of Einstein Great Observatories, Constellation-X and LISA. Constellation-X is a powerful new X-ray observatory dedicated to X-Ray Spectroscopy. LISA is the first spaced based gravitational wave detector. These powerful facilities will blaze new paths to the questions about black holes, the Big Bang and dark energy. The second element is a series of competitively selected Einstein Probes, each focused on one of the science questions and includes a mission dedicated resolving the Dark Energy mystery. The third element is a program of technology development, theoretical studies and education. The Beyond Einstein program is a new element in the proposed NASA budget for 2004. This talk will give an overview of the program and the missions contained within it.

Einstein and Einstein A: A Study in Crater Morphology

NASA Image and Video Library

2017-12-08

NASA image release May 14, 2010 Einstein and Einstein A: A Study in Crater Morphology Located on the western limb of the Moon, Einstein and Einstein A craters (16.3oN, 271.3oE ) are only visible to Earth-based observers during certain lunar lighting and orientation conditions. Einstein A is younger than Einstein, as indicated by the fact that it lies squarely in the middle of the floor of Einstein. When viewed in topographic data, these two craters reveal much about the relative age and shape of an impact crater. To understand further, let's first take a look at Einstein. Einstein is a fairly large crater that spans 198 km across. A crater's size alone however cannot reveal much about age. ÊEinstein's relative age can be determined by examining the frequency and distribution of impact craters overprinted on its rim and floor. Younger craters have had fewer impacts, which enables them to retain their original morphology. Einstein A reveals most of its original structure, including a raised rim and ejecta blanket, and is therefore a relatively young crater as compared to Einstein, whose original structure has been somewhat degraded over time by smaller impacts. The Einstein craters were named after famed physicist, philosopher, and scientist Albert Einstein (1879-1955). To learn more go to: www.nasa.gov/mission_pages/LRO/multimedia/lroimages/lola-... NASA Goddard Space Flight Center is home to the nation's largest organization of combined scientists, engineers and technologists that build spacecraft, instruments and new technology to study the Earth, the sun, our solar system, and the universe.

Gravitational Physics: the birth of a new era

NASA Astrophysics Data System (ADS)

Sakellariadou, Mairi

2017-11-01

We live the golden age of cosmology, while the era of gravitational astronomy has finally begun. Still, fundamental puzzles remain. Standard cosmology is formulated within the framework of Einstein's General theory of Relativity. Notwithstanding, General Relativity is not adequate to explain the earliest stages of cosmic existence, and cannot provide an explanation for the Big Bang itself. Modern early universe cosmology is in need of a rigorous underpinning in Quantum Gravity.

The Gravity Probe B Experiment

NASA Technical Reports Server (NTRS)

Kolodziejczak, Jeffrey

2008-01-01

This presentation briefly describes the Gravity Probe B (GP-B) Experiment which is designed to measure parts of Einstein's general theory of relativity by monitoring gyroscope orientation relative to a distant guide star. To measure the miniscule angles predicted by Einstein's theory, it was necessary to build near-perfect gyroscopes that were approximately 50 million times more precise than the best navigational gyroscopes. A telescope mounted along the central axis of the dewar and spacecraft provided the experiment's pointing reference to a guide star. The telescope's image divide precisely split the star's beam into x-axis and y-axis components whose brightness could be compared. GP-B's 650-gallon dewar, kept the science instrument inside the probe at a cryogenic temperature for 17.3 months and also provided the thruster propellant for precision attitude and translation control. Built around the dewar, the GP-B spacecraft was a total-integrated system, comprising both the space vehicle and payload, dedicated as a single entity to experimentally testing predictions of Einstein's theory.

On the Correct Formulation of the Law of the External Photoelectric Effect

NASA Astrophysics Data System (ADS)

Kalanov, Temur Z.

2017-01-01

The critical and correct scientific analysis of the generally accepted theory of the external photoelectric effect is proposed. The methodological basis for the analysis is the unity of formal logic and of rational dialectics. It is shown that Einstein's formulation of the law of the photoelectric effect is not free from the following objection. The terms of Einstein's formula characterize the quantitative determinacy (i.e., energy) which belongs and is related to the different material objects: ``photon'', ``electron in metal'', and ``electron not in metal''. This signifies that Einstein's formula represents violation of the formal-logical laws of identity and absence (lack) of contradiction. The correct mathematical formulation of the law of the external photoelectric effect within the framework of the system approach is proposed. The correct formulation represents the proportion by relative increments of the energy of the incident photon and the energy of the emitted electron. The proportion describes the linear relationship between the energy of the incident photon and the energy of the emitted electron.

Implications of a positive cosmological constant for general relativity.

PubMed

Ashtekar, Abhay

2017-10-01

Most of the literature on general relativity over the last century assumes that the cosmological constant [Formula: see text] is zero. However, by now independent observations have led to a consensus that the dynamics of the universe is best described by Einstein's equations with a small but positive [Formula: see text]. Interestingly, this requires a drastic revision of conceptual frameworks commonly used in general relativity, no matter how small [Formula: see text] is. We first explain why, and then summarize the current status of generalizations of these frameworks to include a positive [Formula: see text], focusing on gravitational waves.

The absence of gravitational waves and the foundations of Relativistic Cosmology

NASA Astrophysics Data System (ADS)

Djidjian, Robert

2015-07-01

Modern relativistic cosmology is based on Albert Einstein's teaching of general relativity. Observational and experimental impressive verification of general relativity have created among the astrophysicists the conviction that general relativity and relativistic cosmology are absolutely true theories. Unfortunately, the most important conclusion of general relativity is that the necessary existence of gravitational waves has been rejected by all the experiments up to the present time. There is also a kind of direct objection to the conception of expanding Universe: with the expansion of space identically expands the measuring stick, which makes the distances between the galaxies unchanged. So it should be quite reasonable to open discussions regarding the status of both general relativity and relativistic cosmology.

Gravitational Lensing: Einstein's unfinished symphony

NASA Astrophysics Data System (ADS)

Treu, Tommaso; Ellis, Richard S.

2015-01-01

Gravitational lensing - the deflection of light rays by gravitating matter - has become a major tool in the armoury of the modern cosmologist. Proposed nearly a hundred years ago as a key feature of Einstein's theory of general relativity, we trace the historical development since its verification at a solar eclipse in 1919. Einstein was apparently cautious about its practical utility and the subject lay dormant observationally for nearly 60 years. Nonetheless there has been rapid progress over the past twenty years. The technique allows astronomers to chart the distribution of dark matter on large and small scales thereby testing predictions of the standard cosmological model which assumes dark matter comprises a massive weakly-interacting particle. By measuring the distances and tracing the growth of dark matter structure over cosmic time, gravitational lensing also holds great promise in determining whether the dark energy, postulated to explain the accelerated cosmic expansion, is a vacuum energy density or a failure of general relativity on large scales. We illustrate the wide range of applications which harness the power of gravitational lensing, from searches for the earliest galaxies magnified by massive clusters to those for extrasolar planets which temporarily brighten a background star. We summarise the future prospects with dedicated ground and space-based facilities designed to exploit this remarkable physical phenomenon.

Two-pulse control of Raman scattering in liquid methanol: The dominance of classical nonlinear optical effects

NASA Astrophysics Data System (ADS)

Spanner, Michael; Brumer, Paul

2006-02-01

Experimental results on adaptive feedback control of transient (i.e., nonimpulsive) Stokes emission in liquid methanol [Pearson and Bucksbaum, Phys. Rev. Lett. 92, 243003 (2004)] are analyzed. In the experiment, a pump pulse comprising two frequency-shifted Gaussian pulses was used to control the ratio of two Stokes emission lines by varying the relative phase ϕL between the pulses. Extending the theory of stimulated Raman scattering to accommodate two coupled levels, we show that control of this type is possible, in the strongly driven regime, using Raman coupling alone. Control via variation of ϕL is shown to also result from self- and cross-phase-modulation of the pump and Stokes pulses as well as via the focused-beam geometry of the pump pulse. In all cases, the general control mechanism is nonlinear optical modulation between the pump and the Stokes pulse; no coherent quantum interference effects are involved. Finally, although the vibrational populations are affected by the same control mechanisms that affect the Stokes spectra, the ratio of the Stokes spectra peak heights does not directly reflect the ratio of the level populations, as was assumed in the experiment.

Bridging the knowledge gap: An analysis of Albert Einstein's popularized presentation of the equivalence of mass and energy.

PubMed

Kapon, Shulamit

2014-11-01

This article presents an analysis of a scientific article written by Albert Einstein in 1946 for the general public that explains the equivalence of mass and energy and discusses the implications of this principle. It is argued that an intelligent popularization of many advanced ideas in physics requires more than the simple elimination of mathematical formalisms and complicated scientific conceptions. Rather, it is shown that Einstein developed an alternative argument for the general public that bypasses the core of the formal derivation of the equivalence of mass and energy to provide a sense of derivation based on the history of science and the nature of scientific inquiry. This alternative argument is supported and enhanced by variety of explanatory devices orchestrated to coherently support and promote the reader's understanding. The discussion centers on comparisons to other scientific expositions written by Einstein for the general public. © The Author(s) 2013.

Entropy Stable Spectral Collocation Schemes for the Navier-Stokes Equations: Discontinuous Interfaces

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Fisher, Travis C.; Nielsen, Eric J.; Frankel, Steven H.

2013-01-01

Nonlinear entropy stability and a summation-by-parts framework are used to derive provably stable, polynomial-based spectral collocation methods of arbitrary order. The new methods are closely related to discontinuous Galerkin spectral collocation methods commonly known as DGFEM, but exhibit a more general entropy stability property. Although the new schemes are applicable to a broad class of linear and nonlinear conservation laws, emphasis herein is placed on the entropy stability of the compressible Navier-Stokes equations.

Gravitational waves in Einstein-æther and generalized TeVeS theory after GW170817

NASA Astrophysics Data System (ADS)

Gong, Yungui; Hou, Shaoqi; Liang, Dicong; Papantonopoulos, Eleftherios

2018-04-01

In this work we discuss the polarization contents of Einstein-æther theory and the generalized tensor-vector-scalar (TeVeS) theory, as both theories have a normalized timelike vector field. We derive the linearized equations of motion around the flat spacetime background using the gauge-invariant variables to easily separate physical degrees of freedom. We find the plane wave solutions and identify the polarizations by examining the geodesic deviation equations. We find that there are five polarizations in Einstein-æther theory and six polarizations in the generalized TeVeS theory. In particular, the transverse breathing mode is mixed with the pure longitudinal mode. We also discuss the experimental tests of the extra polarizations in Einstein-æther theory using pulsar timing arrays combined with the gravitational-wave speed bound derived from the observations on GW 170817 and GRB 170817A. It turns out that it might be difficult to use pulsar timing arrays to distinguish different polarizations in Einstein-æther theory. The same speed bound also forces one of the propagating modes in the generalized TeVeS theory to travel much faster than the speed of light. Since the strong coupling problem does not exist in some parameter subspaces, the generalized TeVeS theory is excluded in these parameter subspaces.

Reconstruction of the History of the Photoelectric Effect and Its Implications for General Physics Textbooks

ERIC Educational Resources Information Center

Niaz, Mansoor; Klassen, Stephen; McMillan, Barbara; Metz, Don

2010-01-01

The photoelectric effect is an important part of general physics textbooks. To study the presentation of this phenomenon, we have reconstructed six essential, history and philosophy of science (HPS)-related aspects of the events that culminated in Einstein proposing his hypothesis of lightquanta and the ensuing controversy within the scientific…

Optical design for the Laser Astrometric Test of Relativity

NASA Technical Reports Server (NTRS)

Turyshev, Slava G.; Shao, Michael; Nordtvedt, Kenneth L., Jr.

2004-01-01

This paper discusses the Laser Astrometric Test of Relativity (LATOR) mission. LATOR is a Michelson-Morley-type experiment designed to test the pure tensor metric nature of gravitation the fundamental postulate of Einstein's theory of general relativity. With its focus on gravity's action on light propagation it complements other tests which rely on the gravitational dynamics of bodies.

Numerical Relativity

NASA Technical Reports Server (NTRS)

Baker, John G.

2009-01-01

Recent advances in numerical relativity have fueled an explosion of progress in understanding the predictions of Einstein's theory of gravity, General Relativity, for the strong field dynamics, the gravitational radiation wave forms, and consequently the state of the remnant produced from the merger of compact binary objects. I will review recent results from the field, focusing on mergers of two black holes.

Stability of the Einstein static universe in open cosmological models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Canonico, Rosangela; Parisi, Luca; INFN, Sezione di Napoli, GC di Salerno, Via Ponte Don Melillo, I-84081 Baronissi

2010-09-15

The stability properties of the Einstein static solution of general relativity are altered when corrective terms arising from modification of the underlying gravitational theory appear in the cosmological equations. In this paper the existence and stability of static solutions are considered in the framework of two recently proposed quantum gravity models. The previously known analysis of the Einstein static solutions in the semiclassical regime of loop quantum cosmology with modifications to the gravitational sector is extended to open cosmological models where a static neutrally stable solution is found. A similar analysis is also performed in the framework of Horava-Lifshitz gravitymore » under detailed balance and projectability conditions. In the case of open cosmological models the two solutions found can be either unstable or neutrally stable according to the admitted values of the parameters.« less

BOOK REVIEW: The Legacy of Albert Einstein: A Collection of Essays in Celebration of the Year of Physics

NASA Astrophysics Data System (ADS)

Straumann, Norbert

2007-10-01

During the 'World Year of Physics' much has been written on the epoch-making 1905 papers of Albert Einstein and his later great contributions to physics. Why another book on the enormous impact of Einstein's work on 20th-century physics? The short answer is that the present collection of 13 relatively short essays on the legacy of Einstein by outstanding scientists is very pleasant to read and should be of interest to physicists of all branches. Beside looking back, most articles present later and topical developments, whose initiation began with the work of Einstein. During the year 2005, the growing recognition among physicists, historians, and philosophers of Einstein's revolutionary role in quantum theory was often emphasized. It is truly astonishing that most active physicists were largely unaware of this before. Fortunately, the article 'Einstein and the quantum' by V Singh puts the subject in perspective and describes all the main steps, beginning with the truly revolutionary 1905 paper on the light-quantum hypothesis and ending with Einstein's extension of the particle-wave duality to atoms and other particles in 1924 1925. The only point which, in my opinion, is not sufficiently emphasized in the discussion of the 1916 1917 papers on absorption and emission of radiation is the part on the momentum transfer in each elementary process. Einstein's result that there is a directed recoil hν/c—also for spontaneous emission—in complete contrast to classical theory, was particularly important to him. I enjoyed reading the articles on Brownian motion (S Majumdar), Bose Einstein condensation (N Kumar) and strongly correlated electrons (T Ramakrishnan), which are all written for non-experts. Connected with Einstein's most lasting work—general relativity—there are two articles on cosmology. The one by J Narlikar gives a brief historical account of the development that was initiated by the 1917 paper of Einstein. S Sarkar's essay emphasizes the remarkable recent observational progress in cosmology and the emergence of the 'cosmic concordance model', with dark matter and dark energy as the dominant components of the current universe. Their discovery is widely considered as the most direct evidence for fundamental physics beyond the standard model of particle physics. In an introductory section Sarkar recalls the main reasons why the cosmological constant (vacuum energy) problem is of a very profound nature. In spite of some interesting ideas, no satisfactory solution is in sight. The article by B Sathyapakhash on gravitational radiation provides a readable introduction to the status of current detectors and astronomical sources of gravitational radiation. Of great cosmological interest are planned searches for a stochastic background of gravitational waves that is expected to have been produced by quantum processes in the very early universe. More than the first third of the book is devoted to current speculative attempts at creating a quantum theory of gravity, possibly within a unified coherent description of the known four fundamental interactions. Thanks to the enormously large value of the Planck energy in comparison to elementary particle masses, physicists may maintain for a long time, with success, a schizophrenic attitude in working within the framework of our present understanding, based on quantum field theory and classical general relativity. That physics cannot stay with that was already pointed out by Einstein in 1916, as A Ashtekar recalls in his essay. 'Einstein and the search for unification' by D Gross is the first article of the present book. In this he describes the reasons why, for those working in speculative areas, 'Einstein remains an inspiration for his foresight, and his unyielding determination and courage'. This inspiration is also manifest in the essays by M Atiyah, A Sen, and A Dabholkar on string theory. Hopefully, this book will find many readers, especially among graduate students, who can get valuable impressions of what is interesting in physics and what some of the main open problems for future research are.

Thermodynamic properties of charged three-dimensional black holes in the scalar-tensor gravity theory

NASA Astrophysics Data System (ADS)

Dehghani, M.

2018-02-01

Making use of the suitable transformation relations, the action of three-dimensional Einstein-Maxwell-dilaton gravity theory has been obtained from that of scalar-tensor modified gravity theory coupled to the Maxwell's electrodynamics as the matter field. Two new classes of the static three-dimensional charged dilatonic black holes, as the exact solutions to the coupled scalar, electromagnetic and gravitational field equations, have been obtained in the Einstein frame. Also, it has been found that the scalar potential can be written in the form of a generalized Liouville-type potential. The conserved black hole charge and masses as well as the black entropy, temperature, and electric potential have been calculated from the geometrical and thermodynamical approaches, separately. Through comparison of the results arisen from these two alternative approaches, the validity of the thermodynamical first law has been proved for both of the new black hole solutions in the Einstein frame. Making use of the canonical ensemble method, a black hole stability or phase transition analysis has been performed. Regarding the black hole heat capacity, with the black hole charge as a constant, the points of type-1 and type-2 phase transitions have been determined. Also, the ranges of the black hole horizon radius at which the Einstein black holes are thermally stable have been obtained for both of the new black hole solutions. Then making use of the inverse transformation relations, two new classes of the string black hole solutions have been obtained from their Einstein counterpart. The thermodynamics and thermal stability of the new string black hole solutions have been investigated. It has been found that thermodynamic properties of the new charged black holes are identical in the Einstein and Jordan frames.

General very special relativity in Finsler cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kouretsis, A. P.; Stathakopoulos, M.; Stavrinos, P. C.

2009-05-15

General very special relativity (GVSR) is the curved space-time of very special relativity (VSR) proposed by Cohen and Glashow. The geometry of general very special relativity possesses a line element of Finsler geometry introduced by Bogoslovsky. We calculate the Einstein field equations and derive a modified Friedmann-Robertson-Walker cosmology for an osculating Riemannian space. The Friedmann equation of motion leads to an explanation of the cosmological acceleration in terms of an alternative non-Lorentz invariant theory. A first order approach for a primordial-spurionic vector field introduced into the metric gives back an estimation of the energy evolution and inflation.

Conceptual Development of Einstein's Mass-Energy Relationship

ERIC Educational Resources Information Center

Wong, Chee Leong; Yap, Kueh Chin

2005-01-01

Einstein's special theory of relativity was published in 1905. It stands as one of the greatest intellectual achievements in the history of human thought. Einstein described the equivalence of mass and energy as "the most important upshot of the special theory of relativity" (Einstein, 1919). In this paper, we will discuss the evolution of the…

Einstein's Jury: Trial by Telescope

NASA Astrophysics Data System (ADS)

Crelinsten, Jeffrey

2007-03-01

While Einstein's theory of relativity ultimately laid the foundation for modern studies of the universe, it took a long time to be accepted. Between 1905 and 1930, relativity was poorly understood and Einstein worked hard to try to make it more accessible to scientists and scientifically literate laypeople. Its acceptance was largely due to the astronomy community, which undertook precise measurements to test Einstein's astronomical predictions. The well-known 1919 British eclipse expeditions that made Einstein famous did not convince most scientists to accept relativity. The 1920s saw numerous attempts to measure light-bending, as well as solar line displacements and even ether-drift. How astronomers approached the ``Einstein problem'' in these early years before and after the First World War, and how the public reacted to what they reported, helped to shape attitudes we hold today about Einstein and his ideas.

Counterfactual Definiteness and Bell's Inequality

NASA Astrophysics Data System (ADS)

Hess, Karl; Raedt, Hans De; Michielsen, Kristel

Counterfactual definiteness must be used as at least one of the postulates or axioms that are necessary to derive Bell-type inequalities. It is considered by many to be a postulate that is not only commensurate with classical physics (as for example Einstein's special relativity), but also separates and distinguishes classical physics from quantum mechanics. It is the purpose of this paper to show that Bell's choice of mathematical functions and independent variables implicitly includes counterfactual definiteness and reduces the generality of the physics of Bell-type theories so significantly that no meaningful comparison of these theories with actual Einstein-Podolsky-Rosen experiments can be made.

Probing quantum gravity through exactly soluble midi-superspaces I

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ashtekar, A.; Pierri, M.

1996-12-01

It is well-known that the Einstein-Rosen solutions to the 3+1- dimensional vacuum Einstein{close_quote}s equations are in one to one correspondence with solutions of 2+1-dimensional general relativity coupled to axi-symmetric, zero rest mass scalar fields. We first re-examine the quantization of this midi-superspace paying special attention to the asymptotically flat boundary conditions and to certain functional analytic subtleties associated with regularization. We then use the resulting quantum theory to analyze several conceptual and technical issues of quantum gravity. {copyright} {ital 1996 American Institute of Physics.}

Relativity Based on Physical Processes Rather Than Space-Time

NASA Astrophysics Data System (ADS)

Giese, Albrecht

2013-09-01

Physicists' understanding of relativity and the way it is handled is at present dominated by the interpretation of Albert Einstein, who related relativity to specific properties of space and time. The principal alternative to Einstein's interpretation is based on a concept proposed by Hendrik A. Lorentz, which uses knowledge of classical physics to explain relativistic phenomena. In this paper, we will show that on the one hand the Lorentz-based interpretation provides a simpler mathematical way of arriving at the known results for both Special and General Relativity. On the other hand, it is able to solve problems which have remained open to this day. Furthermore, a particle model will be presented, based on Lorentzian relativity, which explains the origin of mass without the use of the Higgs mechanism, based on the finiteness of the speed of light, and which provides the classical results for particle properties that are currently only accessible through quantum mechanics.

Freundlich, Erwin Finlay (1885-1964)

NASA Astrophysics Data System (ADS)

Murdin, P.

2000-11-01

Born in Biebrich, Germany, collaborator with EINSTEIN, making measurements (successfully) of Mercury's orbit and the gravitational redshift (unsuccessfully) to confirm the general theory of relativity. Fled Nazi Germany to become the Napier Professor of Astronomy at the University of St Andrews in Scotland....

The Happiest thought of Einstein's Life

NASA Astrophysics Data System (ADS)

Heller, Michael

Finally, let us have a closer look at the place of the equivalence principle in the logical scheme of Einstein's general relativity theory. First, Einstein new well, from Minkowski's geometric formulation of his own special relativity, that accelerated motions should be represented as curved lines in a flat space-time. Second, the Galileo principle asserts that all bodies are accelerated in the same way in a given gravitational field, and consequently their motions are represented in the flat space-time by curved lines, all exactly in the same way. Third, since all lines representing free motions are curved exactly in the same way in the flat space-time, one can say that the lines remain straight (as far as possible) but the space-time itself becomes curved. Fourth, and last, since acceleration is (locally) equivalent to a gravitational field (here we have the equivalence principle), one is entitled to assert that it is the gravitational field (and not acceleration) that is represented as the curvature of space-time. This looks almost like an Aristotelian syllogism. However, to put all the pieces of evidence into the logical chain took Einstein a few years of hard thinking. The result has been incorporated into the field equations which quantitatively show how the curvature of space-time and gravity are linked together.

Turbulent kinetic energy and a possible hierarchy of length scales in a generalization of the Navier-Stokes alpha theory.

PubMed

Fried, Eliot; Gurtin, Morton E

2007-05-01

We present a continuum-mechanical formulation and generalization of the Navier-Stokes alpha theory based on a general framework for fluid-dynamical theories with gradient dependencies. Our flow equation involves two additional problem-dependent length scales alpha and beta. The first of these scales enters the theory through the internal kinetic energy, per unit mass, alpha2|D|2, where D is the symmetric part of the gradient of the filtered velocity. The remaining scale is associated with a dissipative hyperstress which depends linearly on the gradient of the filtered vorticity. When alpha and beta are equal, our flow equation reduces to the Navier-Stokes alpha equation. In contrast to the original derivation of the Navier-Stokes alpha equation, which relies on Lagrangian averaging, our formulation delivers boundary conditions. For a confined flow, our boundary conditions involve an additional length scale l characteristic of the eddies found near walls. Based on a comparison with direct numerical simulations for fully developed turbulent flow in a rectangular channel of height 2h, we find that alphabeta approximately Re(0.470) and lh approximately Re(-0.772), where Re is the Reynolds number. The first result, which arises as a consequence of identifying the internal kinetic energy with the turbulent kinetic energy, indicates that the choice alpha=beta required to reduce our flow equation to the Navier-Stokes alpha equation is likely to be problematic. The second result evinces the classical scaling relation eta/L approximately Re(-3/4) for the ratio of the Kolmogorov microscale eta to the integral length scale L . The numerical data also suggests that l < or = beta . We are therefore led to conjecture a tentative hierarchy, l < or = beta < alpha , involving the three length scales entering our theory.

Entropy density of an adiabatic relativistic Bose-Einstein condensate star

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khaidir, Ahmad Firdaus; Kassim, Hasan Abu; Yusof, Norhasliza

Inspired by recent works, we investigate how the thermodynamics parameters (entropy, temperature, number density, energy density, etc) of Bose-Einstein Condensate star scale with the structure of the star. Below the critical temperature in which the condensation starts to occur, we study how the entropy behaves with varying temperature till it reaches its own stability against gravitational collapse and singularity. Compared to photon gases (pressure is described by radiation) where the chemical potential, μ is zero, entropy of photon gases obeys the Stefan-Boltzmann Law for a small values of T while forming a spiral structure for a large values of Tmore » due to general relativity. The entropy density of Bose-Einstein Condensate is obtained following the similar sequence but limited under critical temperature condition. We adopt the scalar field equation of state in Thomas-Fermi limit to study the characteristics of relativistic Bose-Einstein condensate under varying temperature and entropy. Finally, we obtain the entropy density proportional to (σT{sup 3}-3T) which obeys the Stefan-Boltzmann Law in ultra-relativistic condition.« less

Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chiodaroli, Marco; Günaydin, Murat; Johansson, Henrik

Using the double-copy construction of Yang-Mills-Einstein theories formulated in our earlier work, we obtain compact presentations for single-trace Yang-Mills-Einstein tree amplitudes with up to five external gravitons and an arbitrary number of gluons. These are written as linear combinations of color-ordered Yang-Mills trees, where the coefficients are given by color/kinematics-satisfying numerators in a Yang-Mills + φ 3 theory. The construction outlined in this paper holds in general dimension and extends straightforwardly to supergravity theories. For one, two, and three external gravitons, our expressions give identical or simpler presentations of amplitudes already constructed through string-theory considerations or the scattering equations formalism.more » Our results are based on color/kinematics duality and gauge invariance, and strongly hint at a recursive structure underlying the single-trace amplitudes with an arbitrary number of gravitons. We also present explicit expressions for all-loop single-graviton Einstein-Yang-Mills amplitudes in terms of Yang-Mills amplitudes and, through gauge invariance, derive new all-loop amplitude relations for Yang-Mills theory.« less

Bounce universe from string-inspired Gauss-Bonnet gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bamba, Kazuharu; Makarenko, Andrey N.; Myagky, Alexandr N.

2015-04-01

We explore cosmology with a bounce in Gauss-Bonnet gravity where the Gauss-Bonnet invariant couples to a dynamical scalar field. In particular, the potential and and Gauss-Bonnet coupling function of the scalar field are reconstructed so that the cosmological bounce can be realized in the case that the scale factor has hyperbolic and exponential forms. Furthermore, we examine the relation between the bounce in the string (Jordan) and Einstein frames by using the conformal transformation between these conformal frames. It is shown that in general, the property of the bounce point in the string frame changes after the frame is movedmore » to the Einstein frame. Moreover, it is found that at the point in the Einstein frame corresponding to the point of the cosmological bounce in the string frame, the second derivative of the scale factor has an extreme value. In addition, it is demonstrated that at the time of the cosmological bounce in the Einstein frame, there is the Gauss-Bonnet coupling function of the scalar field, although it does not exist in the string frame.« less

Focus: the elusive icon: Einstein, 1905-2005. Introduction.

PubMed

Galison, Peter

2004-12-01

As Einstein's portrait comes increasingly to resemble an icon, we lose more than detail--his writings and actions lose all reference. This is as true for his physics as it is for his philosophy and his politics; the best of recent work aims to remove Einstein's interventions from the abstract sphere of Delphic pronouncements and to insert them in the stream of real events, real arguments. Politically, this means attending to McCarthyism, Paul Robeson, the Arab-Israeli conflict. Philosophically, it means tying his concerns, for example, to late nineteenth-century neo-Kantian debates and to his own struggles inside science. And where physics is concerned, it means attending both in the narrow to his responses to others' work and his reactions to his own sometimes misfired early work on, for example, general relativity and to the wider context of technological developments. Einstein remains and will remain a magnet for historians, philosophers, and scientists; the essays assembled here represent a strong sampling--but only a sampling--of a fascinating new generation of work on this perennial figure.

Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy

DOE PAGES

Chiodaroli, Marco; Günaydin, Murat; Johansson, Henrik; ...

2017-07-03

Using the double-copy construction of Yang-Mills-Einstein theories formulated in our earlier work, we obtain compact presentations for single-trace Yang-Mills-Einstein tree amplitudes with up to five external gravitons and an arbitrary number of gluons. These are written as linear combinations of color-ordered Yang-Mills trees, where the coefficients are given by color/kinematics-satisfying numerators in a Yang-Mills + φ 3 theory. The construction outlined in this paper holds in general dimension and extends straightforwardly to supergravity theories. For one, two, and three external gravitons, our expressions give identical or simpler presentations of amplitudes already constructed through string-theory considerations or the scattering equations formalism.more » Our results are based on color/kinematics duality and gauge invariance, and strongly hint at a recursive structure underlying the single-trace amplitudes with an arbitrary number of gravitons. We also present explicit expressions for all-loop single-graviton Einstein-Yang-Mills amplitudes in terms of Yang-Mills amplitudes and, through gauge invariance, derive new all-loop amplitude relations for Yang-Mills theory.« less

Focus: The elusive icon: Einstein, 1905-2005 - Introduction

NASA Astrophysics Data System (ADS)

Galison, Peter

2004-12-01

As Einstein's portrait comes increasingly to resemble an icon, we lose more than detail - his writings and actions lose all reference. This is as true for his physics as it is for his philosophy and his politics; the best of recent work aims to remove Einstein's interventions from the abstract sphere of Delphic pronouncements and to insert them in the stream of real events, real arguments. Politically, this means attending to McCarthyism, Paul Robeson, the Arab-Israeli conflict. Philosophically, it means tying his concerns, for example, to late nineteenth-century neo-Kantian debates and to his own struggles inside science. And where physics is concerned, it means attending both in the narrow to his reponses to others' work and his reactions to this own sometimes misfired early work on, for example, general relativity and to the wider context of technological developments. Einstein remains and will remain a magnet for historians, philosophers, and scientists; the essays assembled here represent a strong sampling - but only a sampling - of a fascinating new generation of work on this perennial figure.

Heterotic reduction of Courant algebroid connections and Einstein-Hilbert actions

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Vysoký, Jan

2016-08-01

We discuss Levi-Civita connections on Courant algebroids. We define an appropriate generalization of the curvature tensor and compute the corresponding scalar curvatures in the exact and heterotic case, leading to generalized (bosonic) Einstein-Hilbert type of actions known from supergravity. In particular, we carefully analyze the process of the reduction for the generalized metric, connection, curvature tensor and the scalar curvature.

Helmholtz, Riemann, and the Sirens: Sound, Color, and the "Problem of Space"

NASA Astrophysics Data System (ADS)

Pesic, Peter

2013-09-01

Emerging from music and the visual arts, questions about hearing and seeing deeply affected Hermann Helmholtz's and Bernhard Riemann's contributions to what became called the "problem of space [ Raumproblem]," which in turn influenced Albert Einstein's approach to general relativity. Helmholtz's physiological investigations measured the time dependence of nerve conduction and mapped the three-dimensional manifold of color sensation. His concurrent studies on hearing illuminated musical evidence through experiments with mechanical sirens that connect audible with visible phenomena, especially how the concept of frequency unifies motion, velocity, and pitch. Riemann's critique of Helmholtz's work on hearing led Helmholtz to respond and study Riemann's then-unpublished lecture on the foundations of geometry. During 1862-1870, Helmholtz applied his findings on the manifolds of hearing and seeing to the Raumproblem by supporting the quadratic distance relation Riemann had assumed as his fundamental hypothesis about geometrical space. Helmholtz also drew a "close analogy … in all essential relations between the musical scale and space." These intersecting studies of hearing and seeing thus led to reconsideration and generalization of the very concept of "space," which Einstein shaped into the general manifold of relativistic space-time.

Mass eigenstates in bimetric theory with matter coupling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schmidt-May, Angnis, E-mail: angnis.schmidt-may@fysik.su.se

2015-01-01

In this paper we study the ghost-free bimetric action extended by a recently proposed coupling to matter through a composite metric. The equations of motion for this theory are derived using a method which avoids varying the square-root matrix that appears in the matter coupling. We make an ansatz for which the metrics are proportional to each other and find that it can solve the equations provided that one parameter in the action is fixed. In this case, the proportional metrics as well as the effective metric that couples to matter solve Einstein's equations of general relativity including a mattermore » source. Around these backgrounds we derive the quadratic action for perturbations and diagonalize it into generalized mass eigenstates. It turns out that matter only interacts with the massless spin-2 mode whose equation of motion has exactly the form of the linearized Einstein equations, while the field with Fierz-Pauli mass term is completely decoupled. Hence, bimetric theory, with one parameter fixed such that proportional solutions exist, is degenerate with general relativity up to linear order around these backgrounds.« less

The theory of spherically symmetric thin shells in conformal gravity

NASA Astrophysics Data System (ADS)

Berezin, Victor; Dokuchaev, Vyacheslav; Eroshenko, Yury

The spherically symmetric thin shells are the nearest generalizations of the point-like particles. Moreover, they serve as the simple sources of the gravitational fields both in General Relativity and much more complex quadratic gravity theories. We are interested in the special and physically important case when all the quadratic in curvature tensor (Riemann tensor) and its contractions (Ricci tensor and scalar curvature) terms are present in the form of the square of Weyl tensor. By definition, the energy-momentum tensor of the thin shell is proportional to Diracs delta-function. We constructed the theory of the spherically symmetric thin shells for three types of gravitational theories with the shell: (1) General Relativity; (2) Pure conformal (Weyl) gravity where the gravitational part of the total Lagrangian is just the square of the Weyl tensor; (3) Weyl-Einstein gravity. The results are compared with these in General Relativity (Israel equations). We considered in detail the shells immersed in the vacuum. Some peculiar properties of such shells are found. In particular, for the traceless ( = massless) shell, it is shown that their dynamics cannot be derived from the matching conditions and, thus, is completely arbitrary. On the contrary, in the case of the Weyl-Einstein gravity, the trajectory of the same type of shell is completely restored even without knowledge of the outside solution.

Astronomers' Race to Test Relativity, 1911-1930

NASA Astrophysics Data System (ADS)

Crelinsten, Jeffrey

2006-11-01

Einstein's theory of relativity changed our notions of space and time and has dramatically altered the way we look at the universe and our place in it. Yet to this day a working knowledge of the theory is beyond most people. In today's popular culture, Einstein is a remote, loveable genius and his theory is incomprehensible. While Einstein's theory ultimately laid the foundation for modern studies of the universe, it took a long time to be accepted. Between 1905 and 1930, relativity was poorly understood and Einstein worked hard to try to make it more accessible to scientists and scientifically literate laypeople. Its acceptance was largely due to the astronomy community, which undertook precise measurements to test Einstein's astronomical predictions. How astronomers approached the ``Einstein problem'' in these early years and how the public reacted to what they reported helped to shape attitudes we hold today about Einstein and his ideas.

Interconversion algorithm between mechanical and dielectric relaxation measurements for acetate of cis- and trans-2-phenyl-5-hydroxymethyl-1,3-dioxane.

PubMed

Garcia-Bernabé, A; Lidón-Roger, J V; Sanchis, M J; Díaz-Calleja, R; del Castillo, L F

2015-10-01

The dielectric and mechanical spectroscopies of acetate of cis- and trans-2-phenyl-5-hydroxymethyl-1,3-dioxane are reported in the frequency domain from 10(-2) to 10(6)Hz. This ester has been selected in this study for its predominant α relaxation with regard to the β relaxation, which can be neglected. This study consists of determining an interconversion algorithm between dielectric and mechanical measurements, given by using a relation between rotational and translational complex viscosities. These important viscosities were obtained from measures of the dielectric complex permittivity and by dynamic mechanical analysis, respectively. The definitions of rotational and translational viscosities were evaluated by means of fractional calculus, by using the fit parameters of the Havriliak-Negami empirical model obtained in the dielectric and mechanical characterization of the α relaxation. This interconversion algorithm is a generalization of the break of the Stokes-Einstein-Debye relationship. It uses a power law with an exponent defined as the shape factor, which modifies the translational viscosity. Two others factors are introduced for the interconversion, a shift factor, which displaces the translational viscosity in the frequency domain, and a scale factor, which makes equal values of the two viscosities. In this paper, the shape factor has been identified as the relation between the slopes of the moduli of the complex viscosities at higher frequency. This is interpreted as the degree of kinetic coupling between the molecular rotation and translational movements. Alternatively, another interconversion algorithm has been expressed by means of dielectric and mechanical moduli.

On the asserted clash between the Freud and the Bianchi identities

NASA Astrophysics Data System (ADS)

Antoci, S.

1995-09-01

Through a constructive method it is shown that the claim advanced in recent times about a clash that should occur between the Freud and the Bianchi identities in Einstein's general theory of relativity is based on a faulty argument.

A New Model of Special Relativity and the Relationship between the Time Warps of General and Special Relativity

ERIC Educational Resources Information Center

Stannard, Warren B.

2018-01-01

Einstein's two theories of relativity were introduced over 100 years ago. High school science students are seldom exposed to these revolutionary ideas as they are often perceived to be too difficult conceptually and mathematically. This paper brings together the two theories of relativity in a way that is logical and consistent and enables the…

Cosmic transit and anisotropic models in f(R,T) gravity

NASA Astrophysics Data System (ADS)

Sahu, S. K.; Tripathy, S. K.; Sahoo, P. K.; Nath, A.

2017-06-01

Accelerating cosmological models are constructed in a modified gravity theory dubbed as $f(R,T)$ gravity at the backdrop of an anisotropic Bianchi type-III universe. $f(R,T)$ is a function of the Ricci scalar $R$ and the trace $T$ of the energy-momentum tensor and it replaces the Ricci scalar in the Einstein-Hilbert action of General Relativity. The models are constructed for two different ways of modification of the Einstein-Hilbert action. Exact solutions of the field equations are obtained by a novel method of integration. We have explored the behaviour of the cosmic transit from an decelerated phase of expansion to an accelerated phase to get the dynamical features of the universe. Within the formalism of the present work, it is found that, the modification of the Einstein-Hilbert action does not affect the scale factor. However the dynamics of the effective dark energy equation of state is significantly affected.

Gravitational catalysis of merons in Einstein-Yang-Mills theory

NASA Astrophysics Data System (ADS)

Canfora, Fabrizio; Oh, Seung Hun; Salgado-Rebolledo, Patricio

2017-10-01

We construct regular configurations of the Einstein-Yang-Mills theory in various dimensions. The gauge field is of meron-type: it is proportional to a pure gauge (with a suitable parameter λ determined by the field equations). The corresponding smooth gauge transformation cannot be deformed continuously to the identity. In the three-dimensional case we consider the inclusion of a Chern-Simons term into the analysis, allowing λ to be different from its usual value of 1 /2 . In four dimensions, the gravitating meron is a smooth Euclidean wormhole interpolating between different vacua of the theory. In five and higher dimensions smooth meron-like configurations can also be constructed by considering warped products of the three-sphere and lower-dimensional Einstein manifolds. In all cases merons (which on flat spaces would be singular) become regular due to the coupling with general relativity. This effect is named "gravitational catalysis of merons".

The Glimm scheme for perfect fluids on plane-symmetric Gowdy spacetimes

NASA Astrophysics Data System (ADS)

Barnes, A. P.; Lefloch, P. G.; Schmidt, B. G.; Stewart, J. M.

2004-11-01

We propose a new, augmented formulation of the coupled Euler Einstein equations for perfect fluids on plane-symmetric Gowdy spacetimes. The unknowns of the augmented system are the density and velocity of the fluid and the first- and second-order spacetime derivatives of the metric. We solve the Riemann problem for the augmented system, allowing propagating discontinuities in both the fluid variables and the first- and second-order derivatives of the geometry coefficients. Our main result, based on Glimm's random choice scheme, is the existence of solutions with bounded total variation of the Euler Einstein equations, up to the first time where a blow-up singularity (unbounded first-order derivatives of the geometry coefficients) occurs. We demonstrate the relevance of the augmented system for numerical relativity. We also consider general vacuum spacetimes and solve a Riemann problem, by relying on a theorem by Rendall on the characteristic value problem for the Einstein equations.

Diffusion of dioxygen in 1-alkenes and biphenyl in perfluoro- n-alkanes

NASA Astrophysics Data System (ADS)

Kowert, Bruce A.; Sobush, Kurtis T.; Dang, Nhan C.; Seele, Louis G., III; Fuqua, Chantel F.; Mapes, Courtney L.

2002-02-01

The translational diffusion constant, D, has been measured for O 2 in the even 1-alkenes 1-C 6H 12 to 1-C 16H 32 and biphenyl in n-C 6F 14 and n-C 9F 20. Deviations from the Stokes-Einstein relation were found; the use of D/ T= A/ ηp gave p=0.560±0.017 for O 2 in the 1-alkenes, the same (within experimental error) as found previously for O 2 in the n-alkanes. The charge transfer (CT) transition used to detect O 2 in the 1-alkenes is at 220 nm. The D values for biphenyl in the perfluoro- n-alkanes (PFAs) are consistent with those in the n-alkanes, where p=0.718±0.004. These results suggest that O 2 has similar solute-solvent interactions in both the 1-alkenes and n-alkanes as does biphenyl in the n-alkanes and PFAs.

Conductance and bulk vertical detachment energy of hydrated sulphate and oxalate dianions: a theoretical study

NASA Astrophysics Data System (ADS)

Pathak, Arup Kumar

2014-06-01

Analytical expressions have been derived for the vertical detachment energy (VDE) for hydrated sulphate (SO2 -4) and oxalate (C2O2 -4) dianions that can be used to calculate the same over a wide range of cluster sizes including the bulk from the knowledge of VDE for a finite number of stable clusters. The calculated bulk detachment energies are found to be very good in agreement (within 5%) with the available experimental results for both the systems. It is observed that two or more water molecules will be essential for the stability of sulphate and oxalate dianions against spontaneous electron loss and this is consistent with the experiment. We have, for the first time, provided a scheme to calculate the radius of the solvent berg for sulphate and oxalate dianions. The calculated conductivity values for the sulphate and oxalate dianions using Stokes-Einstein relation and the radius of solvent berg are found to be very good in agreement (within 4%) with the available experimental results.

Fast Crystallization of the Phase Change Compound GeTe by Large-Scale Molecular Dynamics Simulations.

PubMed

Sosso, Gabriele C; Miceli, Giacomo; Caravati, Sebastiano; Giberti, Federico; Behler, Jörg; Bernasconi, Marco

2013-12-19

Phase change materials are of great interest as active layers in rewritable optical disks and novel electronic nonvolatile memories. These applications rest on a fast and reversible transformation between the amorphous and crystalline phases upon heating, taking place on the nanosecond time scale. In this work, we investigate the microscopic origin of the fast crystallization process by means of large-scale molecular dynamics simulations of the phase change compound GeTe. To this end, we use an interatomic potential generated from a Neural Network fitting of a large database of ab initio energies. We demonstrate that in the temperature range of the programming protocols of the electronic memories (500-700 K), nucleation of the crystal in the supercooled liquid is not rate-limiting. In this temperature range, the growth of supercritical nuclei is very fast because of a large atomic mobility, which is, in turn, the consequence of the high fragility of the supercooled liquid and the associated breakdown of the Stokes-Einstein relation between viscosity and diffusivity.

Lectures on gravitation

NASA Astrophysics Data System (ADS)

Das, Ashok

1. Basics of geometry and relativity. 1.1. Two dimensional geometry. 1.2. Inertial and gravitational masses. 1.3. Relativity -- 2. Relativistic dynamics. 2.1. Relativistic point particle. 2.2. Current and charge densities. 2.3. Maxwell's equations in the presence of sources. 2.4. Motion of a charged particle in EM field. 2.5. Energy-momentum tensor. 2.6. Angular momentum -- 3. Principle of general covariance. 3.1. Principle of equivalence. 3.2. Principle of general covariance. 3.3. Tensor densities -- 4. Affine connection and covariant derivative. 4.1. Parallel transport of a vector. 4.2. Christoffel symbol. 4.3. Covariant derivative of contravariant tensors. 4.4. Metric compatibility. 4.5. Covariant derivative of covariant and mixed tensors. 4.6. Electromagnetic analogy. 4.7. Gradient, divergence and curl -- 5. Geodesic equation. 5.1. Covariant differentiation along a curve. 5.2. Curvature from derivatives. 5.3. Parallel transport along a closed curve. 5.4. Geodesic equation. 5.5. Derivation of geodesic equation from a Lagrangian -- 6. Applications of the geodesic equation. 6.1. Geodesic as representing gravitational effect. 6.2. Rotating coordinate system and the Coriolis force. 6.3. Gravitational red shift. 6.4. Twin paradox and general covariance. 6.5. Other equations in the presence of gravitation -- 7. Curvature tensor and Einstein's equation. 7.1. Curvilinear coordinates versus gravitational field. 7.2. Definition of an inertial coordinate frame. 7.3. Geodesic deviation. 7.4. Properties of the curvature tensor. 7.5. Einstein's equation. 7.6. Cosmological constant. 7.7. Initial value problem. 7.8. Einstein's equation from an action -- 8. Schwarzschild solution. 8.1. Line element. 8.2. Connection. 8.3. Solution of the Einstein equation. 8.4. Properties of the Schwarzschild solution. 8.5. Isotropic coordinates -- 9. Tests of general relativity. 9.1. Radar echo experiment. 9.2. Motion of a particle in a Schwarzschild background. 9.3. Motion of light rays in a Schwarzschild background. 9.4. Perihelion advance of Mercury -- 10. Black holes. 10.1. Singularities of the metric. 10.2. Singularities of the Schwarzschild metric. 10.3. Black holes -- 11. Cosmological models and the big bang theory. 11.1. Homogeneity and isotropy. 11.2. Different models of the universe. 11.3. Hubble's law. 11.4. Evolution equation. 11.5. Big bang theory and blackbody radiation.

Weber's gravitational force as static weak field approximation

NASA Astrophysics Data System (ADS)

Tiandho, Yuant

2016-02-01

Weber's gravitational force (WGF) is one of gravitational model that can accommodate a non-static system because it depends not only on the distance but also on the velocity and the acceleration. Unlike Newton's law of gravitation, WGF can predict the anomalous of Mercury and gravitational bending of light near massive object very well. Then, some researchers use WGF as an alternative model of gravitation and propose a new mechanics theory namely the relational mechanics theory. However, currently we have known that the theory of general relativity which proposed by Einstein can explain gravity with very accurate. Through the static weak field approximation for the non-relativistic object, we also have known that the theory of general relativity will reduce to Newton's law of gravity. In this work, we expand the static weak field approximation that compatible with relativistic object and we obtain a force equation which correspond to WGF. Therefore, WGF is more precise than Newton's gravitational law. The static-weak gravitational field that we used is a solution of the Einstein's equation in the vacuum that satisfy the linear field approximation. The expression of WGF with ξ = 1 and satisfy the requirement of energy conservation are obtained after resolving the geodesic equation. By this result, we can conclude that WGF can be derived from the general relativity.

Space-time philosophy reconstructed via massive Nordström scalar gravities? Laws vs. geometry, conventionality, and underdetermination

NASA Astrophysics Data System (ADS)

Pitts, J. Brian

2016-02-01

What if gravity satisfied the Klein-Gordon equation? Both particle physics from the 1920-30s and the 1890s Neumann-Seeliger modification of Newtonian gravity with exponential decay suggest considering a "graviton mass term" for gravity, which is algebraic in the potential. Unlike Nordström's "massless" theory, massive scalar gravity is strictly special relativistic in the sense of being invariant under the Poincaré group but not the 15-parameter Bateman-Cunningham conformal group. It therefore exhibits the whole of Minkowski space-time structure, albeit only indirectly concerning volumes. Massive scalar gravity is plausible in terms of relativistic field theory, while violating most interesting versions of Einstein's principles of general covariance, general relativity, equivalence, and Mach. Geometry is a poor guide to understanding massive scalar gravity(s): matter sees a conformally flat metric due to universal coupling, but gravity also sees the rest of the flat metric (barely or on long distances) in the mass term. What is the 'true' geometry, one might wonder, in line with Poincaré's modal conventionality argument? Infinitely many theories exhibit this bimetric 'geometry,' all with the total stress-energy's trace as source; thus geometry does not explain the field equations. The irrelevance of the Ehlers-Pirani-Schild construction to a critique of conventionalism becomes evident when multi-geometry theories are contemplated. Much as Seeliger envisaged, the smooth massless limit indicates underdetermination of theories by data between massless and massive scalar gravities-indeed an unconceived alternative. At least one version easily could have been developed before General Relativity; it then would have motivated thinking of Einstein's equations along the lines of Einstein's newly re-appreciated "physical strategy" and particle physics and would have suggested a rivalry from massive spin 2 variants of General Relativity (massless spin 2, Pauli and Fierz found in 1939). The Putnam-Grünbaum debate on conventionality is revisited with an emphasis on the broad modal scope of conventionalist views. Massive scalar gravity thus contributes to a historically plausible rational reconstruction of much of 20th-21st century space-time philosophy in the light of particle physics. An appendix reconsiders the Malament-Weatherall-Manchak conformal restriction of conventionality and constructs the 'universal force' influencing the causal structure. Subsequent works will discuss how massive gravity could have provided a template for a more Kant-friendly space-time theory that would have blocked Moritz Schlick's supposed refutation of synthetic a priori knowledge, and how Einstein's false analogy between the Neumann-Seeliger-Einstein modification of Newtonian gravity and the cosmological constant Λ generated lasting confusion that obscured massive gravity as a conceptual possibility.

Development of real-time rotating waveplate Stokes polarimeter using multi-order retardation for ITER poloidal polarimeter

DOE Office of Scientific and Technical Information (OSTI.GOV)

Imazawa, R., E-mail: imazawa.ryota@jaea.go.jp; Kawano, Y.; Ono, T.

The rotating waveplate Stokes polarimeter was developed for ITER (International Thermonuclear Experimental Reactor) poloidal polarimeter. The generalized model of the rotating waveplate Stokes polarimeter and the algorithm suitable for real-time field-programmable gate array (FPGA) processing were proposed. Since the generalized model takes into account each component associated with the rotation of the waveplate, the Stokes parameters can be accurately measured even in unideal condition such as non-uniformity of the waveplate retardation. Experiments using a He-Ne laser showed that the maximum error and the precision of the Stokes parameter were 3.5% and 1.2%, respectively. The rotation speed of waveplate was 20 000more » rpm and time resolution of measuring the Stokes parameter was 3.3 ms. Software emulation showed that the real-time measurement of the Stokes parameter with time resolution of less than 10 ms is possible by using several FPGA boards. Evaluation of measurement capability using a far-infrared laser which ITER poloidal polarimeter will use concluded that measurement error will be reduced by a factor of nine.« less

Development of real-time rotating waveplate Stokes polarimeter using multi-order retardation for ITER poloidal polarimeter.

PubMed

Imazawa, R; Kawano, Y; Ono, T; Itami, K

2016-01-01

The rotating waveplate Stokes polarimeter was developed for ITER (International Thermonuclear Experimental Reactor) poloidal polarimeter. The generalized model of the rotating waveplate Stokes polarimeter and the algorithm suitable for real-time field-programmable gate array (FPGA) processing were proposed. Since the generalized model takes into account each component associated with the rotation of the waveplate, the Stokes parameters can be accurately measured even in unideal condition such as non-uniformity of the waveplate retardation. Experiments using a He-Ne laser showed that the maximum error and the precision of the Stokes parameter were 3.5% and 1.2%, respectively. The rotation speed of waveplate was 20 000 rpm and time resolution of measuring the Stokes parameter was 3.3 ms. Software emulation showed that the real-time measurement of the Stokes parameter with time resolution of less than 10 ms is possible by using several FPGA boards. Evaluation of measurement capability using a far-infrared laser which ITER poloidal polarimeter will use concluded that measurement error will be reduced by a factor of nine.

Rediscovering Einstein's legacy: How Einstein anticipates Kuhn and Feyerabend on the nature of science.

PubMed

Oberheim, Eric

2016-06-01

Thomas Kuhn and Paul Feyerabend promote incommensurability as a central component of their conflicting accounts of the nature of science. This paper argues that in so doing, they both develop Albert Einstein's views, albeit in different directions. Einstein describes scientific revolutions as conceptual replacements, not mere revisions, endorsing 'Kant-on-wheels' metaphysics in light of 'world change'. Einstein emphasizes underdetermination of theory by evidence, rational disagreement in theory choice, and the non-neutrality of empirical evidence. Einstein even uses the term 'incommensurable' specifically to apply to challenges posed to comparatively evaluating scientific theories in 1949, more than a decade before Kuhn and Feyerabend. This analysis shows how Einstein anticipates substantial components of Kuhn and Feyerabend's views, and suggests that there are strong reasons to suspect that Kuhn and Feyerabend were directly inspired by Einstein's use of the term 'incommensurable', as well as his more general methodological and philosophical reflections. Copyright © 2015 Elsevier Ltd. All rights reserved.

KSC-04pd0940

NASA Image and Video Library

2004-04-20

KENNEDY SPACE CENTER, FLA. - The Gravity Probe B spacecraft, atop a Boeing Delta II vehicle, launches at 12:57:24 p.m. EDT from Space Launch Complex 2 at Vandenberg Air Force Base, Calif. Gravity Probe B is the relativity gyroscope experiment being developed by NASA and Stanford University to test two extraordinary, unverified predictions of Albert Einstein's general theory of relativity.

KSC-04PD-0940

NASA Technical Reports Server (NTRS)

2004-01-01

KENNEDY SPACE CENTER, FLA. The Gravity Probe B spacecraft, atop a Boeing Delta II vehicle, launches at 12:57:24 p.m. EDT from Space Launch Complex 2 at Vandenberg Air Force Base, Calif. Gravity Probe B is the relativity gyroscope experiment being developed by NASA and Stanford University to test two extraordinary, unverified predictions of Albert Einstein's general theory of relativity.

Lunar surface gravimeter experiment

NASA Technical Reports Server (NTRS)

Giganti, J. J.; Larson, J. V.; Richard, J. P.; Tobias, R. L.; Weber, J.

1977-01-01

The lunar surface gravimeter used the moon as an instrumented antenna to search for gravitational waves predicted by Einstein's general theory of relativity. Tidal deformation of the moon was measured. Gravitational radiation is a channel that is capable of giving information about the structure and evolution of the universe.

Black Holes: A Selected Bibliography.

ERIC Educational Resources Information Center

Fraknoi, Andrew

1991-01-01

Offers a selected bibliography pertaining to black holes with the following categories: introductory books; introductory articles; somewhat more advanced articles; readings about Einstein's general theory of relativity; books on the death of stars; articles on the death of stars; specific articles about Supernova 1987A; relevant science fiction…

Gravitational-Wave Tests of General Relativity with Ground-Based Detectors and Pulsar-Timing Arrays.

PubMed

Yunes, Nicolás; Siemens, Xavier

2013-01-01

This review is focused on tests of Einstein's theory of general relativity with gravitational waves that are detectable by ground-based interferometers and pulsar-timing experiments. Einstein's theory has been greatly constrained in the quasi-linear, quasi-stationary regime, where gravity is weak and velocities are small. Gravitational waves will allow us to probe a complimentary, yet previously unexplored regime: the non-linear and dynamical strong-field regime . Such a regime is, for example, applicable to compact binaries coalescing, where characteristic velocities can reach fifty percent the speed of light and gravitational fields are large and dynamical. This review begins with the theoretical basis and the predicted gravitational-wave observables of modified gravity theories. The review continues with a brief description of the detectors, including both gravitational-wave interferometers and pulsar-timing arrays, leading to a discussion of the data analysis formalism that is applicable for such tests. The review ends with a discussion of gravitational-wave tests for compact binary systems.

Book Review: The future of spacetime. Stephen William Hawking (ed.); Kip S. Thorne, Igor Novikov, Timothy Ferris, Alan Lightman, and Richard Price, W.W. Norton & Company, 2002, 224 pp., US 25.95, ISBN 0393020223

NASA Astrophysics Data System (ADS)

Smeenk, Chris

2003-12-01

The study of Einstein's theory of general relativity experienced a renaissance beginning in the early 1960s. Prior to this resurgence of interest, general relativity was isolated from mainstream physics-admired for its elegance, perhaps, but only from a distance. The generation of students who risked their careers by entering this neglected field has now reached the age of festschrifts. In June of 2000, Caltech hosted ;Kipfest,; a conference in honor of Kip Thorne's 60th birthday. Thorne started graduate school at Princeton in 1962 and began research in general relativity under John Wheeler's guidance in the heady early days of the renaissance. Since then, he has played a prominent role in general relativity: as co-author of the influential textbook Gravitation, as a leader in research regarding astrophysical applications of Einstein's theory, and as a co-founder and chief advocate for the Laser Interferometer Gravitational Wave Observatory (LIGO), to mention a few aspects of his far-reaching work. ;Kipfest; included 14 speakers discussing fields to which Thorne has contributed. But the conference also reflected Thorne's long-standing commitment to communicating science to a general audience: Igor Novikov, Stephen Hawking, Timothy Ferris, and Alan Lightman gave popular talks at ;Kipfest,; with Thorne himself tricked into delivering a fifth. The Future of Spacetime gathers adaptations of these five lectures, along with a lengthy introductory essay by Richard Price.

Hamiltonian approach to GR - Part 1: covariant theory of classical gravity

NASA Astrophysics Data System (ADS)

Cremaschini, Claudio; Tessarotto, Massimo

2017-05-01

A challenging issue in General Relativity concerns the determination of the manifestly covariant continuum Hamiltonian structure underlying the Einstein field equations and the related formulation of the corresponding covariant Hamilton-Jacobi theory. The task is achieved by adopting a synchronous variational principle requiring distinction between the prescribed deterministic metric tensor \\widehat{g}(r)≡ { \\widehat{g}_{μ ν }(r)} solution of the Einstein field equations which determines the geometry of the background space-time and suitable variational fields x≡ { g,π } obeying an appropriate set of continuum Hamilton equations, referred to here as GR-Hamilton equations. It is shown that a prerequisite for reaching such a goal is that of casting the same equations in evolutionary form by means of a Lagrangian parametrization for a suitably reduced canonical state. As a result, the corresponding Hamilton-Jacobi theory is established in manifestly covariant form. Physical implications of the theory are discussed. These include the investigation of the structural stability of the GR-Hamilton equations with respect to vacuum solutions of the Einstein equations, assuming that wave-like perturbations are governed by the canonical evolution equations.

Dynamic phase coexistence in glass-forming liquids.

PubMed

Pastore, Raffaele; Coniglio, Antonio; Ciamarra, Massimo Pica

2015-07-09

One of the most controversial hypotheses for explaining the heterogeneous dynamics of glasses postulates the temporary coexistence of two phases characterized by a high and by a low diffusivity. In this scenario, two phases with different diffusivities coexist for a time of the order of the relaxation time and mix afterwards. Unfortunately, it is difficult to measure the single-particle diffusivities to test this hypothesis. Indeed, although the non-Gaussian shape of the van-Hove distribution suggests the transient existence of a diffusivity distribution, it is not possible to infer from this quantity whether two or more dynamical phases coexist. Here we provide the first direct observation of the dynamical coexistence of two phases with different diffusivities, by showing that in the deeply supercooled regime the distribution of the single-particle diffusivities acquires a transient bimodal shape. We relate this distribution to the heterogeneity of the dynamics and to the breakdown of the Stokes-Einstein relation, and we show that the coexistence of two dynamical phases occurs up to a timescale growing faster than the relaxation time on cooling, for some of the considered models. Our work offers a basis for rationalizing the dynamics of supercooled liquids and for relating their structural and dynamical properties.

Stokes solitons in optical microcavities

NASA Astrophysics Data System (ADS)

Yang, Qi-Fan; Yi, Xu; Yang, Ki Youl; Vahala, Kerry

2017-01-01

Solitons are wave packets that resist dispersion through a self-induced potential well. They are studied in many fields, but are especially well known in optics on account of the relative ease of their formation and control in optical fibre waveguides. Besides their many interesting properties, solitons are important to optical continuum generation, in mode-locked lasers, and have been considered as a natural way to convey data over great distances. Recently, solitons have been realized in microcavities, thereby bringing the power of microfabrication methods to future applications. This work reports a soliton not previously observed in optical systems, the Stokes soliton. The Stokes soliton forms and regenerates by optimizing its Raman interaction in space and time within an optical potential well shared with another soliton. The Stokes and the initial soliton belong to distinct transverse mode families and benefit from a form of soliton trapping that is new to microcavities and soliton lasers in general. The discovery of a new optical soliton can impact work in other areas of photonics, including nonlinear optics and spectroscopy.

Cosmic time and reduced phase space of general relativity

NASA Astrophysics Data System (ADS)

Ita, Eyo Eyo; Soo, Chopin; Yu, Hoi-Lai

2018-05-01

In an ever-expanding spatially closed universe, the fractional change of the volume is the preeminent intrinsic time interval to describe evolution in general relativity. The expansion of the universe serves as a subsidiary condition which transforms Einstein's theory from a first class to a second class constrained system when the physical degrees of freedom (d.o.f.) are identified with transverse traceless excitations. The super-Hamiltonian constraint is solved by eliminating the trace of the momentum in terms of the other variables, and spatial diffeomorphism symmetry is tackled explicitly by imposing transversality. The theorems of Maskawa-Nishijima appositely relate the reduced phase space to the physical variables in canonical functional integral and Dirac's criterion for second class constraints to nonvanishing Faddeev-Popov determinants in the phase space measures. A reduced physical Hamiltonian for intrinsic time evolution of the two physical d.o.f. emerges. Freed from the first class Dirac algebra, deformation of the Hamiltonian constraint is permitted, and natural extension of the Hamiltonian while maintaining spatial diffeomorphism invariance leads to a theory with Cotton-York term as the ultraviolet completion of Einstein's theory.

BOOK REVIEW: Einsteins Kosmos. Untersuchungen zur Geschichte der Kosmologie Relativitatstheorie und zu Einsteins Wirken und Nachwirken

NASA Astrophysics Data System (ADS)

Sterken, C.; Duerbeck, H. W.; Dick, W. R.

2006-12-01

This book collects about 15 papers (most of them by one single author) on Einstein and the history of general relativity (GR) and the foundations of relativistic cosmology. The matter not only deals with Einstein and his times, but also with pre-GR ideas, and with the interplay of Einstein and his colleagues (opposing as well as supporting personalities). As the title indicates, all papers are written in German, but they include comprehensive Abstracts both in German and English. The book is illustrated with quite a number classical - but also some far more original though not less beautiful - photographs and facsimiles of documents. The book is edited very well, though the style of references is not quite homogeneous. There is no Index. K. Hentschel covers Einstein's argumentation for the existence of graviational redshift, and the initial search for empirical support. The error analysis of observational evidence supporting relativistic light deflection is discussed in a paper by P. Brosche. In particular, H. Duerbeck and P. Flin - in their description of the life and work of Silberstein, who was quite sceptic on the significance of the observational verifications a la Eddington - include the transcription of two most revealing letters by Silberstein to Sommerfeld (1919) and to Einstein (1934). In the first letter, Silberstein clearly shows his scientific maturity and integrity by scrutinising the observational evidence supporting light deflection, presented at a joint meeting of the Royal Society and the Royal Astronomical Society. The second letter, which is more a personal letter, includes lots of political references and connotations. Some of Einstein's political views are also revealed by D.B. Herrmann on the basis of his own correspondence with E.G. Straus, a collaborator of Einstein's. In a consequent paper, S. Grundmann gives remarks on Herrmann's contribution and illustrates Einstein's attitude towards Marx, Engels, Lenin and Stalin. M. Schemmel discusses Schwarzschild's cosmological speculations, and wonders why some people do immediately grasp the meaning and consequence of newly proposed doctrines, whereas the bulk of the contemporaneous scientists respond in a rather low profile. T. Jung reviews Einstein's contribution to cosmology, leading to the Friedmann-Einstein and Einstein-de Sitter universes (with a detailed Appendix on the Friedmann-Lemaitre cosmology), and also presents the cosmological work of Selety, and his correspondence with Einstein. In a subsequent paper, H.-J. Schmidt comments on Einstein's criticism on de Sitter's solution of the Einstein field equations. Controversies with Einstein are elaborated by G. Singer (on Friedmann) and by K. Roessler (on Lemaitre). J. Renn and T. Sauer discuss Mandl's role in the publication history of Einstein's papers, notably Einstein's short paper on gravitational lensing. Finally, the book concludes with a contribution by D.B. Herrmann about the relationship between Einstein and Archenhold Observatory (where Einstein gave his first Berlin popular lecture in 1915), the transcription of H.-J. Treder's 1979 public address at the Einstein memorial plaque, and an inventory list of about 50 Einstein memorabilia - monuments, busts, plaques - compiled by W.R. Dick. This book is based on ideas approached in a historical context from the individual perspective of the authors. It is a real treasure trove of information and basic references on the history of GR, and it also covers quite some grounds with mathematical equations.

Einstein: A Historical Perspective

NASA Astrophysics Data System (ADS)

Kormos-Buchwald, Diana

2015-04-01

In late 1915, Albert Einstein (1879-1955) completed as series of papers on a generalized theory of gravitation that were to constitute a major conceptual change in the history of modern physics and the crowning achievement of his scientific career. But this accomplishment came after a decade of intense intellectual struggle and was received with muted enthusiasm. Einstein's previously unpublished writings and massive correspondence, edited by the Einstein Papers Project, provide vivid insights into the historical, personal, and scientific context of the formulation, completion, and reception of GR during the first decades of the 20th century.

Spin coefficients and gauge fixing in the Newman-Penrose formalism

NASA Astrophysics Data System (ADS)

Nerozzi, Andrea

2017-03-01

Since its introduction in 1962, the Newman-Penrose formalism has been widely used in analytical and numerical studies of Einstein's equations, like for example for the Teukolsky master equation, or as a powerful wave extraction tool in numerical relativity. Despite the many applications, Einstein's equations in the Newman-Penrose formalism appear complicated and not easily applicable to general studies of spacetimes, mainly because physical and gauge degrees of freedom are mixed in a nontrivial way. In this paper we approach the whole formalism with the goal of expressing the spin coefficients as functions of tetrad invariants once a particular tetrad is chosen. We show that it is possible to do so, and give for the first time a general recipe for the task, as well as an indication of the quantities and identities that are required.

Space-time slicing in Horndeski theories and its implications for non-singular bouncing solutions

NASA Astrophysics Data System (ADS)

Ijjas, Anna

2018-02-01

In this paper, we show how the proper choice of gauge is critical in analyzing the stability of non-singular cosmological bounce solutions based on Horndeski theories. We show that it is possible to construct non-singular cosmological bounce solutions with classically stable behavior for all modes with wavelengths above the Planck scale where: (a) the solution involves a stage of null-energy condition violation during which gravity is described by a modification of Einstein's general relativity; and (b) the solution reduces to Einstein gravity both before and after the null-energy condition violating stage. Similar considerations apply to galilean genesis scenarios.

Einstein’s Legacy to Astronomy: From Black Holes to the Expanding Universe

NASA Astrophysics Data System (ADS)

Bartusiak, Marcia

2006-12-01

Albert Einstein placed a formidable imprint on astronomy. Not since the time of Isaac Newton, three centuries ago, has a single individual so influenced the field. Many of the great astronomical findings of the 20th century--the expanding universe, compact stars, origin of the Sun’s power, black holes, gravitational lensing, dark energy, gravity waves--are rooted in the physics that Einstein so brilliantly deduced. This illustrated presentation, the Gemant Award Lecture sponsored by the American Institute of Physics, will provide a guided tour through the cosmos and explain how our understanding of the universe was transformed by Einstein’s theories of special and general relativity.

Generalized wave operators, weighted Killing fields, and perturbations of higher dimensional spacetimes

NASA Astrophysics Data System (ADS)

Araneda, Bernardo

2018-04-01

We present weighted covariant derivatives and wave operators for perturbations of certain algebraically special Einstein spacetimes in arbitrary dimensions, under which the Teukolsky and related equations become weighted wave equations. We show that the higher dimensional generalization of the principal null directions are weighted conformal Killing vectors with respect to the modified covariant derivative. We also introduce a modified Laplace–de Rham-like operator acting on tensor-valued differential forms, and show that the wave-like equations are, at the linear level, appropriate projections off shell of this operator acting on the curvature tensor; the projection tensors being made out of weighted conformal Killing–Yano tensors. We give off shell operator identities that map the Einstein and Maxwell equations into weighted scalar equations, and using adjoint operators we construct solutions of the original field equations in a compact form from solutions of the wave-like equations. We study the extreme and zero boost weight cases; extreme boost corresponding to perturbations of Kundt spacetimes (which includes near horizon geometries of extreme black holes), and zero boost to static black holes in arbitrary dimensions. In 4D our results apply to Einstein spacetimes of Petrov type D and make use of weighted Killing spinors.

The simplicial Ricci tensor

NASA Astrophysics Data System (ADS)

Alsing, Paul M.; McDonald, Jonathan R.; Miller, Warner A.

2011-08-01

The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The three-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The four-dimensional Ric is the Einstein tensor for such spacetimes. More recently, the Ric was used by Hamilton to define a nonlinear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincarè conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area—an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimensions.

Stokes parameters of phase-locked partially coherent flat-topped array laser beams propagating through turbulent atmosphere

NASA Astrophysics Data System (ADS)

Golmohammady, Sh; Ghafary, B.

2016-06-01

In this study, generalized Stokes parameters of a phase-locked partially coherent flat-topped array beam based on the extended Huygens-Fresnel principle and the unified theory of coherence and polarization have been reported. Analytical formulas for 2  ×  2 cross-spectral density matrix elements, and consequently Stokes parameters of a phase-locked partially coherent flat-topped array beam propagating through the turbulent atmosphere have been formulated. Effects of many physical attributes such as wavelength, turbulence strength, flatness order and other source parameters on the Stokes parameters, and therefore spectral degree of polarization upon propagation have been studied thoroughly. The behaviour of the spectral degree of coherence of a delineated beam for different source conditions has been investigated. It can be shown that four generalized Stokes parameters increase by raising the flatness order at the same propagation distance. Increasing the number of beams leads to a decrease in the Stokes parameters to zero slowly. The results are of utmost importance for optical communications.

General relativity in two dimensions: A Hamilton-Jacobi analysis

NASA Astrophysics Data System (ADS)

Bertin, M. C.; Pimentel, B. M.; Pompeia, P. J.

2010-11-01

We analyzed the constraint structure of the Einstein-Hilbert first-order action in two dimensions using the Hamilton-Jacobi approach. We were able to find a set of involutive, as well as a set of non-involutive constraints. Using generalized brackets we showed how to assure integrability of the theory, to eliminate the set of non-involutive constraints and how to build the field equations.

On static black holes solutions in Einstein and Einstein-Gauss-Bonnet gravity with topology [Formula: see text].

PubMed

Dadhich, Naresh; Pons, Josep M

We study static black hole solutions in Einstein and Einstein-Gauss-Bonnet gravity with the topology of the product of two spheres, [Formula: see text], in higher dimensions. There is an unusual new feature of the Gauss-Bonnet black hole: the avoidance of a non-central naked singularity prescribes a mass range for the black hole in terms of [Formula: see text]. For an Einstein-Gauss-Bonnet black hole a limited window of negative values for [Formula: see text] is also permitted. This topology encompasses black strings, branes, and generalized Nariai metrics. We also give new solutions with the product of two spheres of constant curvature.

The prototype design of the Stanford Relativity Gyro Experiment

NASA Technical Reports Server (NTRS)

Parkinson, Bradford W.; Everitt, C. W. Francis; Turneaure, John P.; Parmley, Richard T.

1987-01-01

The Stanford Relativity Gyroscope Experiment constitutes a fundamental test of Einstein's General Theory of Relativity, probing such heretofore untested aspects of the theory as those that relate to spin by means of drag-free satellite-borne gyroscopes. General Relativity's prediction of two orthogonal precessions (motional and geodetic) for a perfect Newtonian gyroscope in polar orbit has not yet been experimentally assessed, and will mark a significant advancement in experimental gravitation. The technology employed in the experiment has been under development for 25 years at NASA's Marshall Space Flight Center. Four fused quartz gyroscopes will be used.

Those Elusive Gravitational Waves

ERIC Educational Resources Information Center

MOSAIC, 1976

1976-01-01

The presence of gravitational waves was predicted by Einstein in his theory of General Relativity. Since then, scientists have been attempting to develop a detector sensitive enough to measure these cosmic signals. Once the presence of gravitational waves is confirmed, scientists can directly study star interiors, galaxy cores, or quasars. (MA)

New method for the detection of light deflection by solar gravity.

PubMed

Shapiro, I I

1967-08-18

The prediction of Einstein's theory of general relativity that light will be deflected by the sun may be tested by sending radio waves from the earth to Venus or Mercury when either passes behind the sun and detecting the echoes with a radar interferometer.

Arguments concerning Relativity and Cosmology.

PubMed

Klein, O

1971-01-29

In the first place I have reviewed the true foundation of Einstein's theory of general relativity, the so-called principle of equivalence, according to which there is no essential difference between "genuine" gravitation and inertial forces, well known from accelerated vehicles. By means of a comparison with Gaussian geometry of curved surfaces-the background of Riemannian geometry, the tool used by Einstein for the mathematical formulation of his theory-it is made clear that this principle is incompatible with the idea proposed by Mach and accepted by Einstein as an incitement to his attempt to describe the main situation in the universe as an analogy in three dimensions to the closed surface of a sphere. In the later attempts toward a mathematical description of the universe, where Einstein's cosmology was adapted to the discovery by Hubble that its observed part is expanding, the socalled cosmological postulate has been used as a kind of axiomatic background which, when analyzed, makes it probable that this expansion is shared by a very big, but still bounded system. This implies that our expanding metagalaxy is probably just one of a type of stellar objects in different phases of evolution, some expanding and some contracting. Some attempts toward the description of this evolution are sketched in the article with the hope that further investigation, theoretical and observational, may lead to an interesting advance in this part of astrophysics.

The Friedmann-Lemaître-Robertson-Walker Big Bang Singularities are Well Behaved

NASA Astrophysics Data System (ADS)

Stoica, Ovidiu Cristinel

2016-01-01

We show that the Big Bang singularity of the Friedmann-Lemaître-Robertson-Walker model does not raise major problems to General Relativity. We prove a theorem showing that the Einstein equation can be written in a non-singular form, which allows the extension of the spacetime before the Big Bang. The physical interpretation of the fields used is discussed. These results follow from our research on singular semi-Riemannian geometry and singular General Relativity.

Testing general relativity in space-borne and astronomical laboratories

NASA Technical Reports Server (NTRS)

Will, Clifford M.

1989-01-01

The current status of space-based experiments and astronomical observations designed to test the theory of general relativity is surveyed. Consideration is given to tests of post-Newtonian gravity, searches for feeble short-range forces and gravitomagnetism, improved measurements of parameterized post-Newtonian parameter values, explorations of post-Newtonian physics, tests of the Einstein equivalence principle, observational tests of post-Newtonian orbital effects, and efforts to detect quadrupole and dipole radiation damping. Recent numerical results are presented in tables.

Magnetic field topology of τ Scorpii. The uniqueness problem of Stokes V ZDI inversions

NASA Astrophysics Data System (ADS)

Kochukhov, O.; Wade, G. A.

2016-02-01

Context. The early B-type star τ Sco exhibits an unusually complex, relatively weak surface magnetic field. Its topology was previously studied with the Zeeman Doppler imaging (ZDI) modelling of high-resolution circular polarisation (Stokes V) observations. Aims: Here we assess the robustness of the Stokes V ZDI reconstruction of the magnetic field geometry of τ Sco and explore the consequences of using different parameterisations of the surface magnetic maps. Methods: This analysis is based on the archival ESPaDOnS high-resolution Stokes V observations and employs an independent ZDI magnetic inversion code. Results: We succeeded in reproducing previously published magnetic field maps of τ Sco using both general harmonic expansion and a direct, pixel-based representation of the magnetic field. These maps suggest that the field topology of τ Sco is comprised of comparable contributions of the poloidal and toroidal magnetic components. At the same time, we also found that available Stokes V observations can be successfully fitted with restricted harmonic expansions, by either neglecting the toroidal field altogether, or linking the radial and horizontal components of the poloidal field as required by the widely used potential field extrapolation technique. These alternative modelling approaches lead to a stronger and topologically more complex surface field structure. The field distributions, which were recovered with different ZDI options, differ significantly and yield indistinguishable Stokes V profiles but different linear polarisation (Stokes Q and U) signatures. Conclusions: Our investigation underscores the well-known problem of non-uniqueness of the Stokes V ZDI inversions. For the magnetic stars with properties similar to τ Sco (relatively complex field, slow rotation) the outcome of magnetic reconstruction strongly depends on the adopted field parameterisation, rendering photospheric magnetic mapping and determination of the extended magnetospheric field topology ambiguous. Stokes Q and U spectropolarimetric observations represent the only way of breaking the degeneracy of surface magnetic field models. Based on observations obtained at the Canada-France-Hawaii Telescope (CFHT) which is operated by the National Research Council of Canada, the Institut National des Sciences de l'Univers of the Centre National de la Recherche Scientifique of France, and the University of Hawaii.

Continuous Diffusion Model for Concentration Dependence of Nitroxide EPR Parameters in Normal and Supercooled Water.

PubMed

Merunka, Dalibor; Peric, Miroslav

2017-05-25

Electron paramagnetic resonance (EPR) spectra of radicals in solution depend on their relative motion, which modulates the Heisenberg spin exchange and dipole-dipole interactions between them. To gain information on radical diffusion from EPR spectra demands both reliable spectral fitting to find the concentration coefficients of EPR parameters and valid expressions between the concentration and diffusion coefficients. Here, we measured EPR spectra of the 14 N- and 15 N-labeled perdeuterated TEMPONE radicals in normal and supercooled water at various concentrations. By fitting the EPR spectra to the functions based on the modified Bloch equations, we obtained the concentration coefficients for the spin dephasing, coherence transfer, and hyperfine splitting parameters. Assuming the continuous diffusion model for radical motion, the diffusion coefficients of radicals were calculated from the concentration coefficients using the standard relations and the relations derived from the kinetic equations for the spin evolution of a radical pair. The latter relations give better agreement between the diffusion coefficients calculated from different concentration coefficients. The diffusion coefficients are similar for both radicals, which supports the presented method. They decrease with lowering temperature slower than is predicted by the Stokes-Einstein relation and slower than the rotational diffusion coefficients, which is similar to the diffusion of water molecules in supercooled water.

Teaching Einsteinian physics at schools: part 1, models and analogies for relativity

NASA Astrophysics Data System (ADS)

Kaur, Tejinder; Blair, David; Moschilla, John; Stannard, Warren; Zadnik, Marjan

2017-11-01

The Einstein-First project aims to change the paradigm of school science teaching through the introduction of modern Einsteinian concepts of space and time, gravity and quanta at an early age. These concepts are rarely taught to school students despite their central importance to modern science and technology. The key to implementing the Einstein-First curriculum is the development of appropriate models and analogies. This paper is the first part of a three-paper series. It presents the conceptual foundation of our approach, based on simple physical models and analogies, followed by a detailed description of the models and analogies used to teach concepts of general and special relativity. Two accompanying papers address the teaching of quantum physics (Part 2) and research outcomes (Part 3).

The Einstein Dossiers: Science and Politics - Einstein's Berlin Period with an Appendix on Einstein's FBI File

NASA Astrophysics Data System (ADS)

Grundmann, Siegfried

In 1919 the Prussian Ministry of Science, Arts and Culture opened a dossier on "Einstein's Theory of Relativity." It was rediscovered by the author in 1961 and is used in conjunction with numerous other subsequently identified 'Einstein' files as the basis of this fascinating book. In particular, the author carefully scrutinizes Einstein's FBI file from 1950-55 against mostly unpublished material from European including Soviet sources and presents hitherto unknown documentation on Einstein's alleged contacts with the German Communist Party and the Comintern.

Liquid Water, the ``Most Complex'' Liquid: New Results in Bulk, Nanoconfined, and Biological Environments

NASA Astrophysics Data System (ADS)

Stanley, H. Eugene

2010-03-01

We will introduce some of the 63 anomalies of the most complex of liquids, water. We will demonstrate some recent progress in understanding these anomalies by combining information provided by recent experiments and simulations on water in bulk, nanoconfined, and biological environments. We will interpret evidence from recent experiments designed to test the hypothesis that liquid water may display ``polymorphism'' in that it can exist in two different phases---and discuss recent work on water's transport anomalies [1] as well as the unusual behavior of water in biological environments [2]. Finally, we will discuss how the general concept of liquid polymorphism [3] is proving useful in understanding anomalies in other liquids, such as silicon, silica, and carbon, as well as metallic glasses, which have in common that they are characterized by two characteristic length scales in their interactions. This work was supported by NSF Chemistry Division, and carried out in collaboration with a number of colleagues, chief among whom are C. A. Angell, M. C. Barbosa, M. C. Bellissent, L. Bosio, F. Bruni, S. V. Buldyrev, M. Canpolat, S. -H. Chen, P. G. Debenedetti, U. Essmann,G. Franzese, A. Geiger, N. Giovambattista, S. Han, P. Kumar, E. La Nave,G. Malescio, F. Mallamace, M. G. Mazza, O. Mishima, P. Netz, P. H. Poole, P. J. Rossky, R. Sadr,S. Sastry, A. Scala, F. Sciortino, A. Skibinsky, F. W. Starr, K. C. Stokely J. Teixeira, L. Xu, and Z. Yan.[4pt] [1] L. Xu, F. Mallamace, Z. Yan, F. W. Starr, S. V. Buldyrev, and H. E. Stanley, ``Appearance of a Fractional Stokes-Einstein Relation in Water and a Structural Interpretation of Its Onset,'' Nature Physics 5, 565--569 (2009). [0pt] [2] P. Kumar, Z. Yan, L. Xu, M. G. Mazza, S. V. Buldyrev, S. -H. Chen. S. Sastry, and H. E. Stanley, ``Glass Transition in Biomolecules and the Liquid-Liquid Critical Point of Water,'' Phys. Rev. Lett. 97, 177802 (2006). [0pt] [3] H. E. Stanley, ed. , Liquid Polymorphism [Advances in Chemical Physics], series edited by S. A. Rice (Wiley, New York, 2010).

Mistaken Identity and Mirror Images: Albert and Carl Einstein, Leiden and Berlin, Relativity and Revolution

NASA Astrophysics Data System (ADS)

van Dongen, Jeroen

2012-06-01

Albert Einstein accepted a "special" visiting professorship at the University of Leiden in the Netherlands in February 1920. Although his appointment should have been a mere formality, it took until October of that year before Einstein could occupy his special chair. Why the delay? The explanation involves a case of mistaken identity with Carl Einstein, Dadaist art, and a particular Dutch fear of revolutions. But what revolutions was one afraid of? The story of Einstein's Leiden chair throws new light on the reception of relativity and its creator in the Netherlands and in Germany.

A Particle Model Explaining Mass and Relativity in a Physical Way

NASA Astrophysics Data System (ADS)

Giese, Albrecht

Physicists' understanding of relativity and the way it is handled is up to present days dominated by the interpretation of Albert Einstein, who related relativity to specific properties of space and time. The principal alternative to Einstein's interpretation is based on a concept proposed by Hendrik A. Lorentz, which uses knowledge of classical physics alone to explain relativistic phenomena. In this paper, we will show that on the one hand the Lorentz-based interpretation provides a simpler mathematical way of arriving at the known results for both Special and General Relativity. On the other hand, it is able to solve problems which have remained open to this day. Furthermore, a particle model will be presented, based on Lorentzian relativity and the quantum mechanical concept of Louis de Broglie, which explains the origin of mass without the use of the Higgs mechanism. It is based on the finiteness of the speed of light and provides classical results for particle properties which are currently only accessible through quantum mechanics.

Boundary stress tensor and asymptotically AdS3 non-Einstein spaces at the chiral point

NASA Astrophysics Data System (ADS)

Giribet, Gaston; Goya, Andrés; Leston, Mauricio

2011-09-01

Chiral gravity admits asymptotically AdS3 solutions that are not locally equivalent to AdS3; meaning that solutions do exist which, while obeying the strong boundary conditions usually imposed in general relativity, happen not to be Einstein spaces. In topologically massive gravity (TMG), the existence of non-Einstein solutions is particularly connected to the question about the role played by complex saddle points in the Euclidean path integral. Consequently, studying (the existence of) nonlocally AdS3 solutions to chiral gravity is relevant to understanding the quantum theory. Here, we discuss a special family of nonlocally AdS3 solutions to chiral gravity. In particular, we show that such solutions persist when one deforms the theory by adding the higher-curvature terms of the so-called new massive gravity. Moreover, the addition of higher-curvature terms to the gravity action introduces new nonlocally AdS3 solutions that have no analogues in TMG. Both stationary and time-dependent, axially symmetric solutions that asymptote AdS3 space without being locally equivalent to it appear. Defining the boundary stress tensor for the full theory, we show that these non-Einstein geometries have associated vanishing conserved charges.

Getting to the Point in Pinpoint Landing

NASA Technical Reports Server (NTRS)

1998-01-01

Assisted by Langley Research Center's Small Business Technology Transfer (STTR) Program, IntegriNautics has developed a commercialized precision landing system. The idea finds its origins in Stanford University work on a satellite test of Einstein's General Theory of Relativity, where Stanford has designed a new high-performance altitude-determining hardware.

Black Holes and the Information Paradox

NASA Astrophysics Data System (ADS)

't Hooft, Gerard

In electromagnetism, like charges repel, opposite charges attract. A remarkable feature of the gravitational force is that like masses attract. This gives rise to an instability: the more mass you have, the stronger the attractive force, until an inevitable implosion follows, leading to a "black hole". It is in the black hole where an apparent conflict between Einstein's General Relativity and the laws of Quantum Mechanics becomes manifest. Most physicists now agree that a black hole should be described by a Schrödinger equation, with a Hermitean Hamiltonian, but this requires a modification of general relativity. Both General Relativity and Quantum mechanics are shaking on their foundations.

Symmetry as Bias: Rediscovering Special Relativity

NASA Technical Reports Server (NTRS)

Lowry, Michael R.

1992-01-01

This paper describes a rational reconstruction of Einstein's discovery of special relativity, validated through an implementation: the Erlanger program. Einstein's discovery of special relativity revolutionized both the content of physics and the research strategy used by theoretical physicists. This research strategy entails a mutual bootstrapping process between a hypothesis space for biases, defined through different postulated symmetries of the universe, and a hypothesis space for physical theories. The invariance principle mutually constrains these two spaces. The invariance principle enables detecting when an evolving physical theory becomes inconsistent with its bias, and also when the biases for theories describing different phenomena are inconsistent. Structural properties of the invariance principle facilitate generating a new bias when an inconsistency is detected. After a new bias is generated. this principle facilitates reformulating the old, inconsistent theory by treating the latter as a limiting approximation. The structural properties of the invariance principle can be suitably generalized to other types of biases to enable primal-dual learning.

On a modified form of navier-stokes equations for three-dimensional flows.

PubMed

Venetis, J

2015-01-01

A rephrased form of Navier-Stokes equations is performed for incompressible, three-dimensional, unsteady flows according to Eulerian formalism for the fluid motion. In particular, we propose a geometrical method for the elimination of the nonlinear terms of these fundamental equations, which are expressed in true vector form, and finally arrive at an equivalent system of three semilinear first order PDEs, which hold for a three-dimensional rectangular Cartesian coordinate system. Next, we present the related variational formulation of these modified equations as well as a general type of weak solutions which mainly concern Sobolev spaces.

On a Modified Form of Navier-Stokes Equations for Three-Dimensional Flows

PubMed Central

Venetis, J.

2015-01-01

A rephrased form of Navier-Stokes equations is performed for incompressible, three-dimensional, unsteady flows according to Eulerian formalism for the fluid motion. In particular, we propose a geometrical method for the elimination of the nonlinear terms of these fundamental equations, which are expressed in true vector form, and finally arrive at an equivalent system of three semilinear first order PDEs, which hold for a three-dimensional rectangular Cartesian coordinate system. Next, we present the related variational formulation of these modified equations as well as a general type of weak solutions which mainly concern Sobolev spaces. PMID:25918743

Accuracy of unmodified Stokes' integration in the R-C-R procedure for geoid computation

NASA Astrophysics Data System (ADS)

Ismail, Zahra; Jamet, Olivier

2015-06-01

Geoid determinations by the Remove-Compute-­Restore (R-C-R) technique involves the application of Stokes' integral on reduced gravity anomalies. Numerical Stokes' integration produces an error depending on the choice of the integration radius, grid resolution and Stokes' kernel function. In this work, we aim to evaluate the accuracy of Stokes' integral through a study on synthetic gravitational signals derived from EGM2008 on three different landscape areas with respect to the size of the integration domain and the resolution of the anomaly grid. The influence of the integration radius was studied earlier by several authors. Using real data, they found that the choice of relatively small radii (less than 1°) enables to reach an optimal accuracy. We observe a general behaviour coherent with these earlier studies. On the other hand, we notice that increasing the integration radius up to 2° or 2.5° might bring significantly better results. We note that, unlike the smallest radius corresponding to a local minimum of the error curve, the optimal radius in the range 0° to 6° depends on the terrain characteristics. We also find that the high frequencies, from degree 600, improve continuously with the integration radius in both semi-­mountainous and mountain areas. Finally, we note that the relative error of the computed geoid heights depends weakly on the anomaly spherical harmonic degree in the range from degree 200 to 2000. It remains greater than 10 % for any integration radii up to 6°. This result tends to prove that a one centimetre accuracy cannot be reached in semi-mountainous and mountainous regions with the unmodified Stokes' kernel.

Nonmetricity formulation of general relativity and its scalar-tensor extension

NASA Astrophysics Data System (ADS)

Järv, Laur; Rünkla, Mihkel; Saal, Margus; Vilson, Ott

2018-06-01

Einstein's celebrated theory of gravitation can be presented in three forms: general relativity, teleparallel gravity, and the rarely considered before symmetric teleparallel gravity. Extending the latter, we introduce a new class of theories where a scalar field is coupled nonminimally to nonmetricity Q , which here encodes the gravitational effects like curvature R in general relativity or torsion T in teleparallel gravity. We point out the similarities and differences with analogous scalar-curvature and scalar-torsion theories by discussing the field equations, role of connection, conformal transformations, relation to f (Q ) theory, and cosmology. The equations for a spatially flat universe coincide with those of teleparallel dark energy, thus allowing us to explain accelerating expansion.

Dynamics of a thermo-responsive microgel colloid near to the glass transition

NASA Astrophysics Data System (ADS)

Di, Xiaojun; Peng, Xiaoguang; McKenna, Gregory B.

2014-02-01

In a previous study, we used diffusing wave spectroscopy (DWS) to investigate the aging signatures of a thermo-sensitive colloidal glass and compared them with those of molecular glasses from the perspective of the Kovacs temperature-jump, volume recovery experiments [X. Di, K. Z. Win, G. B. McKenna, T. Narita, F. Lequeux, S. R. Pullela, and Z. Cheng, Phys. Rev. Lett. 106, 095701 (2011)]. In order to further look into the glassy behavior of colloidal systems, we have synthesized a new core/shell particle with lower temperature sensitivity and studied the aging signatures of concentrated systems, again following Kovacs' protocol. Similar signatures of aging to those observed previously were seen in this new system. Moreover, a systematic study of the temperature dependence of the dynamics of the new system for different weight concentrations was performed and the dynamic fragility index m was determined. We have also explored the use of the properties determined from the DWS measurements to obtain macroscopic rheological parameters - storage modulus G'(ω) and loss modulus G″(ω) - using a generalized Stokes-Einstein approach. The micro-rheological and macro-rheological values are in reasonable agreement.

Mass loss due to gravitational waves with Λ > 0

NASA Astrophysics Data System (ADS)

Saw, Vee-Liem

2017-07-01

The theoretical basis for the energy carried away by gravitational waves that an isolated gravitating system emits was first formulated by Hermann Bondi during the ’60s. Recent findings from the observation of distant supernovae revealed that the rate of expansion of our universe is accelerating, which may be well explained by sticking a positive cosmological constant into the Einstein field equations for general relativity. By solving the Newman-Penrose equations (which are equivalent to the Einstein field equations), we generalize this notion of Bondi mass-energy and thereby provide a firm theoretical description of how an isolated gravitating system loses energy as it radiates gravitational waves, in a universe that expands at an accelerated rate. This is in line with the observational front of LIGO’s first announcement in February 2016 that gravitational waves from the merger of a binary black hole system have been detected.

Unified theory of nonlinear electrodynamics and gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Torres-Gomez, Alexander; Krasnov, Kirill; Scarinci, Carlos

2011-01-15

We describe a class of unified theories of electromagnetism and gravity. The Lagrangian is of the BF type, with a potential for the B field, the gauge group is U(2) (complexified). Given a choice of the potential function the theory is a deformation of (complex) general relativity and electromagnetism, and describes just two propagating polarizations of the graviton and two of the photon. When gravity is switched off the theory becomes the usual nonlinear electrodynamics with a general structure function. The Einstein-Maxwell theory can be recovered by sending some of the parameters of the defining potential to zero, but formore » any generic choice of the potential the theory is indistinguishable from Einstein-Maxwell at low energies. A real theory is obtained by imposing suitable reality conditions. We also study the spherically-symmetric solution and show how the usual Reissner-Nordstrom solution is recovered.« less

Drifting solutions with elliptic symmetry for the compressible Navier-Stokes equations with density-dependent viscosity

DOE Office of Scientific and Technical Information (OSTI.GOV)

An, Hongli, E-mail: kaixinguoan@163.com; Yuen, Manwai, E-mail: nevetsyuen@hotmail.com

2014-05-15

In this paper, we investigate the analytical solutions of the compressible Navier-Stokes equations with dependent-density viscosity. By using the characteristic method, we successfully obtain a class of drifting solutions with elliptic symmetry for the Navier-Stokes model wherein the velocity components are governed by a generalized Emden dynamical system. In particular, when the viscosity variables are taken the same as Yuen [M. W. Yuen, “Analytical solutions to the Navier-Stokes equations,” J. Math. Phys. 49, 113102 (2008)], our solutions constitute a generalization of that obtained by Yuen. Interestingly, numerical simulations show that the analytical solutions can be used to explain the driftingmore » phenomena of the propagation wave like Tsunamis in oceans.« less

Navier-Stokes and viscous-inviscid interaction

NASA Technical Reports Server (NTRS)

Steger, Joseph L.; Vandalsem, William R.

1989-01-01

Some considerations toward developing numerical procedures for simulating viscous compressible flows are discussed. Both Navier-Stokes and boundary layer field methods are considered. Because efficient viscous-inviscid interaction methods have been difficult to extend to complex 3-D flow simulations, Navier-Stokes procedures are more frequently being utilized even though they require considerably more work per grid point. It would seem a mistake, however, not to make use of the more efficient approximate methods in those regions in which they are clearly valid. Ideally, a general purpose compressible flow solver that can optionally take advantage of approximate solution methods would suffice, both to improve accuracy and efficiency. Some potentially useful steps toward this goal are described: a generalized 3-D boundary layer formulation and the fortified Navier-Stokes procedure.

Mixed mimetic spectral element method for Stokes flow: A pointwise divergence-free solution

NASA Astrophysics Data System (ADS)

Kreeft, Jasper; Gerritsma, Marc

2013-05-01

In this paper we apply the recently developed mimetic discretization method to the mixed formulation of the Stokes problem in terms of vorticity, velocity and pressure. The mimetic discretization presented in this paper and in Kreeft et al. [51] is a higher-order method for curvilinear quadrilaterals and hexahedrals. Fundamental is the underlying structure of oriented geometric objects, the relation between these objects through the boundary operator and how this defines the exterior derivative, representing the grad, curl and div, through the generalized Stokes theorem. The mimetic method presented here uses the language of differential k-forms with k-cochains as their discrete counterpart, and the relations between them in terms of the mimetic operators: reduction, reconstruction and projection. The reconstruction consists of the recently developed mimetic spectral interpolation functions. The most important result of the mimetic framework is the commutation between differentiation at the continuous level with that on the finite dimensional and discrete level. As a result operators like gradient, curl and divergence are discretized exactly. For Stokes flow, this implies a pointwise divergence-free solution. This is confirmed using a set of test cases on both Cartesian and curvilinear meshes. It will be shown that the method converges optimally for all admissible boundary conditions.

Strong binary pulsar constraints on Lorentz violation in gravity.

PubMed

Yagi, Kent; Blas, Diego; Yunes, Nicolás; Barausse, Enrico

2014-04-25

Binary pulsars are excellent laboratories to test the building blocks of Einstein's theory of general relativity. One of these is Lorentz symmetry, which states that physical phenomena appear the same for all inertially moving observers. We study the effect of violations of Lorentz symmetry in the orbital evolution of binary pulsars and find that it induces a much more rapid decay of the binary's orbital period due to the emission of dipolar radiation. The absence of such behavior in recent observations allows us to place the most stringent constraints on Lorentz violation in gravity, thus verifying one of the cornerstones of Einstein's theory much more accurately than any previous gravitational observation.

A conformal approach for the analysis of the non-linear stability of radiation cosmologies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Luebbe, Christian, E-mail: c.luebbe@ucl.ac.uk; Department of Mathematics, University of Leicester, University Road, LE1 8RH; Valiente Kroon, Juan Antonio, E-mail: j.a.valiente-kroon@qmul.ac.uk

2013-01-15

The conformal Einstein equations for a trace-free (radiation) perfect fluid are derived in terms of the Levi-Civita connection of a conformally rescaled metric. These equations are used to provide a non-linear stability result for de Sitter-like trace-free (radiation) perfect fluid Friedman-Lemaitre-Robertson-Walker cosmological models. The solutions thus obtained exist globally towards the future and are future geodesically complete. - Highlights: Black-Right-Pointing-Pointer We study the Einstein-Euler system in General Relativity using conformal methods. Black-Right-Pointing-Pointer We analyze the structural properties of the associated evolution equations. Black-Right-Pointing-Pointer We establish the non-linear stability of pure radiation cosmological models.

A new golden age: testing general relativity with cosmology.

PubMed

Bean, Rachel; Ferreira, Pedro G; Taylor, Andy

2011-12-28

Gravity drives the evolution of the Universe and is at the heart of its complexity. Einstein's field equations can be used to work out the detailed dynamics of space and time and to calculate the emergence of large-scale structure in the distribution of galaxies and radiation. Over the past few years, it has become clear that cosmological observations can be used not only to constrain different world models within the context of Einstein gravity but also to constrain the theory of gravity itself. In this article, we look at different aspects of this new field in which cosmology is used to test theories of gravity with a wide range of observations.

Perfect fluids in the Einstein-Cartan theory

NASA Technical Reports Server (NTRS)

Ray, J. R.; Smalley, L. J.

1982-01-01

It is pointed out that whereas most of the discussion of the Einstein-Cartan (EC) theory involves the relationship between gravitation and elementary particles, it is possible that the theory, if correct, may be important in certain extreme astrophysical and cosmological problems. The latter would include something like the collapse of a spinning star or an early universe with spin. A set of equations that describe a macroscopic perfect fluid in the EC theory is derived and examined. The equations are derived starting from the fundamental variational principle for a perfect fluid in general relativity. A brief review of the study by Ray (1972) is included, and the results for the EC theory are presented.

REVIEWS OF TOPICAL PROBLEMS: Experimental tests of general relativity: recent progress and future directions

NASA Astrophysics Data System (ADS)

Turyshev, S. G.

2009-01-01

Einstein's general theory of relativity is the standard theory of gravity, especially where the needs of astronomy, astrophysics, cosmology, and fundamental physics are concerned. As such, this theory is used for many practical purposes involving spacecraft navigation, geodesy, and time transfer. We review the foundations of general relativity, discuss recent progress in tests of relativistic gravity, and present motivations for the new generation of high-accuracy tests of new physics beyond general relativity. Space-based experiments in fundamental physics are presently capable of uniquely addressing important questions related to the fundamental laws of nature. We discuss the advances in our understanding of fundamental physics that are anticipated in the near future and evaluate the discovery potential of a number of recently proposed space-based gravitational experiments.

Unimodular Einstein-Cartan gravity: Dynamics and conservation laws

NASA Astrophysics Data System (ADS)

Bonder, Yuri; Corral, Cristóbal

2018-04-01

Unimodular gravity is an interesting approach to address the cosmological constant problem, since the vacuum energy density of quantum fields does not gravitate in this framework, and the cosmological constant appears as an integration constant. These features arise as a consequence of considering a constrained volume element 4-form that breaks the diffeomorphisms invariance down to volume preserving diffeomorphisms. In this work, the first-order formulation of unimodular gravity is presented by considering the spin density of matter fields as a source of spacetime torsion. Even though the most general matter Lagrangian allowed by the symmetries is considered, dynamical restrictions arise on their functional dependence. The field equations are obtained and the conservation laws associated with the symmetries are derived. It is found that, analogous to torsion-free unimodular gravity, the field equation for the vierbein is traceless; nevertheless, torsion is algebraically related to the spin density as in standard Einstein-Cartan theory. The particular example of massless Dirac spinors is studied, and comparisons with standard Einstein-Cartan theory are shown.

Einstein Universe Revisited and End of Dark ERA

NASA Astrophysics Data System (ADS)

Nurgaliev, Ildus S.

2015-01-01

Historically the earliest general relativistic cosmological solution was received by Einstein himself as homogenous, isotropic one. In accordance with European cosmology it was expected static. The Eternal Universe as scientific model is conflicting with the existed theological model of the Universe created by God, therefore, of the limited age. Christianity, younger Islam, older Judaism are based on creationism. Much older oriental traditions such us Hinduism and Buddhism are based on conceptions of eternal and cyclic Universe which are closer to scientific worldview. To have static universe Einstein needed a factor to counteract gravity and postulated cosmological term and considered it as a disadvantage of the theory. This aesthetic dissatisfaction was amplified by interpretation distance-redshift relationship as a cosmological expansion effect. Emerged scientific cosmological community (excluding Hubble himself - almost always) endorsed the concept of expanding Universe. At the same time, as it is shown in this report, a natural well known factors do exist to counteract gravity. They are inertial centrifugal and Coriolis forces finding their geometrical presentation in the relativity theory.

New non-naturally reductive Einstein metrics on exceptional simple Lie groups

NASA Astrophysics Data System (ADS)

Chen, Huibin; Chen, Zhiqi; Deng, Shaoqiang

2018-01-01

In this article, we construct several non-naturally reductive Einstein metrics on exceptional simple Lie groups, which are found through the decomposition arising from generalized Wallach spaces. Using the decomposition corresponding to the two involutions, we calculate the non-zero coefficients in the formulas of the components of Ricci tensor with respect to the given metrics. The Einstein metrics are obtained as solutions of a system of polynomial equations, which we manipulate by symbolic computations using Gröbner bases. In particular, we discuss the concrete numbers of non-naturally reductive Einstein metrics for each case up to isometry and homothety.

Einstein Session of the Pontifical Academy.

ERIC Educational Resources Information Center

Science, 1980

1980-01-01

The texts of four speeches, given at the 1979 Einstein Session of the Pontifical Academy held in Rome, are presented. Each address relates to some aspect of the life and times of Albert Einstein. (SA)

On the `simple' form of the gravitational action and the self-interacting graviton

NASA Astrophysics Data System (ADS)

Tomboulis, E. T.

2017-09-01

The so-called ΓΓ-form of the gravitational Lagrangian, long known to provide its most compact expression as well as the most efficient generation of the graviton vertices, is taken as the starting point for discussing General Relativity as a theory of the self-interacting graviton. A straightforward but general method of converting to a covariant formulation by the introduction of a reference metric is given. It is used to recast the Einstein field equation as the equation of motion of a spin-2 particle interacting with the canonical energy-momentum tensor symmetrized by the standard Belinfante method applicable to any field carrying nonzero spin. This represents the graviton field equation in a form complying with the precepts of standard field theory. It is then shown how representations based on other, at face value completely unrelated definitions of energy-momentum (pseudo)tensors are all related by the addition of appropriate superpotential terms. Specifically, the superpotentials are explicitly constructed which connect to: i) the common definition consisting simply of the nonlinear part of the Einstein tensor; ii) the Landau-Lifshitz definition.

Rotating black holes in the teleparallel equivalent of general relativity

NASA Astrophysics Data System (ADS)

Nashed, Gamal G. L.

2016-05-01

We derive set of solutions with flat transverse sections in the framework of a teleparallel equivalent of general relativity which describes rotating black holes. The singularities supported from the invariants of torsion and curvature are explained. We investigate that there appear more singularities in the torsion scalars than in the curvature ones. The conserved quantities are discussed using Einstein-Cartan geometry. The physics of the constants of integration is explained through the calculations of conserved quantities. These calculations show that there is a unique solution that may describe true physical black hole.

Possible experiment with two counter-orbiting drag-free satellites to obtain a new test of Einstein's general theory of relativity and improved measurements in geodesy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Van Patten, R.A.; Everitt, C.W.F.

1976-03-22

In 1918, Lense and Thirring calculated that a moon orbiting a rotating planet would experience a nodal dragging effect due to general relativity. We describe an experiment to measure this effect to 1% with two counter-orbiting drag-free satellites in polar earth orbit. In addition to tracking data from existing ground stations, satellite-to-satellite Doppler ranging data are taken near the poles. New geophysical information is inherent in the polar data. (AIP)

Bose-Einstein condensation. Twenty years after

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bagnato, V. S.; Frantzeskakis, D. J.; Kevrekidis, P. G.

The aim of this introductory article is two-fold. First, we aim to offer a general introduction to the theme of Bose-Einstein condensates, and briefly discuss the evolution of a number of relevant research directions during the last two decades. Second, we introduce and present the articles that appear in this Special Volume of Romanian Reports in Physics celebrating the conclusion of the second decade since the experimental creation of Bose-Einstein condensation in ultracold gases of alkali-metal atoms.

PEOPLE IN PHYSICS: Albert Einstein's personal papers: a physics teaching resource

NASA Astrophysics Data System (ADS)

Derman, Samuel

2000-01-01

The concept of `Einstein the man' is put forward as a way of generating interest in the study of physics amongst students. Einstein provides an instantly recognizable face for science and thus a gateway into the subject through discussion of the man. Supporting this is the great volume of archive material which is available to students, teachers and the general public and in particular the archives of the Jewish National & University Library in Jerusalem.

Bose-Einstein condensation. Twenty years after

DOE PAGES

Bagnato, V. S.; Frantzeskakis, D. J.; Kevrekidis, P. G.; ...

2015-02-23

The aim of this introductory article is two-fold. First, we aim to offer a general introduction to the theme of Bose-Einstein condensates, and briefly discuss the evolution of a number of relevant research directions during the last two decades. Second, we introduce and present the articles that appear in this Special Volume of Romanian Reports in Physics celebrating the conclusion of the second decade since the experimental creation of Bose-Einstein condensation in ultracold gases of alkali-metal atoms.

Optimization of anisotropic photonic density of states for Raman cooling of solids

NASA Astrophysics Data System (ADS)

Chen, Yin-Chung; Ghosh, Indronil; Schleife, André; Carney, P. Scott; Bahl, Gaurav

2018-04-01

Optical refrigeration of solids holds tremendous promise for applications in thermal management. It can be achieved through multiple mechanisms including inelastic anti-Stokes Brillouin and Raman scattering. However, engineering of these mechanisms remains relatively unexplored. The major challenge lies in the natural unfavorable imbalance in transition rates for Stokes and anti-Stokes scattering. We consider the influence of anisotropic photonic density of states on Raman scattering and derive expressions for cooling in such photonically anisotropic systems. We demonstrate optimization of the Raman cooling figure of merit considering all possible orientations for the material crystal and two example photonic crystals. We find that the anisotropic description of the photonic density of states and the optimization process is necessary to obtain the best Raman cooling efficiency for systems having lower symmetry. This general result applies to a wide array of other laser cooling methods in the presence of anisotropy.

The Confrontation between General Relativity and Experiment.

PubMed

Will, Clifford M

2006-01-01

The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is reviewed. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eötvös experiment, tests of special relativity, and the gravitational redshift experiment. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, and the Nordtvedt effect in lunar motion. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and other binary pulsar systems have yielded other tests, especially of strong-field effects. When direct observation of gravitational radiation from astrophysical sources begins, new tests of general relativity will be possible.

The Confrontation between General Relativity and Experiment.

PubMed

Will, Clifford M

2001-01-01

The status of experimental tests of general relativity and of theoretical frameworks for analysing them are reviewed. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eötvös experiment, tests of special relativity, and the gravitational redshift experiment. Future tests of EEP and of the inverse square law will search for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light defl ection the Shapiro time delay, the perihelion advance of Mercury, and the Nordtvedt effect in lunar motion. Gravitational wave damping has been detected in an amount that agrees with general relativity to half a percent using the Hulse-Taylor binary pulsar, and new binary pulsar systems may yield further improvements. When direct observation of gravitational radiation from astrophysical sources begins, new tests of general relativity will be possible.

Validation of a rotational coherent anti-Stokes Raman spectroscopy model for carbon dioxide using high-resolution detection in the temperature range 294-1143 K.

PubMed

Vestin, Fredrik; Nilsson, Kristin; Bengtsson, Per-Erik

2008-04-10

Experiments were performed in the temperature range of 294-1143 K in pure CO(2) using high-resolution rotational coherent anti-Stokes Raman spectroscopy (CARS), in the dual-broadband approach. Experimental single-shot spectra were recorded with high spectral resolution using a single-mode Nd:YAG laser and a relay imaging lens system on the exit of a 1 m spectrometer. A theoretical rotational CARS model for CO(2) was developed for evaluation of the experimental spectra. The evaluated mean temperatures of the recorded single-shot dual-broadband rotational coherent anti-Stokes Raman spectroscopy (DB-RCARS) spectra using this model showed good agreement with thermocouple temperatures, and the relative standard deviation of evaluated single-shot temperatures was generally 2-3%. Simultaneous thermometry and relative CO(2)/N(2)-concentration measurements were demonstrated in the product gas of premixed laminar CO/air flames at atmospheric pressure. Although the model proved to be accurate for thermometry up to 1143 K, limitations were observed at flame temperatures where temperatures were overestimated and relative CO(2)/N(2) concentrations were underestimated. Potential sources for these discrepancies are discussed.

Observation of Single-Protein and DNA Macromolecule Collisions on Ultramicroelectrodes.

PubMed

Dick, Jeffrey E; Renault, Christophe; Bard, Allen J

2015-07-08

Single-molecule detection is the ultimate sensitivity in analytical chemistry and has been largely unavailable in electrochemical analysis. Here, we demonstrate the feasibility of detecting electrochemically inactive single biomacromolecules, such as enzymes, antibodies, and DNA, by blocking a solution redox reaction when molecules adsorb and block electrode sites. By oxidizing a large concentration of potassium ferrocyanide on an ultramicroelectrode (UME, radius ≤150 nm), time-resolved, discrete adsorption events of antibodies, enzymes, DNA, and polystyrene nanospheres can be differentiated from the background by their "footprint". Further, by assuming that the mass transport of proteins to the electrode surface is controlled mainly by diffusion, a size estimate using the Stokes-Einstein relationship shows good agreement of electrochemical data with known protein sizes.

Translational diffusion coefficients of volatile compounds in various aqueous solutions at low and subzero temperatures.

PubMed

Covarrubias-Cervantes, Marco; Champion, Dominique; Debeaufort, Frédéric; Voilley, Andrée

2005-08-24

Translational diffusion coefficients (D(12)) of volatile compounds were measured in model media with the profile concentration method. The influence of sample temperature (from 25 to -10 degrees C) was studied on translational diffusion in sucrose or maltodextrin solutions at various concentrations. Results show that diffusivity of volatile compounds in sucrose solutions is controlled by temperature, molecule size, and the viscosity of the liquid phase as expected with the Stokes-Einstein equation; moreover, physicochemical interactions between volatile compounds and the medium are determinant for diffusion estimation. At negative temperature, the winding path induced by an ice crystal content of >70% lowered volatile compound diffusion. On the contrary, no influence on translational diffusion coefficients was observed for lower ice content.

Fluids and vortex from constrained fluctuations around C-metric black holes

NASA Astrophysics Data System (ADS)

Hao, Xin; Wu, Bin; Zhao, Liu

2017-08-01

By foliating the four-dimensional C-metric black hole spacetime, we consider a kind of initial-value-like formulation of the vacuum Einstein's equation, the holographic initial data is a double consisting of the induced metric and the Brown-York energy momentum tensor on an arbitrary initial hypersurface. Then by perturbing the initial data that generates the background spacetime, it is shown that, in an appropriate limit, the fluctuation modes are governed by the continuity equation and the compressible Navier-Stokes equation which describe the momentum transport in non-relativistic viscous fluid on a flat Newtonian space. It turns out that the flat space fluid behaves as a pure vortex and the viscosity to entropy ratio is subjected to the black hole acceleration.

Turbulent MHD transport coefficients - An attempt at self-consistency

NASA Technical Reports Server (NTRS)

Chen, H.; Montgomery, D.

1987-01-01

In this paper, some multiple scale perturbation calculations of turbulent MHD transport coefficients begun in earlier papers are first completed. These generalize 'alpha effect' calculations by treating the velocity field and magnetic field on the same footing. Then the problem of rendering such calculations self-consistent is addressed, generalizing an eddy-viscosity hypothesis similar to that of Heisenberg for the Navier-Stokes case. The method also borrows from Kraichnan's direct interaction approximation. The output is a set of integral equations relating the spectra and the turbulent transport coefficients. Previous 'alpha effect' and 'beta effect' coefficients emerge as limiting cases. A treatment of the inertial range can also be given, consistent with a -5/3 energy spectrum power law. In the Navier-Stokes limit, a value of 1.72 is extracted for the Kolmogorov constant. Further applications to MHD are possible.

Inhomogeneous Einstein-Rosen string cosmology

NASA Astrophysics Data System (ADS)

Clancy, Dominic; Feinstein, Alexander; Lidsey, James E.; Tavakol, Reza

1999-08-01

Families of anisotropic and inhomogeneous string cosmologies containing non-trivial dilaton and axion fields are derived by applying the global symmetries of the string effective action to a generalized Einstein-Rosen metric. The models exhibit a two-dimensional group of Abelian isometries. In particular, two classes of exact solutions are found that represent inhomogeneous generalizations of the Bianchi type VIh cosmology. The asymptotic behavior of the solutions is investigated and further applications are briefly discussed.

Conversations With Albert Einstein. II

ERIC Educational Resources Information Center

Shankland, R. S.

1973-01-01

Discusses Einstein's views on the role of Michelson-Morley, Fizeau, and Miller experiments in the development of relativity and his attitude toward the theories of new quantum mechanics. Indicates that Einstein's opposition to quantum mechanics is beyond dispute. (CC)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khodam-Mohammadi, A.; Monshizadeh, M.

We give a review of the existence of Taub-NUT/bolt solutions in Einstein Gauss-Bonnet gravity with the parameter {alpha} in six dimensions. Although the spacetime with base space S{sup 2}xS{sup 2} has a curvature singularity at r=N, which does not admit NUT solutions, we may proceed with the same computations as in the CP{sup 2} case. The investigation of thermodynamics of NUT/bolt solutions in six dimensions is carried out. We compute the finite action, mass, entropy, and temperature of the black hole. Then the validity of the first law of thermodynamics is demonstrated. It is shown that in NUT solutions allmore » thermodynamic quantities for both base spaces are related to each other by substituting {alpha}{sup CP{sup k}}=[(k+1)/k]{alpha}{sup S{sup 2}}{sup xS{sup 2}}{sup x...S{sub k}{sup 2}}. So, no further information is given by investigating NUT solutions in the S{sup 2}xS{sup 2} case. This relation is not true for bolt solutions. A generalization of the thermodynamics of black holes to arbitrary even dimensions is made using a new method based on the Gibbs-Duhem relation and Gibbs free energy for NUT solutions. According to this method, the finite action in Einstein Gauss-Bonnet is obtained by considering the generalized finite action in Einstein gravity with an additional term as a function of {alpha}. Stability analysis is done by investigating the heat capacity and entropy in the allowed range of {alpha}, {lambda}, and N. For NUT solutions in d dimensions, there exists a stable phase at a narrow range of {alpha}. In six-dimensional bolt solutions, the metric is completely stable for B=S{sup 2}xS{sup 2} and is completely unstable for the B=CP{sup 2} case.« less

New Frontiers at the Interface of General Relativity and Quantum Optics

NASA Astrophysics Data System (ADS)

Feiler, C.; Buser, M.; Kajari, E.; Schleich, W. P.; Rasel, E. M.; O'Connell, R. F.

2009-12-01

In the present paper we follow three major themes: (i) concepts of rotation in general relativity, (ii) effects induced by these generalized rotations, and (iii) their measurement using interferometry. Our journey takes us from the Foucault pendulum via the Sagnac interferometer to manifestations of gravito-magnetism in double binary pulsars and in Gödel’s Universe. Throughout our article we emphasize the emerging role of matter wave interferometry based on cold atoms or Bose-Einstein condensates leading to superior inertial sensors. In particular, we advertise recent activities directed towards the operation of a coherent matter wave interferometer in an extended free fall.

General flat four-dimensional world pictures and clock systems

NASA Technical Reports Server (NTRS)

Hsu, J. P.; Underwood, J. A.

1978-01-01

We explore the mathematical structure and the physical implications of a general four-dimensional symmetry framework which is consistent with the Poincare-Einstein principle of relativity for physical laws and with experiments. In particular, we discuss a four-dimensional framework in which all observers in different frames use one and the same grid of clocks. The general framework includes special relativity and a recently proposed new four-dimensional symmetry with a nonuniversal light speed as two special simple cases. The connection between the properties of light propagation and the convention concerning clock systems is also discussed, and is seen to be nonunique within the four-dimensional framework.

Why did Einstein reject the November tensor in 1912-1913, only to come back to it in November 1915?

NASA Astrophysics Data System (ADS)

Weinstein, Galina

2018-05-01

The question of Einstein's rejection of the November tensor is re-examined in light of conflicting answers by several historians. I discuss these conflicting conjectures in view of three questions that should inform our thinking: Why did Einstein reject the November tensor in 1912, only to come back to it in 1915? Why was it hard for Einstein to recognize that the November tensor is a natural generalization of Newton's law of gravitation? Why did it take him three years to realize that the November tensor is not incompatible with Newton's law? I first briefly describe Einstein's work in the Zurich Notebook. I then discuss a number of interpretive conjectures formulated by historians and what may be inferred from them. Finally, I offer a new combined conjecture that answers the above questions.

Einstein as a Missionary of Science

NASA Astrophysics Data System (ADS)

Renn, Jürgen

2013-10-01

The paper reviews Einstein's engagement as a mediator and popularizer of science. It discusses the formative role of popular scientific literature for the young Einstein, showing that not only his broad scientific outlook but also his internationalist political views were shaped by these readings. Then, on the basis of recent detailed studies, Einstein's travels and their impact on the dissemination of relativity theory are examined. These activities as well as Einstein's own popular writings are interpreted in the context of his understanding of science as part of human culture.

Einstein 1905-1955: His Approach to Physics

NASA Astrophysics Data System (ADS)

Damour, Thibault

We review Einstein's epistemological conceptions, and indicate their philosophical roots. The particular importance of the ideas of Hume, Kant, Mach, and Poincaré is highlighted. The specific characteristics of Einstein's approach to physics are underlined. Lastly, we consider the practical application of Einstein's methodological principles to the two theories of relativity, and to quantum theory. We emphasize a Kantian approach to quantum theory.

Electrical, thermal, and species transport properties of liquid eutectic Ga-In and Ga-In-Sn from first principles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yu, Seungho; Kaviany, Massoud, E-mail: kaviany@umich.edu

2014-02-14

Using ab initio molecular dynamics, the atomic structure and transport properties of eutectic Ga-In and Ga-In-Sn are investigated. The Kubo-Greenwood (K-G) and the Ziman-Faber (Z-F) formulations and the Wiedemann-Franz (W-F) law are used for the electrical and electronic thermal conductivity. The species diffusivity and the viscosity are also predicted using the mean square displacement and the Stokes-Einstein (S-E) relation. Alloying Ga causes more disordered structure, i.e., broadening the atomic distance near the In and Sn atoms, which reduces the transport properties and the melting temperature. The K-G treatment shows excellent agreement with the experimental results while Z-F treatment formula slightlymore » overestimates the electrical conductivity. The predicted thermal conductivity also shows good agreement with the experiments. The species diffusivity and the viscosity are slightly reduced by the alloying of Ga with In and Sn atoms. Good agreements are found with available experimental results and new predicted transport-property results are provided.« less

Diffusion behavior of lipid vesicles in entangled polymer solutions.

PubMed Central

Cao, X; Bansil, R; Gantz, D; Moore, E W; Niu, N; Afdhal, N H

1997-01-01

Dynamic light scattering was used to follow the tracer diffusion of phospholipid/cholesterol vesicles in aqueous polyacrylamide solutions and compared with the diffusive behavior of polystyrene (PS) latex spheres of comparable diameters. Over the range of the matrix concentration examined (Cp = 0.1-10 mg/ml), the diffusivities of the PS spheres and the large multilamellar vesicles exhibited the Stokes-Einstein (SE) relation, while the diffusivity of the unilamellar vesicles did not follow the increase of the solution's viscosity caused by the presence of the matrix molecules. The difference between the diffusion behaviors of unilamellar vesicles and hard PS spheres of similar size is possibly due to the flexibility of the lipid bilayer of the vesicles. The unilamellar vesicles are capable of changing their shape to move through the entangled polymer solution so that the hindrance to their diffusion due to the presence of the polymer chains is reduced, while the rigid PS spheres have little flexibility and they encounter greater resistance. The multilamellar vesicles are less flexible, thus their diffusion is similar to the hard PS spheres of similar diameter. Images FIGURE 2 PMID:9336189

Quantifying the deformation of the red blood cell skeleton in shear flow

NASA Astrophysics Data System (ADS)

Peng, Zhangli; Zhu, Qiang

2012-02-01

To quantitatively predict the response of red blood cell (RBC) membrane in shear flow, we carried out multiphysics simulations by coupling a three-level multiscale approach of RBC membranes with a Boundary Element Method (BEM) for surrounding flows. Our multiscale approach includes a model of spectrins with the domain unfolding feature, a molecular-based model of the junctional complex with detailed protein connectivity and a whole cell Finite Element Method (FEM) model with the bilayer-skeleton friction derived from measured transmembrane protein diffusivity based on the Einstein-Stokes relation. Applying this approach, we investigated the bilayer-skeleton slip and skeleton deformation of healthy RBCs and RBCs with hereditary spherocytosis anemia during tank-treading motion. Compared with healthy cells, cells with hereditary spherocytosis anemia sustain much larger skeleton-bilayer slip and area deformation of the skeleton due to deficiency of transmembrane proteins. This leads to extremely low skeleton density and large bilayer-skeleton interaction force, both of which may cause bilayer loss. This finding suggests a possible mechanism of the development of hereditary spherocytosis anemia.

Simon Newcomb: America's Unofficial Astronomer Royal

NASA Astrophysics Data System (ADS)

Graham, John

2007-10-01

Bill Carter and Merri Sue Carter Mantazas; xiii + 213 pp.; ISBN 1-59113-803-5 2006; $26.95 This book introduced me to a commanding figure in American science from the late nineteenth century: Simon Newcomb. Newcomb has been called the nineteenth-century equivalent of Carl Sagan and Albert Einstein. He rose from humble beginnings to be the preeminent American astronomer of his generation. He made basic, far-reaching, and enduring contributions to positional astronomy and planetary dynamics. On the more practical side, he determined a remarkably accurate value for the velocity of light, one within 0.01% of the value accepted today. His work provided an experimental grounding for the special and general theories of relativity to be formulated by Einstein in the coming twentieth century.

Measurement incompatibility and Schrödinger-Einstein-Podolsky-Rosen steering in a class of probabilistic theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Banik, Manik, E-mail: manik11ju@gmail.com

Steering is one of the most counter intuitive non-classical features of bipartite quantum system, first noticed by Schrödinger at the early days of quantum theory. On the other hand, measurement incompatibility is another non-classical feature of quantum theory, initially pointed out by Bohr. Recently, Quintino et al. [Phys. Rev. Lett. 113, 160402 (2014)] and Uola et al. [Phys. Rev. Lett. 113, 160403 (2014)] have investigated the relation between these two distinct non-classical features. They have shown that a set of measurements is not jointly measurable (i.e., incompatible) if and only if they can be used for demonstrating Schrödinger-Einstein-Podolsky-Rosen steering. Themore » concept of steering has been generalized for more general abstract tensor product theories rather than just Hilbert space quantum mechanics. In this article, we discuss that the notion of measurement incompatibility can be extended for general probability theories. Further, we show that the connection between steering and measurement incompatibility holds in a border class of tensor product theories rather than just quantum theory.« less

Quantum Landau damping in dipolar Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Mendonça, J. T.; Terças, H.; Gammal, A.

2018-06-01

We consider Landau damping of elementary excitations in Bose-Einstein condensates (BECs) with dipolar interactions. We discuss quantum and quasiclassical regimes of Landau damping. We use a generalized wave-kinetic description of BECs which, apart from the long-range dipolar interactions, also takes into account the quantum fluctuations and the finite-energy corrections to short-range interactions. Such a description is therefore more general than the usual mean-field approximation. The present wave-kinetic approach is well suited for the study of kinetic effects in BECs, such as those associated with Landau damping, atom trapping, and turbulent diffusion. The inclusion of quantum fluctuations and energy corrections changes the dispersion relation and the damping rates, leading to possible experimental signatures of these effects. Quantum Landau damping is described with generality, and particular examples of dipolar condensates in two and three dimensions are studied. The occurrence of roton-maxon excitations, and their relevance to Landau damping, are also considered in detail. The present approach is mainly based on a linear perturbative procedure, but the nonlinear regime of Landau damping, which includes atom trapping and atom diffusion, is also briefly discussed.

String Theory: Big Problem for Small Size

ERIC Educational Resources Information Center

Sahoo, S.

2009-01-01

String theory is the most promising candidate theory for a unified description of all the fundamental forces that exist in nature. It provides a mathematical framework that combines quantum theory with Einstein's general theory of relativity. The typical size of a string is of the order of 10[superscript -33] cm, called the Planck length. But due…

Why Do Things Fall? How to Explain Why Gravity Is Not a Force

ERIC Educational Resources Information Center

Stannard, Warren B.

2018-01-01

In most high school physics classes, gravity is described as an attractive force between two masses as formulated by Newton over 300 years ago. Einstein's general theory of relativity implies that gravitational effects are instead the result of a "curvature" of space-time. However, explaining why things fall without resorting to Newton's…

Interactive Visualization of a Thin Disc around a Schwarzschild Black Hole

ERIC Educational Resources Information Center

Muller, Thomas; Frauendiener, Jorg

2012-01-01

In a first course in general relativity, the Schwarzschild spacetime is the most discussed analytic solution to Einstein's field equations. Unfortunately, there is rarely enough time to study the optical consequences of the bending of light for some advanced examples. In this paper, we present how the visual appearance of a thin disc around a…

Geometry as an Object of Experience: The Missed Debate between Poincare and Einstein

ERIC Educational Resources Information Center

Hacyan, Shahen

2009-01-01

According to Poincare, a geometry cannot be an object of experience since any geometrical experiment must be realized with physical objects, such as rulers and light rays, and it is only their properties that can be tested. This position was apparently refuted by general relativity and the successful confirmation of its predictions by astronomical…

Blood coagulation profiling in patients using optical thromboelastography (OTEG) (Conference Presentation)

NASA Astrophysics Data System (ADS)

Tripathi, Markandey M.; Tshikudi, Diane M.; Hajjarian, Zeinab; Van Cott, Elizabeth M.; Nadkarni, Seemantini K.

2016-02-01

Impaired blood coagulation is often associated with increased postoperative mortality and morbidity in cardiovascular patients. The capability for blood coagulation profiling rapidly at the bedside will enable the timely detection of coagulation defects and open the opportunity for tailoring therapy to correct specific coagulation deficits Optical Thromboelastography (OTEG), is an optical approach to quantify blood coagulation status within minutes using a few drops of whole blood. The goal of the current study is to evaluate the diagnostic accuracy of OTEG for rapid coagulation profiling in patients. In OTEG, temporal laser speckle intensity fluctuations from a drop of clotting blood are measured using a CMOS camera. To quantify coagulation status, the speckle intensity autocorrelation function is measured, the mean square displacement of scattering particles is extracted, and viscoelastic modulus (G), during coagulation is measured via the generalized Stokes-Einstein relation. By quantifying time-resolved changes in G, the coagulation parameters, reaction time (R), clot progression time (K), clot progression rate (Angle), and maximum clot strength (MA) are derived. In this study, the above coagulation parameters were measured using OTEG in 269 patients and compared with standard mechanical Thromboelastography (TEG). Our results showed a strong correlation between OTEG and TEG measurements for all parameters: R-time (R=0.80, p<0.001), clotting time (R=0.78, p<0.001), Angle (R=0.58, p<0.001), and MA (R=0.60, p<0.001). These results demonstrate the unique capability of OTEG for rapid quantification of blood coagulation status to potentially improve clinical capability for identifying impaired coagulation in cardiovascular patients at the point of care.

Bose-Einstein distribution of money in a free-market economy. II

NASA Astrophysics Data System (ADS)

Kürten, K. E.; Kusmartsev, F. V.

2011-01-01

We argue about the application of methods of statistical mechanics to free economy (Kusmartsev F. V., Phys. Lett. A, 375 (2011) 966) and find that the most general distribution of money or income in a free-market economy has a general Bose-Einstein distribution form. Therewith the market is described by three parameters: temperature, chemical potential and the space dimensionality. Numerical simulations and a detailed analysis of a generic model confirm this finding.

An Exact Solution of Einstein-Maxwell Gravity Coupled to a Scalar Field

NASA Technical Reports Server (NTRS)

Turyshev, S. G.

1995-01-01

The general solution to low-energy string theory representing static spherically symmetric solution of the Einstein-Maxwell gravity with a massless scalar field has been found. Some of the partial cases appear to coincide with known solutions to black holes, naked singularities, and gravity and electromagnetic fields.

Gravitational Waves from Isolated Systems: Surprising Consequences of a Positive Cosmological Constant.

PubMed

Ashtekar, Abhay; Bonga, Béatrice; Kesavan, Aruna

2016-02-05

There is a deep tension between the well-developed theory of gravitational waves from isolated systems and the presence of a positive cosmological constant Λ, however tiny. In particular a generalization of Einstein's 1918 quadrupole formula that would allow a positive Λ is not yet available. We first explain the principal difficulties and then show that it is possible to overcome them in the weak field limit. These results also provide concrete hints for constructing the Λ>0 generalization of the Bondi-Sachs framework for full, nonlinear general relativity.

Gravitational Waves from Isolated Systems: Surprising Consequences of a Positive Cosmological Constant

NASA Astrophysics Data System (ADS)

Ashtekar, Abhay; Bonga, Béatrice; Kesavan, Aruna

2016-02-01

There is a deep tension between the well-developed theory of gravitational waves from isolated systems and the presence of a positive cosmological constant Λ , however tiny. In particular a generalization of Einstein's 1918 quadrupole formula that would allow a positive Λ is not yet available. We first explain the principal difficulties and then show that it is possible to overcome them in the weak field limit. These results also provide concrete hints for constructing the Λ >0 generalization of the Bondi-Sachs framework for full, nonlinear general relativity.

Generalized INF-SUP condition for Chebyshev approximation of the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Bernardi, Christine; Canuto, Claudio; Maday, Yvon

1986-01-01

An abstract mixed problem and its approximation are studied; both are well-posed if and only if several inf-sup conditions are satisfied. These results are applied to a spectral Galerkin method for the Stokes problem in a square, when it is formulated in Chebyshev weighted Sobolev spaces. Finally, a collocation method for the Navier-Stokes equations at Chebyshev nodes is analyzed.

On Einstein, Light Quanta, Radiation, and Relativity in 1905

ERIC Educational Resources Information Center

Miller, Arthur I.

1976-01-01

Analyzes section 8 of Einstein's relativity paper of 1905, "On the Electrodynamics of Moving Bodies," in its historical context. Relates this section to the rest of the relativity paper, to the genesis of relativity theory, and to contemporaneous work on radiation theory. (Author/MLH)

Vacuum stress energy density and its gravitational implications

NASA Astrophysics Data System (ADS)

Estrada, Ricardo; Fulling, Stephen A.; Kaplan, Lev; Kirsten, Klaus; Liu, Zhonghai; Milton, Kimball A.

2008-04-01

In nongravitational physics the local density of energy is often regarded as merely a bookkeeping device; only total energy has an experimental meaning—and it is only modulo a constant term. But in general relativity the local stress-energy tensor is the source term in Einstein's equation. In closed universes, and those with Kaluza-Klein dimensions, theoretical consistency demands that quantum vacuum energy should exist and have gravitational effects, although there are no boundary materials giving rise to that energy by van der Waals interactions. In the lab there are boundaries, and in general the energy density has a nonintegrable singularity as a boundary is approached (for idealized boundary conditions). As pointed out long ago by Candelas and Deutsch, in this situation there is doubt about the viability of the semiclassical Einstein equation. Our goal is to show that the divergences in the linearized Einstein equation can be renormalized to yield a plausible approximation to the finite theory that presumably exists for realistic boundary conditions. For a scalar field with Dirichlet or Neumann boundary conditions inside a rectangular parallelepiped, we have calculated by the method of images all components of the stress tensor, for all values of the conformal coupling parameter and an exponential ultraviolet cutoff parameter. The qualitative features of contributions from various classes of closed classical paths are noted. Then the Estrada-Kanwal distributional theory of asymptotics, particularly the moment expansion, is used to show that the linearized Einstein equation with the stress-energy near a plane boundary as source converges to a consistent theory when the cutoff is removed. This paper reports work in progress on a project combining researchers in Texas, Louisiana and Oklahoma. It is supported by NSF Grants PHY-0554849 and PHY-0554926.

Equivalent off-diagonal cosmological models and ekpyrotic scenarios in -modified, massive, and einstein gravity

NASA Astrophysics Data System (ADS)

Vacaru, Sergiu I.

2015-04-01

We reinvestigate how generic off-diagonal cosmological solutions depending, in general, on all spacetime coordinates can be constructed in massive and -modified gravity using the anholonomic frame deformation method. New classes of locally anisotropic and (in-) homogeneous cosmological metrics are constructed with open and closed spatial geometries. By resorting to such solutions, we show that they describe the late time acceleration due to effective cosmological terms induced by nonlinear off-diagonal interactions, possible modifications of the gravitational action and graviton mass. The cosmological metrics and related Stückelberg fields are constructed in explicit form up to nonholonomic frame transforms of the Friedmann-Lamaître-Robertson-Walker (FLRW) coordinates. The solutions include matter, graviton mass, and other effective sources modeling nonlinear gravitational and matter field interactions with polarization of physical constants and deformations of metrics, which may explain dark energy and dark matter effects. However, we argue that it is not always necessary to modify gravity if we consider the effective generalized Einstein equations with nontrivial vacuum and/or non-minimal coupling with matter. Indeed, we state certain conditions when such configurations mimic interesting solutions in general relativity and modifications, for instance, when we can extract the general Painlevé-Gullstrand and FLRW metrics. In a more general context, we elaborate on a reconstruction procedure for off-diagonal cosmological solutions which describe cyclic and ekpyrotic universes. Finally, open issues and further perspectives are discussed.

Covariant Conformal Decomposition of Einstein Equations

NASA Astrophysics Data System (ADS)

Gourgoulhon, E.; Novak, J.

It has been shown1,2 that the usual 3+1 form of Einstein's equations may be ill-posed. This result has been previously observed in numerical simulations3,4. We present a 3+1 type formalism inspired by these works to decompose Einstein's equations. This decomposition is motivated by the aim of stable numerical implementation and resolution of the equations. We introduce the conformal 3-``metric'' (scaled by the determinant of the usual 3-metric) which is a tensor density of weight -2/3. The Einstein equations are then derived in terms of this ``metric'', of the conformal extrinsic curvature and in terms of the associated derivative. We also introduce a flat 3-metric (the asymptotic metric for isolated systems) and the associated derivative. Finally, the generalized Dirac gauge (introduced by Smarr and York5) is used in this formalism and some examples of formulation of Einstein's equations are shown.

Characteristics of sediment transport at selected sites along the Missouri River, 2011–12

USGS Publications Warehouse

Rus, David L.; Galloway, Joel M.; Alexander, Jason S.

2015-10-22

The Modified-Einstein Procedure tended to predict greater total-sediment loads when compared to measured values. These differences may be the result of sediment deficits in the Missouri River that lead to an overprediction by the Modified-Einstein Procedure, the unsampled zone above the streambed that leads to an underprediction by the suspended sampler, or general uncertainty in the sampling approach. The differences between total-sediment load obtained through measurements and that estimated from applied theoretical procedures such as the Modified-Einstein Procedure pose a challenge for reliably characterizing total-sediment transport. Though it is not clear which of the two techniques is more accurate, the general tendency of the two to be within an order of magnitude of one another may be adequate for many sediment studies.

Double-black-hole solutions of the Einstein-Maxwell-dilaton theory in five dimensions

NASA Astrophysics Data System (ADS)

Stelea, Cristian

2018-01-01

We describe a solution-generating technique that maps a static charged solution of the Einstein-Maxwell theory in four (or five) dimensions to a five-dimensional solution of the Einstein-Maxwell-Dilaton theory. As examples of this technique first we show how to construct the dilatonic version of the Reissner-Nordström solution in five dimensions and then we consider the more general case of the double black hole solutions and describe some of their properties. We found that in the general case the value of the conical singularities in between the black holes is affected by the dilaton's coupling constant to the gauge field and only in the particular case when all charges are proportional to the masses this dependence cancels out.

Einstein's Cosmos (German Title: Einsteins Kosmos)

NASA Astrophysics Data System (ADS)

Duerbeck, Hilmar W.; Dick, Wolfgang R.

The different contributions of the present volume illuminate the interaction between Einstein and his colleagues when the foundations of modern cosmology were laid: First, the relativistic effects in the solar system, the gravitational redshift in the solar spectrum, and Einstein's relations with Freundlich and Eddington. Second, the cosmological models of Einstein, de Sitter, Friedmann, and Lemaître, which were discussed controversely till the end of the 1920s. Other scientists have also widened or critically questioned Einstein's insight and knowledge: Schwarzschild, Selety, Silberstein, and Mandl, whose life and work is discussed in separate articles. In those days, politics more than ever in history had influenced the lifes of scientists. Therefore, some comments on the ``political cosmos'' that has influenced decisively Einstein's life are also given. A special role in popularizing Einstein's world view was played by Archenhold Observatory in Berlin. A list of Einstein memorial places and a bibliographic list conclude the present book. All papers are written in German, and have English abstracts.

Solar physics in Potsdam. (German Title: Sonnenphysik in Potsdam)

NASA Astrophysics Data System (ADS)

Staude, Jürgen

Solar research initiated the establishment of the Astrophysical Observatory Potsdam (AOP) in 1874. The present contribution outlines the development of solar physics in Potsdam from the early history of the AOP to this day. The main topics are the work of Karl Schwarzschild, the investigations related to the general theory of relativity, the foundation of the Einstein tower, Walter Grotrian's founding of modern coronal physics, and the investigations of sunspot magnetic fields.

It’s About Time -- Understanding China’s Strategic Patience

DTIC Science & Technology

2012-03-18

Einstein and Stephen 3 Hawking, made conceptualizing time easier to accept by linking time with space. Time and space are inherently linked together...same regardless of how you were moving - exactly as experiments and mathematics of the day showed them to be. In 1905, Albert Einstein published...speeds relative to each other. Einstein explained that when two objects are moving at independent constant speeds, emphasizing the relative motion

Variation of fundamental constants on sub- and super-Hubble scales: From the equivalence principle to the multiverse

NASA Astrophysics Data System (ADS)

Uzan, Jean-Philippe

2013-02-01

Fundamental constants play a central role in many modern developments in gravitation and cosmology. Most extensions of general relativity lead to the conclusion that dimensionless constants are actually dynamical fields. Any detection of their variation on sub-Hubble scales would signal a violation of the Einstein equivalence principle and hence a lead to gravity beyond general relativity. On super-Hubble scales, or maybe should we say on super-universe scales, such variations are invoked as a solution to the fine-tuning problem, in connection with an anthropic approach.

Relativistic thermodynamics, a Lagrangian field theory for general flows including rotation

NASA Astrophysics Data System (ADS)

Frønsdal, Christian

Any theory that is based on an action principle has a much greater predictive power than one that does not have such a formulation. The formulation of a dynamical theory of General Relativity, including matter, is here viewed as a problem of coupling Einstein’s theory of pure gravity to an independently chosen and well-defined field theory of matter. It is well known that this is accomplished in a most natural way when both theories are formulated as relativistic, Lagrangian field theories, as is the case with Einstein-Maxwell theory. Special matter models of this type have been available; here a more general thermodynamical model that allows for vortex flows is presented. In a wider context, the problem of subjecting hydrodynamics and thermodynamics to an action principle is one that has been pursued for at least 150 years. A solution to this problem has been known for some time, but only under the strong restriction to potential flows. A variational principle for general flows has become available. It represents a development of the Navier-Stokes-Fourier approach to fluid dynamics. The principal innovation is the recognition that two kinds of flow velocity fields are needed, one the gradient of a scalar field and the other the time derivative of a vector field, the latter closely associated with vorticity. In the relativistic theory that is presented here, the latter is the Hodge dual of an exact 3-form, well known as the notoph field of Ogievetskij and Palubarinov, the B-field of Kalb and Ramond and the vorticity field of Lund and Regge. The total number of degrees of freedom of a unary system, including the density and the two velocity fields is 4, as expected — as in classical hydrodynamics. In this paper, we do not reduce Einstein’s dynamical equation for the metric to phenomenology, which would have denied the relevance of any intrinsic dynamics for the matter sector, nor do we abandon the equation of continuity - the very soul of hydrodynamics.

Ambitwistor formulations of R 2 gravity and ( DF)2 gauge theories

NASA Astrophysics Data System (ADS)

Azevedo, Thales; Engelund, Oluf Tang

2017-11-01

We consider D-dimensional amplitudes in R 2 gravities (conformal gravity in D = 4) and in the recently introduced ( DF)2 gauge theory, from the perspective of the CHY formulae and ambitwistor string theory. These theories are related through the BCJ double-copy construction, and the ( DF)2 gauge theory obeys color-kinematics duality. We work out the worldsheet details of these theories and show that they admit a formulation as integrals on the support of the scattering equations, or alternatively, as ambitwistor string theories. For gravity, this generalizes the work done by Berkovits and Witten on conformal gravity to D dimensions. The ambitwistor is also interpreted as a D-dimensional generalization of Witten's twistor string (SYM + conformal supergravity). As part of our ambitwistor investigation, we discover another ( DF)2 gauge theory containing a photon that couples to Einstein gravity. This theory can provide an alternative KLT description of Einstein gravity compared to the usual Yang-Mills squared.

Bulk entanglement gravity without a boundary: Towards finding Einstein's equation in Hilbert space

NASA Astrophysics Data System (ADS)

Cao, ChunJun; Carroll, Sean M.

2018-04-01

We consider the emergence from quantum entanglement of spacetime geometry in a bulk region. For certain classes of quantum states in an appropriately factorized Hilbert space, a spatial geometry can be defined by associating areas along codimension-one surfaces with the entanglement entropy between either side. We show how radon transforms can be used to convert these data into a spatial metric. Under a particular set of assumptions, the time evolution of such a state traces out a four-dimensional spacetime geometry, and we argue using a modified version of Jacobson's "entanglement equilibrium" that the geometry should obey Einstein's equation in the weak-field limit. We also discuss how entanglement equilibrium is related to a generalization of the Ryu-Takayanagi formula in more general settings, and how quantum error correction can help specify the emergence map between the full quantum-gravity Hilbert space and the semiclassical limit of quantum fields propagating on a classical spacetime.

Cosmological Models and Stability

NASA Astrophysics Data System (ADS)

Andersson, Lars

Principles in the form of heuristic guidelines or generally accepted dogma play an important role in the development of physical theories. In particular, philosophical considerations and principles figure prominently in the work of Albert Einstein. As mentioned in the talk by Jiří Bičák at this conference, Einstein formulated the equivalence principle, an essential step on the road to general relativity, during his time in Prague 1911-1912. In this talk, I would like to discuss some aspects of cosmological models. As cosmology is an area of physics where "principles" such as the "cosmological principle" or the "Copernican principle" play a prominent role in motivating the class of models which form part of the current standard model, I will start by comparing the role of the equivalence principle to that of the principles used in cosmology. I will then briefly describe the standard model of cosmology to give a perspective on some mathematical problems and conjectures on cosmological models, which are discussed in the later part of this paper.

General Theory of Relativity: Will It Survive the Next Decade?

NASA Technical Reports Server (NTRS)

Bertolami, Orfeu; Paramos, Jorge; Turyshev, Slava G.

2006-01-01

The nature of gravity is fundamental to our understanding of our own solar system, the galaxy and the structure and evolution of the Universe. Einstein's general theory of relativity is the standard model that is used for almost ninety years to describe gravitational phenomena on these various scales. We review the foundations of general relativity, discuss the recent progress in the tests of relativistic gravity, and present motivations for high-accuracy gravitational experiments in space. We also summarize the science objectives and technology needs for the laboratory experiments in space with laboratory being the entire solar system. We discuss the advances in our understanding of fundamental physics anticipated in the near future and evaluate discovery potential for the recently proposed gravitational experiments.

Generalized second-order slip boundary condition for nonequilibrium gas flows

NASA Astrophysics Data System (ADS)

Guo, Zhaoli; Qin, Jishun; Zheng, Chuguang

2014-01-01

It is a challenging task to model nonequilibrium gas flows within a continuum-fluid framework. Recently some extended hydrodynamic models in the Navier-Stokes formulation have been developed for such flows. A key problem in the application of such models is that suitable boundary conditions must be specified. In the present work, a generalized second-order slip boundary condition is developed in which an effective mean-free path considering the wall effect is used. By combining this slip scheme with certain extended Navier-Stokes constitutive relation models, we obtained a method for nonequilibrium gas flows with solid boundaries. The method is applied to several rarefied gas flows involving planar or curved walls, including the Kramers' problem, the planar Poiseuille flow, the cylindrical Couette flow, and the low speed flow over a sphere. The results show that the proposed method is able to give satisfied predictions, indicating the good potential of the method for nonequilibrium flows.

About Some Regge-Like Relations for (stable) Black Holes

NASA Astrophysics Data System (ADS)

Recami, E.; Tonin-Zanchin, V.; del Popolo, A.; Gambera, M.

1997-08-01

We associated, in a classical formulation of "strong gravity", hadron constituents with suitable stationary, axisymmetric solutions of some new Einstein-type equations supposed to describe the strong field inside hadrons. These new equations can be obtained by the Einstein equations with cosmological term Lambda. As a consequence, Lambda and the masses M result in our theory to be scaled up, and transformed into a "hadronic constant" and into "strong masses", respectively. Due to the unusual range of Lambda and M values considered, we met a series of solutions of the Kerr-Newman-de Sitter (hereafter KNdS) type with rather interesting properties. The requirement that those solutions be stable, i.e., that their temperature (or surface gravity) be vanishingly small, implies the coincidence of at least two of their (in general, three) horizons. Imposing the stability condition of a certain horizon does yield (once chosen the values of J, q and Lambda) mass and radius of the associated black-hole (hereafter BH). In the case of ordinary Einstein equations and for stable BHs of the KNdS type, we get in particular Regge-like (hereafter RL) relations among mass M, angular momentum J, charge q and cosmological constant Lambda; which did not receive enough attention in the previous literature. Besides, we show some particular and interesting cases of these relations. Another interesting point is that, with few exceptions, all such relations (among M, J, q, Lambda) lead to solutions that can be regarded as (stable) cosmological models.

Bose-Einstein condensation of light: general theory.

PubMed

Sob'yanin, Denis Nikolaevich

2013-08-01

A theory of Bose-Einstein condensation of light in a dye-filled optical microcavity is presented. The theory is based on the hierarchical maximum entropy principle and allows one to investigate the fluctuating behavior of the photon gas in the microcavity for all numbers of photons, dye molecules, and excitations at all temperatures, including the whole critical region. The master equation describing the interaction between photons and dye molecules in the microcavity is derived and the equivalence between the hierarchical maximum entropy principle and the master equation approach is shown. The cases of a fixed mean total photon number and a fixed total excitation number are considered, and a much sharper, nonparabolic onset of a macroscopic Bose-Einstein condensation of light in the latter case is demonstrated. The theory does not use the grand canonical approximation, takes into account the photon polarization degeneracy, and exactly describes the microscopic, mesoscopic, and macroscopic Bose-Einstein condensation of light. Under certain conditions, it predicts sub-Poissonian statistics of the photon condensate and the polarized photon condensate, and a universal relation takes place between the degrees of second-order coherence for these condensates. In the macroscopic case, there appear a sharp jump in the degrees of second-order coherence, a sharp jump and kink in the reduced standard deviations of the fluctuating numbers of photons in the polarized and whole condensates, and a sharp peak, a cusp, of the Mandel parameter for the whole condensate in the critical region. The possibility of nonclassical light generation in the microcavity with the photon Bose-Einstein condensate is predicted.

Integrability of geodesics and action-angle variables in Sasaki-Einstein space T^{1,1}

NASA Astrophysics Data System (ADS)

Visinescu, Mihai

2016-09-01

We briefly describe the construction of Stäkel-Killing and Killing-Yano tensors on toric Sasaki-Einstein manifolds without working out intricate generalized Killing equations. The integrals of geodesic motions are expressed in terms of Killing vectors and Killing-Yano tensors of the homogeneous Sasaki-Einstein space T^{1,1}. We discuss the integrability of geodesics and construct explicitly the action-angle variables. Two pairs of frequencies of the geodesic motions are resonant giving way to chaotic behavior when the system is perturbed.

Shear free, twisting Einstein-Maxwell metrics in the Newman-Penrose formalism

NASA Technical Reports Server (NTRS)

Lind, R. W.

1972-01-01

The problem of finding algebraically special solutions to the vacuum Einstein-Maxwell equations was investigated using a spin coefficient formalism. The general case in which the degenerate null vectors are not hypersurface orthogonal is reduced to a problem of solving five coupled differential equations that are no longer dependent on the affine parameter along the degenerate null directions. It is shown that the most general regular, shear-free, nonradiating solution to these equations is the Kerr-Newman metric.

Dynamical spacetimes in conformal gravity

NASA Astrophysics Data System (ADS)

Zhang, Hongsheng; Zhang, Yi; Li, Xin-Zhou

2017-08-01

The conformal gravity remarkably boosts our prehension of gravity theories. We find a series of dynamical solutions in the W2-conformal gravity, including generalized Schwarzschild-Friedmann-Robertson-Walker (GSFRW), charged generalized Schwarzschild-Friedmann-Robertson-Walker (CGSFRW), especially rotating Friedmann-Robertson-Walker (RFRW), charged rotating Friedmann-Robertson-Walker (CRFRW), and a dynamical cylindrically symmetric solutions. The RFRW, CRFRW and the dynamical cylindrically symmetric solutions are never found in the Einstein gravity and modified gravities. The GSFRW and CGSFRW solutions take different forms from the corresponding solutions in the Einstein gravity.

Towards a second law for Lovelock theories

NASA Astrophysics Data System (ADS)

Bhattacharyya, Sayantani; Haehl, Felix M.; Kundu, Nilay; Loganayagam, R.; Rangamani, Mukund

2017-03-01

In classical general relativity described by Einstein-Hilbert gravity, black holes behave as thermodynamic objects. In particular, the laws of black hole mechanics can be interpreted as laws of thermodynamics. The first law of black hole mechanics extends to higher derivative theories via the Noether charge construction of Wald. One also expects the statement of the second law, which in Einstein-Hilbert theory owes to Hawking's area theorem, to extend to higher derivative theories. To argue for this however one needs a notion of entropy for dynamical black holes, which the Noether charge construction does not provide. We propose such an entropy function for the family of Lovelock theories, treating the higher derivative terms as perturbations to the Einstein-Hilbert theory. Working around a dynamical black hole solution, and making no assumptions about the amplitude of departure from equilibrium, we construct a candidate entropy functional valid to all orders in the low energy effective field theory. This entropy functional satisfies a second law, modulo a certain subtle boundary term, which deserves further investigation in non-spherically symmetric situations.

Measuring Starlight Deflection during the 2017 Eclipse: Repeating the Experiment that made Einstein Famous

NASA Astrophysics Data System (ADS)

Bruns, Donald

2016-05-01

In 1919, astronomers performed an experiment during a solar eclipse, attempting to measure the deflection of stars near the sun, in order to verify Einstein's theory of general relativity. The experiment was very difficult and the results were marginal, but the success made Albert Einstein famous around the world. Astronomers last repeated the experiment in 1973, achieving an error of 11%. In 2017, using amateur equipment and modern technology, I plan to repeat the experiment and achieve a 1% error. The best available star catalog will be used for star positions. Corrections for optical distortion and atmospheric refraction are better than 0.01 arcsec. During totality, I expect 7 or 8 measurable stars down to magnitude 9.5, based on analysis of previous eclipse measurements taken by amateurs. Reference images, taken near the sun during totality, will be used for precise calibration. Preliminary test runs performed during twilight in April 2016 and April 2017 can accurately simulate the sky conditions during totality, providing an accurate estimate of the final uncertainty.

Classes of exact Einstein Maxwell solutions

NASA Astrophysics Data System (ADS)

Komathiraj, K.; Maharaj, S. D.

2007-12-01

We find new classes of exact solutions to the Einstein Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric field intensity; in particular we generate the Einstein universe for particular parameter values.

Gravitation: Foundations and Frontiers

NASA Astrophysics Data System (ADS)

Padmanabhan, T.

2010-01-01

1. Special relativity; 2. Scalar and electromagnetic fields in special relativity; 3. Gravity and spacetime geometry: the inescapable connection; 4. Metric tensor, geodesics and covariant derivative; 5. Curvature of spacetime; 6. Einstein's field equations and gravitational dynamics; 7. Spherically symmetric geometry; 8. Black holes; 9. Gravitational waves; 10. Relativistic cosmology; 11. Differential forms and exterior calculus; 12. Hamiltonian structure of general relativity; 13. Evolution of cosmological perturbations; 14. Quantum field theory in curved spacetime; 15. Gravity in higher and lower dimensions; 16. Gravity as an emergent phenomenon; Notes; Index.

Relativity and indeterminism

NASA Astrophysics Data System (ADS)

Byrne, Patrick H.

1981-12-01

It is well known that Albert Einstein adhered to a deterministic world view throughout his career. Nevertheless, his developments of the special and general theories of relativity prove to be incompatible with that world view. Two different forms of determinism—classical Laplacian determinism and the determinism of isolated systems—are considered. Through careful considerations of what concretely is involved in predicting future states of the entire universe, or of isolated systems, it is shown that the demands of the theories of relativity make these deterministic positions untenable.

Astrophysical observations: lensing and eclipsing Einstein's theories.

PubMed

Bennett, Charles L

2005-02-11

Albert Einstein postulated the equivalence of energy and mass, developed the theory of special relativity, explained the photoelectric effect, and described Brownian motion in five papers, all published in 1905, 100 years ago. With these papers, Einstein provided the framework for understanding modern astrophysical phenomena. Conversely, astrophysical observations provide one of the most effective means for testing Einstein's theories. Here, I review astrophysical advances precipitated by Einstein's insights, including gravitational redshifts, gravitational lensing, gravitational waves, the Lense-Thirring effect, and modern cosmology. A complete understanding of cosmology, from the earliest moments to the ultimate fate of the universe, will require developments in physics beyond Einstein, to a unified theory of gravity and quantum physics.

The Confrontation between General Relativity and Experiment.

PubMed

Will, Clifford M

2014-01-01

The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is reviewed and updated. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eötvös experiment, tests of local Lorentz invariance and clock experiments. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, the Nordtvedt effect in lunar motion, and frame-dragging. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and a growing family of other binary pulsar systems is yielding new tests, especially of strong-field effects. Current and future tests of relativity will center on strong gravity and gravitational waves.

Review of Software Platforms for Agent Based Models

DTIC Science & Technology

2008-04-01

EINSTein 4.3.2 Battlefield Python (optional, for batch runs) MANA 4.3.3 Battlefield N/A MASON 4.3.4 General Java NetLogo 4.3.5 General Logo-variant...through the use of relatively simple Python scripts. It also has built-in functions for parameter sweeps, and can plot the resulting fitness landscape ac...Nonetheless its ease of use, and support for automatic drawing of agents in 2D or 3D2 makes this a suitable platform for beginner programmers. 2Only in the

f (R ,Rμν 2) at one loop

NASA Astrophysics Data System (ADS)

Ohta, N.; Percacci, R.; Pereira, A. D.

2018-05-01

We compute the one-loop divergences in a theory of gravity with a Lagrangian of the general form f (R ,Rμ νRμ ν), on an Einstein background. We also establish that the one-loop effective action is invariant under a duality that consists of changing certain parameters in the relation between the metric and the quantum fluctuation field. Finally, we discuss the unimodular version of such a theory and establish its equivalence at one-loop order with the general case.

Conventionalism and integrable Weyl geometry

NASA Astrophysics Data System (ADS)

Pucheu, M. L.

2015-03-01

Since the appearance of Einstein's general relativity, gravitation has been associated to the space-time curvature. This theory introduced a geometrodynamic language which became a convenient tool to predict matter behaviour. However, the properties of space-time itself cannot be measurable by experiments. Taking Poincaré idea that the geometry of space-time is merely a convention, we show that the general theory of relativity can be completely reformulated in a more general setting, a generalization of Riemannian geometry, namely, the Weyl integrable geometry. The choice of this new mathematical language implies, among other things, that the path of particles and light rays should now correspond to Weylian geodesies. Such modification in the dynamic of bodies brings a new perception of physical phenomena that we will explore.

General technique for discrete retardation-modulation polarimetry

NASA Technical Reports Server (NTRS)

Saxena, Indu

1993-01-01

The general theory and rigorous solutions of the Stokes parameters of light of a new technique in time-resolved ellipsometry are outlined. In this technique the phase of the linear retarder is stepped over three discrete values over a time interval for which the Stokes vector is determined. The technique has an advantage over synchronous detection techniques, as it can be implemented as a digitizable system.

Generalization of uncertainty relation for quantum and stochastic systems

NASA Astrophysics Data System (ADS)

Koide, T.; Kodama, T.

2018-06-01

The generalized uncertainty relation applicable to quantum and stochastic systems is derived within the stochastic variational method. This relation not only reproduces the well-known inequality in quantum mechanics but also is applicable to the Gross-Pitaevskii equation and the Navier-Stokes-Fourier equation, showing that the finite minimum uncertainty between the position and the momentum is not an inherent property of quantum mechanics but a common feature of stochastic systems. We further discuss the possible implication of the present study in discussing the application of the hydrodynamic picture to microscopic systems, like relativistic heavy-ion collisions.

Einstein and the "Crucial" Experiment

ERIC Educational Resources Information Center

Holton, Gerald

1969-01-01

Examines the widespread view that it was the crucial Michelson-Morley experiment that led Einstein to formulate the special relativity theory. From Einstein's writings, evidence is presented that no such direct genetic connection exists. The author suggests that the historian of science must resist the experimenticist's fallacy of imposing a…

Development of a time-dependent incompressible Navier-Stokes solver based on a fractional-step method

NASA Technical Reports Server (NTRS)

Rosenfeld, Moshe

1990-01-01

The main goals are the development, validation, and application of a fractional step solution method of the time-dependent incompressible Navier-Stokes equations in generalized coordinate systems. A solution method that combines a finite volume discretization with a novel choice of the dependent variables and a fractional step splitting to obtain accurate solutions in arbitrary geometries is extended to include more general situations, including cases with moving grids. The numerical techniques are enhanced to gain efficiency and generality.

Lichnerowicz-type equations with sign-changing nonlinearities on complete manifolds with boundary

NASA Astrophysics Data System (ADS)

Albanese, Guglielmo; Rigoli, Marco

2017-12-01

We prove an existence theorem for positive solutions to Lichnerowicz-type equations on complete manifolds with boundary (M , ∂ M , 〈 , 〉) and nonlinear Neumann conditions. This kind of nonlinear problems arise quite naturally in the study of solutions for the Einstein-scalar field equations of General Relativity in the framework of the so called Conformal Method.

Static and Dynamic Traversable Wormholes

NASA Astrophysics Data System (ADS)

Adamiak, Jaroslaw P.

2008-09-01

The aim of this work is to discuss the effects found in static and dynamic wormholes that occur as a solution of Einstein equations in general relativity. The ground is prepared by presentation of faster than light effects, then the focus is narrowed to Morris-Thorne framework for a static spherically symmetric wormhole. Two types of dynamic worm-holes, evolving and rotating, are considered.

Rectification of General Relativity, Experimental Verifications, and Errors of the Wheeler School

NASA Astrophysics Data System (ADS)

Lo, C. Y.

2013-09-01

General relativity is not yet consistent. Pauli has misinterpreted Einstein's 1916 equivalence principle that can derive a valid field equation. The Wheeler School has distorted Einstein's 1916 principle to be his 1911 assumption of equivalence, and created new errors. Moreover, errors on dynamic solutions have allowed the implicit assumption of a unique coupling sign that violates the principle of causality. This leads to the space-time singularity theorems of Hawking and Penrose who "refute" applications for microscopic phenomena, and obstruct efforts to obtain a valid equation for the dynamic case. These errors also explain the mistakes in the press release of the 1993 Nobel Committee, who was unaware of the non-existence of dynamic solutions. To illustrate the damages to education, the MIT Open Course Phys. 8.033 is chosen. Rectification of errors confirms that E = mc2 is only conditionally valid, and leads to the discovery of the charge-mass interaction that is experimentally confirmed and subsequently the unification of gravitation and electromagnetism. The charge-mass interaction together with the unification predicts the weight reduction (instead of increment) of charged capacitors and heated metals, and helps to explain NASA's Pioneer anomaly and potentially other anomalies as well.

Cosmological applications of singular hypersurfaces in general relativity

NASA Astrophysics Data System (ADS)

Laguna-Castillo, Pablo

Three applications to cosmology of surface layers, based on Israel's formalism of singular hypersurfaces and thin shells in general relativity, are presented. Einstein's field equations are analyzed in the presence of a bubble nucleated in vacuum phase transitions within the context of the old inflationary universe scenario. The evolution of a bubble with vanishing surface energy density is studied. It is found that such bubbles lead to a worm-hole matching. Next, the observable four-dimensional universe is considered as a singular hypersurface of discontinuity embedded in a five-dimensional Kaluza-Klein cosmology. It is possible to rewrite the projected five-dimensional Einstein equations on the surface layer in a similar way to the four-dimensional Robertson-Walker cosmology equations. Next, a model is described for an infinite-length, straight U(1) cosmic string as a cylindrical, singular shell enclosing a region of false vacuum. A set of equations is introduced which are required to develop a three-dimensional computer code whose purpose is to study the process of intercommuting cosmic strings with the inclusion of gravitational effects. The outcome is evolution and constraint equations for the gravitational, scalar and gauge field of two initially separated, perpendicular, cosmic strings.

The Stokes-Einstein relationship and the levitation effect: size-dependent diffusion maximum in dense fluids and close-packed disordered solids.

PubMed

Ghorai, Pradip Kr; Yashonath, S

2005-03-31

We report a molecular dynamics study of a binary mixture consisting of a large (host) particle and a smaller (guest) particle whose radius is varied over a range. These simulations investigate the possible existence of a diffusion anomaly or levitation effect in dense fluids, previously seen for guest molecules diffusing within porous solids. The voids in the larger component have been characterized in terms of void and neck distributions by means of Voronoi polyhedral analysis. Four different mixtures with differing ratios of guest to host diffusivities (D) have been studied. The results suggest that the diffusion anomaly is seen in both close-packed solids with disorder and dense fluids. In the latter, the void network is constantly and dynamically changing and possesses a considerable degree of disorder. The two regimes, viz., the linear regime (LR) and the anomalous regime (AR), found for porous solids are shown to exist for a dense medium as well. The linear regime is characterized by D(g) proportional to 1/sigma(gg)(2), where sigma(gg) is the diameter of the guest. The anomalous regime exhibits a maximum in D up to rather high temperatures (T = 1.663), even though in porous solids the maximum disappears at higher temperatures. In agreement with previous studies on porous solids, a particle in the AR is associated with lower activation energy, lower friction, and less backscattering in the velocity autocorrelation function when compared to a particle in the LR. Wavevector dependent self-diffusivity, Delta, and decay of the intermediate scattering function, F(s)(k, t), exhibit contrasting behaviors for the LR and AR. For LR, Delta exhibits a minimum at values of k at which there are spatial correlations in S(k) while a smooth decrease with k is seen for AR. For LR, F(s)(k, t) shows a biexponential decay corresponding to two different time scales of motion. Probably, the fast decay is associated with motion within the first shell of solvent neighbors and the slow decay with motion past these shells. For AR, a single-exponential decay is seen. The results indicate a breakdown of the Stokes-Einstein (SE) relationship. The relevant quantity that determines the validity of the SE relationship is the levitation parameter which is indirectly related to the solute/solvent radius ratio and not either the size of the solute or the solvent alone.

On the existence of topological dyons and dyonic black holes in anti-de Sitter Einstein-Yang-Mills theories with compact semisimple gauge groups

NASA Astrophysics Data System (ADS)

Baxter, J. Erik

2018-05-01

Here we study the global existence of "hairy" dyonic black hole and dyon solutions to four-dimensional, anti-de Sitter Einstein-Yang-Mills theories for a general simply connected and semisimple gauge group G, for the so-called topologically symmetric systems, concentrating here on the regular case. We generalise here cases in the literature which considered purely magnetic spherically symmetric solutions for a general gauge group and topological dyonic solutions for s u (N ) . We are able to establish the global existence of non-trivial solutions to all such systems, both near existing embedded solutions and as |Λ| → ∞. In particular, we can identify non-trivial solutions where the gauge field functions have no zeroes, which in the s u (N ) case proved important to stability. We believe that these are the most general analytically proven solutions in 4D anti-de Sitter Einstein-Yang-Mills systems to date.

Predicting Binary Black Hole Collisions Using Numerical Methods in Collaboration with LIGO

NASA Astrophysics Data System (ADS)

Afshari, Nousha; Lovelace, Geoffrey

2015-04-01

Detecting astronomical gravitational waves will soon open a new window on the universe. The effects of gravitational waves have already been seen indirectly, but a direct observation of these waves will test Einstein's theory of general relativity under the most extreme conditions. The Laser Interferometer Gravitational-Wave Observatory, or LIGO, will soon begin searching for gravitational waves, and the first direct detections are likely in the next few years. To help LIGO detect as many gravitational waves as possible, a major research effort is underway to accurately predict the expected waves. In this presentation, I will discuss new supercomputer simulations of merging black holes--some of the brightest sources of gravitational waves--that I have completed using the Spectral Einstein Code (http://www.black-holes.org/SpEC.html).

Theory and experiment in gravitational physics

NASA Technical Reports Server (NTRS)

Will, C. M.

1981-01-01

New technological advances have made it feasible to conduct measurements with precision levels which are suitable for experimental tests of the theory of general relativity. This book has been designed to fill a new need for a complete treatment of techniques for analyzing gravitation theory and experience. The Einstein equivalence principle and the foundations of gravitation theory are considered, taking into account the Dicke framework, basic criteria for the viability of a gravitation theory, experimental tests of the Einstein equivalence principle, Schiff's conjecture, and a model theory devised by Lightman and Lee (1973). Gravitation as a geometric phenomenon is considered along with the parametrized post-Newtonian formalism, the classical tests, tests of the strong equivalence principle, gravitational radiation as a tool for testing relativistic gravity, the binary pulsar, and cosmological tests.

Theory and experiment in gravitational physics

NASA Astrophysics Data System (ADS)

Will, C. M.

New technological advances have made it feasible to conduct measurements with precision levels which are suitable for experimental tests of the theory of general relativity. This book has been designed to fill a new need for a complete treatment of techniques for analyzing gravitation theory and experience. The Einstein equivalence principle and the foundations of gravitation theory are considered, taking into account the Dicke framework, basic criteria for the viability of a gravitation theory, experimental tests of the Einstein equivalence principle, Schiff's conjecture, and a model theory devised by Lightman and Lee (1973). Gravitation as a geometric phenomenon is considered along with the parametrized post-Newtonian formalism, the classical tests, tests of the strong equivalence principle, gravitational radiation as a tool for testing relativistic gravity, the binary pulsar, and cosmological tests.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiménez, Jose Beltrán; Heisenberg, Lavinia; Olmo, Gonzalo J., E-mail: jose.beltran@uclouvain.be, E-mail: Lavinia.Heisenberg@unige.ch, E-mail: gonzalo.olmo@csic.es

We generalize the ultraviolet sector of gravitation via a Born-Infeld action using lessons from massive gravity. The theory contains all of the elementary symmetric polynomials and is treated in the Palatini formalism. We show how the connection can be solved algebraically to be the Levi-Civita connection of an effective metric. The non-linearity of the algebraic equations yields several branches, one of which always reduces to General Relativity at low curvatures. We explore in detail a minimal version of the theory, for which we study solutions in the presence of a perfect fluid with special attention to the cosmological evolution. Inmore » vacuum we recover Ricci-flat solutions, but also an additional physical solution corresponding to an Einstein space. The existence of two physical branches remains for non-vacuum solutions and, in addition, the branch that connects to the Einstein space in vacuum is not very sensitive to the specific value of the energy density. For the branch that connects to the General Relativity limit we generically find three behaviours for the Hubble function depending on the equation of state of the fluid, namely: either there is a maximum value for the energy density that connects continuously with vacuum, or the energy density can be arbitrarily large but the Hubble function saturates and remains constant at high energy densities, or the energy density is unbounded and the Hubble function grows faster than in General Relativity. The second case is particularly interesting because it could offer an interesting inflationary epoch even in the presence of a dust component. Finally, we discuss the possibility of avoiding certain types of singularities within the minimal model.« less

Implications of Einstein-Weyl Causality on Quantum Mechanics

NASA Astrophysics Data System (ADS)

Bendaniel, David

A fundamental physical principle that has consequences for the topology of space-time is the principle of Einstein-Weyl causality. This also has quantum mechanical manifestations. Borchers and Sen have rigorously investigated the mathematical implications of Einstein-Weyl causality and shown the denumerable space-time Q2 would be implied. They were left with important philosophical paradoxes regarding the nature of the physical real line E, e.g., whether E = R, the real line of mathematics. In order to remove these paradoxes an investigation into a constructible foundation is suggested. We have pursued such a program and find it indeed provides a dense, denumerable space-time and, moreover, an interesting connection with quantum mechanics. We first show that this constructible theory contains polynomial functions which are locally homeomorphic with a dense, denumerable metric space R* and are inherently quantized. Eigenfunctions governing fields can then be effectively obtained by computational iteration. Postulating a Lagrangian for fields in a compactified space-time, we get a general description of which the Schrodinger equation is a special case. From these results we can then also show that this denumerable space-time is relational (in the sense that space is not infinitesimally small if and only if it contains a quantized field) and, since Q2 is imbedded in R*2, it directly fulfills the strict topological requirements for Einstein-Weyl causality. Therefore, the theory predicts that E = R*.

The space-time solution element method: A new numerical approach for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Scott, James R.; Chang, Sin-Chung

1995-01-01

This paper is one of a series of papers describing the development of a new numerical method for the Navier-Stokes equations. Unlike conventional numerical methods, the current method concentrates on the discrete simulation of both the integral and differential forms of the Navier-Stokes equations. Conservation of mass, momentum, and energy in space-time is explicitly provided for through a rigorous enforcement of both the integral and differential forms of the governing conservation laws. Using local polynomial expansions to represent the discrete primitive variables on each cell, fluxes at cell interfaces are evaluated and balanced using exact functional expressions. No interpolation or flux limiters are required. Because of the generality of the current method, it applies equally to the steady and unsteady Navier-Stokes equations. In this paper, we generalize and extend the authors' 2-D, steady state implicit scheme. A general closure methodology is presented so that all terms up through a given order in the local expansions may be retained. The scheme is also extended to nonorthogonal Cartesian grids. Numerous flow fields are computed and results are compared with known solutions. The high accuracy of the scheme is demonstrated through its ability to accurately resolve developing boundary layers on coarse grids. Finally, we discuss applications of the current method to the unsteady Navier-Stokes equations.

Semigroup characterization of Besov type Morrey spaces and well-posedness of generalized Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Lin, Chin-Cheng; Yang, Qixiang

The well-posedness of generalized Navier-Stokes equations with initial data in some critical homogeneous Besov spaces and in some critical Q spaces was known. In this paper, we establish a wavelet characterization of Besov type Morrey spaces under the action of semigroup. As an application, we obtain the well-posedness of smooth solution for the generalized Navier-Stokes equations with initial data in some critical homogeneous Besov type Morrey spaces ( (1/2 ><β<1, γ1-γ2=1-2β), 1

Shape Optimization for Navier-Stokes Equations with Algebraic Turbulence Model: Existence Analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bulicek, Miroslav; Haslinger, Jaroslav; Malek, Josef

2009-10-15

We study a shape optimization problem for the paper machine headbox which distributes a mixture of water and wood fibers in the paper making process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The mathematical formulation leads to an optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by a generalized stationary Navier-Stokes system with nontrivial mixed boundary conditions. In this paper we prove the existence of solutions both to the generalized Navier-Stokes system and tomore » the shape optimization problem.« less

Einstein, the Universe, and All That: An Introduction to Relativity

NASA Technical Reports Server (NTRS)

Prescod-Weinstein, Chandra

2011-01-01

Black holes) an expanding universe) space and time inextricably tied together) GPS ... What was this Einstein guy thinking?!? In this tutorial) I'll give an overview of Einstein's theories of relativity and the wild things they say about our Universe. What really happens when a particle crosses an event horizon? What is the future of the Universe? And how can we know it? Wh I'll try to touch on these questions and in so doing) give the talks in the Cosmology) Gravitation and Relativity sessions some context.

An Out-of-Math Experience: Einstein, Relativity, and the Developmental Mathematics Student.

ERIC Educational Resources Information Center

Fiore, Greg

2000-01-01

Discusses Einstein's special relativity theory and some of the developmental mathematics involved. Presents motivational classroom materials used in discussing relative-motion problems, evaluating a radical expression, graphing with asymptotes, interpreting a graph, studying variation, and solving literal and radical equations. (KHR)

Hidden symmetries on Kerr-NUT-(A)dS metrics of Einstein-Sasaki type

NASA Astrophysics Data System (ADS)

Visinescu, Mihai

2013-01-01

The hidden symmetries of higher dimensional Euclideanised Kerr-NUT-(A)dS metrics are investigated. In certain scaling limits these metrics are related to the Einstein-Sasaki ones. The complete set of Killing-Yano tensors of the Einstein-Sasaki spaces are presented. For this purpose the Killing forms of the Calabi-Yau cone over the Einstein-Sasaki manifold are constructed. Two new Killing forms on Einstein-Sasaki manifolds are identified associated with the complex volume form of the cone manifolds. As a concrete example we present the complete set of Killing-Yano tensors on the five-dimensional Einstein-Sasaki Y(p, q) spaces. The corresponding hidden symmetries are not anomalous and the geodesic equations are superintegrable.

Locality, reflection, and wave-particle duality

NASA Astrophysics Data System (ADS)

Mugur-Schächter, Mioara

1987-08-01

Bell's theorem is believed to establish that the quantum mechanical predictions do not generally admit a causal representation compatible with Einsten's principle of separability, thereby proving incompatibility between quantum mechanics and relativity. This interpretation is contested via two convergent approaches which lead to a sharp distinction between quantum nonseparability and violation of Einstein's theory of relativity. In a first approach we explicate from the quantum mechanical formalism a concept of “reflected dependence.” Founded on this concept, we produce a causal representation of the quantum mechanical probability measure involved in Bell's proof, which is clearly separable in Einstein's sense, i.e., it does not involve supraluminal velocities, and nevertheless is “nonlocal” in Bell's sense. So Bell locality and Einstein separability are distinct qualifications, and Bell nonlocality (or Bell nonseparability) and Einstein separability are not incompatible. It is then proved explicitly that with respect to the mentioned representation Bell's derivation does not hold. So Bell's derivation does not establish that any Einstein-separable representation is incompatible with quantum mechanics. This first—negative—conclusion is a syntactic fact. The characteristics of the representation and of the reasoning involved in the mentioned counterexample to the usual interpretation of Bell's theorem suggest that the representation used—notwithstanding its ability to bring forth the specified syntactic fact—is not factually true. Factual truth and syntactic properties also have to be radically distinguished in their turn. So, in a second approach, starting from de Broglie's initial relativistic model of a microsystem, a deeper, factually acceptable representation is constructed. The analyses leading to this second representation show that quantum mechanics does indeed involve basically a certain sort of nonseparability, called here de Broglie-Bohr quantum nonseparability. But the de Broglie-Bohr quantum nonseparability is shown to stem directly from the relativistic character of the considerations which led Louis de Broglie to the fundamental relation p = h/λ, thereby being essentially consistent with relativity. As to Einstein separability, it appears to be a still insufficiently specified concept of which a future, improved specification, will probably be explicitly harmonizable with the de Broglie-Bohr quantum nonseparability. The ensemble of the conclusions obtained here brings forth a new concept of causality, a concept of folded, zigzag, reflexive causality, with respect to which the type of causality conceived of up to now appears as a particular case of outstretched, one-way causality. The reflexive causality is found compatible with the results of Aspect's experiment, and it suggests new experiments. Considered globally, the conclusions obtained in the present work might convert the conceptual situation created by Bell's proof into a process of unification of quantum mechanics and relativity.

Einstein and Millikan

NASA Astrophysics Data System (ADS)

Erwin, Charlotte

2005-03-01

Albert Einstein traveled to America by boat during the great depression to consult with scientists at the California Institute of Technology. He was a theoretical physicist, a Nobel Prize winner, and a 20th century folk hero. Few members of the general public understood his theories, but they idolized him all the same. The invitation came from physicist Robert Millikan, who had initiated a visiting-scholars program at Caltech shortly after he became head of the school in 1921. Einstein's visits to the campus in 1931, 1932, and 1933 capped Millikan's campaign to make Caltech one of the physics capitals of the world. Mount Wilson astronomer Edwin Hubble's discovery that redshifts are proportional to their distances from the observer challenged Einstein's cosmological picture of a static universe. The big question at Caltech in 1931 was whether Einstein would give up his cosmological constant and accept the idea of an expanding universe. By day, Einstein discussed his theory and its interpretation at length with Richard Tolman, Hubble, and the other scientists on the campus. By night, Einstein filled his travel diary with his personal impressions. During his third visit, Einstein sidestepped as long as possible the question of whether conditions in Germany might prevent his return there. After the January 30 announcement that Hitler had become chancellor of Germany, the question could no longer be evaded. He postponed his return trip for a few weeks and then went to Belgium for several months instead of to Berlin. In the fall of 1933, Albert Einstein returned to the United States as an emigre and became a charter member of Abraham Flexner's new Institute for Advanced Study in Princeton, New Jersey. Why did Einstein go to Princeton and not Pasadena?

Equivalence principles and electromagnetism

NASA Technical Reports Server (NTRS)

Ni, W.-T.

1977-01-01

The implications of the weak equivalence principles are investigated in detail for electromagnetic systems in a general framework. In particular, it is shown that the universality of free-fall trajectories (Galileo weak equivalence principle) does not imply the validity of the Einstein equivalence principle. However, the Galileo principle plus the universality of free-fall rotation states does imply the Einstein principle.

From Solvent-Free to Dilute Electrolytes: Essential Components for a Continuum Theory.

PubMed

Gavish, Nir; Elad, Doron; Yochelis, Arik

2018-01-04

The increasing number of experimental observations on highly concentrated electrolytes and ionic liquids show qualitative features that are distinct from dilute or moderately concentrated electrolytes, such as self-assembly, multiple-time relaxation, and underscreening, which all impact the emergence of fluid/solid interfaces, and the transport in these systems. Because these phenomena are not captured by existing mean-field models of electrolytes, there is a paramount need for a continuum framework for highly concentrated electrolytes and ionic liquid mixtures. In this work, we present a self-consistent spatiotemporal framework for a ternary composition that comprises ions and solvent employing a free energy that consists of short- and long-range interactions, along with an energy dissipation mechanism obtained by Onsager's relations. We show that the model can describe multiple bulk and interfacial morphologies at steady-state. Thus, the dynamic processes in the emergence of distinct morphologies become equally as important as the interactions that are specified by the free energy. The model equations not only provide insights into transport mechanisms beyond the Stokes-Einstein-Smoluchowski relations but also enable qualitative recovery of three distinct regions in the full range of the nonmonotonic electrical screening length that has been recently observed in experiments in which organic solvent is used to dilute ionic liquids.

Lilienfeld Prize Talk: New Results on Water in Bulk, Nanoconfined, and Biological Environments

NASA Astrophysics Data System (ADS)

Stanley, H. Eugene

2008-04-01

This talk will introduce some of the 63 unsolved mysteries of water, and will demonstrate some recent progress in solving them combining information provided by water in bulk, nanoconfined, and biological environments. In particular, we will present evidence from experiments designed to test the hypothesis that water displays ``polymorphism'' in that it can exist in two liquid different phases and display a novel liquid-liquid critical point. The concept of liquid polymorphism is also proving useful in understanding some of the anomalies of other liquids with local tetrahedral symmetry, such as silicon, silica, and carbon. In particular, the talk will discuss changes in dynamic transport properties [1], and water in biological environments, including a possible physical explanation for the phenomenon known as the protein glass transition [2]. [1] P. Kumar, S. V. Buldyrev, S. L. Becker, P. H. Poole, F. W. Starr, and H. E. Stanley, ``Relation between the Widom line and the Breakdown of the Stokes--Einstein Relation in Supercooled Water,'' Proc. Natl. Acad. Sci. USA 104, 9575-9579 (2007). [2] P. Kumar, Z. Yan, L. Xu, M. G. Mazza, S. V. Buldyrev, S.-H. Chen. S. Sastry, and H. E. Stanley, ``Glass Transition in Biomolecules and the Liquid-Liquid Critical Point of Water,'' Phys. Rev. Lett. 97, 177802 (2006).

Dynamic decoupling and local atomic order of a model multicomponent metallic glass-former.

PubMed

Kim, Jeongmin; Sung, Bong June

2015-06-17

The dynamics of multicomponent metallic alloys is spatially heterogeneous near glass transition. The diffusion coefficient of one component of the metallic alloys may also decouple from those of other components, i.e., the diffusion coefficient of each component depends differently on the viscosity of metallic alloys. In this work we investigate the dynamic heterogeneity and decoupling of a model system for multicomponent Pd43Cu27Ni10P20 melts by using a hard sphere model that considers the size disparity of alloys but does not take chemical effects into account. We also study how such dynamic behaviors would relate to the local atomic structure of metallic alloys. We find, from molecular dynamics simulations, that the smallest component P of multicomponent Pd43Cu27Ni10P20 melts becomes dynamically heterogeneous at a translational relaxation time scale and that the largest major component Pd forms a slow subsystem, which has been considered mainly responsible for the stabilization of amorphous state of alloys. The heterogeneous dynamics of P atoms accounts for the breakdown of Stokes-Einstein relation and also leads to the dynamic decoupling of P and Pd atoms. The dynamically heterogeneous P atoms decrease the lifetime of the local short-range atomic orders of both icosahedral and close-packed structures by orders of magnitude.

The probability density function (PDF) of Lagrangian Turbulence

NASA Astrophysics Data System (ADS)

Birnir, B.

2012-12-01

The statistical theory of Lagrangian turbulence is derived from the stochastic Navier-Stokes equation. Assuming that the noise in fully-developed turbulence is a generic noise determined by the general theorems in probability, the central limit theorem and the large deviation principle, we are able to formulate and solve the Kolmogorov-Hopf equation for the invariant measure of the stochastic Navier-Stokes equations. The intermittency corrections to the scaling exponents of the structure functions require a multiplicative (multipling the fluid velocity) noise in the stochastic Navier-Stokes equation. We let this multiplicative noise, in the equation, consists of a simple (Poisson) jump process and then show how the Feynmann-Kac formula produces the log-Poissonian processes, found by She and Leveque, Waymire and Dubrulle. These log-Poissonian processes give the intermittency corrections that agree with modern direct Navier-Stokes simulations (DNS) and experiments. The probability density function (PDF) plays a key role when direct Navier-Stokes simulations or experimental results are compared to theory. The statistical theory of turbulence is determined, including the scaling of the structure functions of turbulence, by the invariant measure of the Navier-Stokes equation and the PDFs for the various statistics (one-point, two-point, N-point) can be obtained by taking the trace of the corresponding invariant measures. Hopf derived in 1952 a functional equation for the characteristic function (Fourier transform) of the invariant measure. In distinction to the nonlinear Navier-Stokes equation, this is a linear functional differential equation. The PDFs obtained from the invariant measures for the velocity differences (two-point statistics) are shown to be the four parameter generalized hyperbolic distributions, found by Barndorff-Nilsen. These PDF have heavy tails and a convex peak at the origin. A suitable projection of the Kolmogorov-Hopf equations is the differential equation determining the generalized hyperbolic distributions. Then we compare these PDFs with DNS results and experimental data.

Perturbation of a planetary orbit by the Lambda-term (dark energy) in Einstein equations

NASA Astrophysics Data System (ADS)

Dumin, Yurii

The problem of cosmological influences at small (e.g. interplanetary) scales is discussed for a few decades, starting from the early 1930's, but still remains unsolved definitively by now [1]. This subject became especially topical in the context of the dark-energy-dominated cosmology, because the commonly-used arguments against the local Hubble expansion (such as Einstein-Straus theorem [2]) are inapplicable when the most contribution to the energy density of the Universe comes from the perfectly-uniform dark energy (Lambda-term). Moreover, there are some empirical evidences in favor of the local cosmological influences. For example, inclusion of the local Hubble expansion into dynamics of the Earth-Moon system enables us to resolve a long-standing discrepancy in the rates of secular increase of the lunar semi-major axis (a) mea-sured by the lunar laser ranging and (b) derived from the astrometric observations of the Earth's rotation deceleration [3, 4]. The aim of the present report is to provide a detailed mathematical treatment of the respective two-body problem in the framework of General Relativity, which is based on the Kottler metric reduced to the Robertson-Walker cosmological asymptotics, as outlined in our earlier work [5]. References: 1. W.B. Bonnor. Gen. Rel. Grav., v.32, p.1005 (2000). 2. A. Einstein and E.G. Straus. Rev. Mod. Phys., v.17, p.120 (1945). 3. Yu.V. Dumin. Adv. Space Res., v.31, p.2461 (2003). 4. Yu.V. Dumin. In Proc. 11th Marcel Grossmann Meeting on General Relativity, World Sci., Singapore, p.1752 (2008). 5. Yu.V. Dumin. Phys. Rev. Lett., v.98, p.059001 (2007).

Complete integrability of geodesics in toric Sasaki-Einstein spaces

NASA Astrophysics Data System (ADS)

Visinescu, Mihai

2016-01-01

We describe a method for constructing Killing-Yano tensors on toric Sasaki- Einstein manifolds using their geometrical properties. We take advantage of the fact that the metric cones of these spaces are Calabi-Yau manifolds. The complete list of special Killing forms can be extracted making use of the description of the Calabi-Yau manifolds in terms of toric data. This general procedure for toric Sasaki-Einstein manifolds is exemplified in the case of the 5-dimensional spaces Yp,q and T1,1. Finally we discuss the integrability of geodesic motion in these spaces.

General Relativity and Spacetime Relationism.

NASA Astrophysics Data System (ADS)

Hoefer, Carl

1992-01-01

This dissertation takes up the project of showing that, in the context of the general theory of relativity (GTR), spacetime relationism is not a refuted or hopeless view, as many in the recent literature have maintained (John Earman, Michael Friedman, and others). Most of the challenges to the relationist view in General Relativity can be satisfactorily answered; in addition, the opposing absolutist and substantivalist views of spacetime can be shown to be problematic. The crucial burden for relationists concerned with GTR is to show that the realistic cosmological models, i.e. those that may be roughly accurate representations of our universe, satisfy Mach's ideas about the origin of inertia. This dissertation clears the way for and begins such a demonstration. After a brief discussion of the problem of the nature of spacetime and its history in the Introduction, chapters 2 and 3 provide conceptual analysis and criticism of contemporary philosophical arguments about relationism, absolutism, and particularly substantivalism. The current best arguments in favor of substantivalism are shown to be flawed, with the exception of the argument from inertial and metrical structure; and on this issue, it is shown that both relationism and substantivalism need to argue for modifications of GTR (restriction of its models to those with certain features) in order to have a non-trivial explanation of inertial and metrical structure. For relationists, a Machian account of the origin of inertia in some models of GTR is required. Chapter 4 demonstrates that such a Machian account is equivalent to the demand for a truly general relativity of motion. Chapter 5 explores the history of Einstein's commitment to Mach's ideas in his work on GTR. Through an examination of the history of Einstein's attempts to impose Machian constraints on the models of General Relativity, further insight into the nature of this problem is obtained, as are reasons to believe that the project is by no means hopeless.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Krtous, Pavel; Frolov, Valeri P.; Kubiznak, David

We prove that the most general solution of the Einstein equations with the cosmological constant which admits a principal conformal Killing-Yano tensor is the Kerr-NUT-(A)dS metric. Even when the Einstein equations are not imposed, any spacetime admitting such hidden symmetry can be written in a canonical form which guarantees the following properties: it is of the Petrov type D, it allows the separation of variables for the Hamilton-Jacobi, Klein-Gordon, and Dirac equations, the geodesic motion in such a spacetime is completely integrable. These results naturally generalize the results obtained earlier in four dimensions.

Growth histories in bimetric massive gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berg, Marcus; Buchberger, Igor; Enander, Jonas

2012-12-01

We perform cosmological perturbation theory in Hassan-Rosen bimetric gravity for general homogeneous and isotropic backgrounds. In the de Sitter approximation, we obtain decoupled sets of massless and massive scalar gravitational fluctuations. Matter perturbations then evolve like in Einstein gravity. We perturb the future de Sitter regime by the ratio of matter to dark energy, producing quasi-de Sitter space. In this more general setting the massive and massless fluctuations mix. We argue that in the quasi-de Sitter regime, the growth of structure in bimetric gravity differs from that of Einstein gravity.

Competition between Bose-Einstein Condensation and Spin Dynamics.

PubMed

Naylor, B; Brewczyk, M; Gajda, M; Gorceix, O; Maréchal, E; Vernac, L; Laburthe-Tolra, B

2016-10-28

We study the impact of spin-exchange collisions on the dynamics of Bose-Einstein condensation by rapidly cooling a chromium multicomponent Bose gas. Despite relatively strong spin-dependent interactions, the critical temperature for Bose-Einstein condensation is reached before the spin degrees of freedom fully thermalize. The increase in density due to Bose-Einstein condensation then triggers spin dynamics, hampering the formation of condensates in spin-excited states. Small metastable spinor condensates are, nevertheless, produced, and they manifest in strong spin fluctuations.

Scalar-tensor Theories of Gravity: Some personal history

NASA Astrophysics Data System (ADS)

Brans, Carl H.

2008-12-01

From a perspective of some 50 years or more, this paper reviews my recall of the early days of scalar-tensor alternatives to standard Einstein general relativistic theory of gravity. Of course, the story begins long before my involvement, going back to the proposals of Nordström in 1914, and that of Kaluza, Klein, et al., a few years later, sol include reviews of these seminal ideas and those that followed in the 1920's through the 1940's. This early work concerned the search for a Unified Field Theory, unifying gravity and Electromagnetism, using five dimensional manifolds. This formalism included not only the electromagnetic spacetime vector potential within the five-metric, but also a spacetime scalar as the five-five metric component. Although this was at first regarded more as a nuisance, to be set to a constant, it turned out later that Fierz, Jordan, Einstein and Bergmann noticed that this scalar could be a field, possibly related to the Newtonian gravitational constant. Relatively little theoretical and experimental attention was given to these ideas until after the second world war when Bob Dicke, motivated by the ideas of Mach, Dirac, and others, suggested that this additional scalar, coupled only to the metric and matter, could provide a reasonable and viable alternative to standard Einstein theory. This is the point of my direct involvement with these topics. However, it was Dicke's prominence and expertise in experimental work, together with the blossoming of NASA's experimental tools, that caused the explosion of interest, experimental and theoretical, in this possible alternative to standard Einstein theory. This interest has waxed and waned over the last 50 years, and we summarize some of this work.

[THE ROLE OF PHILOSOPHICAL REFLECTIONS OF STANISLAW ZAREMBA IN THE CONTEXT OF A DISPUTE ON THE FOUNDATIONS OF THE THEORY OF RELATIVITY].

PubMed

Polak, Paweł

2014-01-01

The aim of this paper is to present the philosophical background of Stanisław Zaremba's critique of Einstein's theory of relativity. In the 1920s, Zaremba was the most prominent Polish opponent of this theory. His papers influenced some discussions related to Einstein's theory, especially in France and in Poland. This paper takes also into account the development of Zaremba's critique. The analysis of his papers shows that he never became a follower of the Einstein's theory of relativity. Such a statement compels us to confront it with the previous interpretations of Zaremba's thought.

The general theory of relativity - Why 'It is probably the most beautiful of all existing theories'

NASA Astrophysics Data System (ADS)

Chandrasekhar, S.

1984-03-01

An attempt is made to objectively evaluate the frequent judgment of Einstein's general theory of relativity, by such distinguished physicists as Pauli (1921), Dirac, Born, and Rutherford, as 'beautiful' and 'a work of art'. The criteria applied are that of Francis Bacon ('There is no excellent beauty that hath not some strangeness in the proportions') and that of Heisenberg ('Beauty is the proper conformity of the parts to one another and to the whole'). The strangeness in the proportions of the theory of general relativity consists in its relating, through juxtaposition, the concepts of space and time and those of matter and motion; these had previously been considered entirely independent. The criterion of 'conformity' is illustrated through the directness with which the theory allows the description of black holes.

What is Gravitational Lensing? (LBNL Summer Lecture Series)

ScienceCinema

Leauthaud, Alexie [Univ. of California, Berkeley, CA (United States). Berkeley Center for Cosmological Physics (BCCP); Nakajima, Reiko [Univ. of California, Berkeley, CA (United States). Berkeley Center for Cosmological Physics (BCCP)

2018-05-04

Summer Lecture Series 2009: Gravitational lensing is explained by Einstein's general theory of relativity: galaxies and clusters of galaxies, which are very massive objects, act on spacetime by causing it to become curved. Alexie Leauthaud and Reiko Nakajima, astrophysicists with the Berkeley Center for Cosmological Physics, will discuss how scientists use gravitational lensing to investigate the nature of dark energy and dark matter in the universe.

What is Gravitational Lensing? (LBNL Summer Lecture Series)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leauthaud, Alexie; Nakajima, Reiko

2009-07-28

Summer Lecture Series 2009: Gravitational lensing is explained by Einstein's general theory of relativity: galaxies and clusters of galaxies, which are very massive objects, act on spacetime by causing it to become curved. Alexie Leauthaud and Reiko Nakajima, astrophysicists with the Berkeley Center for Cosmological Physics, will discuss how scientists use gravitational lensing to investigate the nature of dark energy and dark matter in the universe.

Experimental constraints on metric and non-metric theories of gravity

NASA Technical Reports Server (NTRS)

Will, Clifford M.

1989-01-01

Experimental constraints on metric and non-metric theories of gravitation are reviewed. Tests of the Einstein Equivalence Principle indicate that only metric theories of gravity are likely to be viable. Solar system experiments constrain the parameters of the weak field, post-Newtonian limit to be close to the values predicted by general relativity. Future space experiments will provide further constraints on post-Newtonian gravity.

Gravitational Lensing

ScienceCinema

Lincoln, Don

2018-01-16

In a long line of intellectual triumphs, Einstein’s theory of general relativity was his greatest and most imaginative. It tells us that what we experience as gravity can be most accurately described as the bending of space itself. This idea leads to consequences, including gravitational lensing, which is caused by light traveling in this curved space. This is works in a way analogous to a lens (and hence the name). In this video, Fermilab’s Dr. Don Lincoln explains a little general relativity, a little gravitational lensing, and tells us how this phenomenon allows us to map out the matter of the entire universe, including the otherwise-invisible dark matter.

A superconducting gyroscope to test Einstein's general theory of relativity

NASA Technical Reports Server (NTRS)

Everitt, C. W. F.

1978-01-01

Schiff (1960) proposed a new test of general relativity based on measuring the precessions of the spin axes of gyroscopes in earth orbit. Since 1963 a Stanford research team has been developing an experiment to measure the two effects calculated by Schiff. The gyroscope consists of a uniform sphere of fused quartz 38 mm in diameter, coated with superconductor, electrically suspended and spinning at about 170 Hz in vacuum. The paper describes the proposed flight apparatus and the current state of development of the gyroscope, including techniques for manufacturing and measuring the gyro rotor and housing, generating ultralow magnetic fields, and mechanizing the readout.

Amazonia Introduced to General Relativity: The May 29, 1919, Solar Eclipse from a North-Brazilian Point of View

NASA Astrophysics Data System (ADS)

Crispino, Luís C. B.; de Lima, Marcelo C.

2016-12-01

In 1919, A. C. D. Crommelin and C. R. Davidson, British astronomers from the Greenwich Observatory in England, passed by Amazonia on their Brazilian journey aiming to measure the bending of stars' light rays during the total solar eclipse of May 29, 1919, and thereby put the theory of general relativity to the test. In the context of Crommelin's and Davidson's visit, we discuss how Amazonia was introduced to Einstein's theory of gravitation, and also the observations and repercussions of the May 29, 1919, solar eclipse in Belém, capital city of the North-Brazilian Pará state.

First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity

NASA Technical Reports Server (NTRS)

Cai, Z.; Manteuffel, T. A.; McCormick, S. F.

1996-01-01

Following our earlier work on general second-order scalar equations, here we develop a least-squares functional for the two- and three-dimensional Stokes equations, generalized slightly by allowing a pressure term in the continuity equation. By introducing a velocity flux variable and associated curl and trace equations, we are able to establish ellipticity in an H(exp 1) product norm appropriately weighted by the Reynolds number. This immediately yields optimal discretization error estimates for finite element spaces in this norm and optimal algebraic convergence estimates for multiplicative and additive multigrid methods applied to the resulting discrete systems. Both estimates are uniform in the Reynolds number. Moreover, our pressure-perturbed form of the generalized Stokes equations allows us to develop an analogous result for the Dirichlet problem for linear elasticity with estimates that are uniform in the Lame constants.

Three-variable solution in the (2+1)-dimensional null-surface formulation

NASA Astrophysics Data System (ADS)

Harriott, Tina A.; Williams, J. G.

2018-04-01

The null-surface formulation of general relativity (NSF) describes gravity by using families of null surfaces instead of a spacetime metric. Despite the fact that the NSF is (to within a conformal factor) equivalent to general relativity, the equations of the NSF are exceptionally difficult to solve, even in 2+1 dimensions. The present paper gives the first exact (2+1)-dimensional solution that depends nontrivially upon all three of the NSF's intrinsic spacetime variables. The metric derived from this solution is shown to represent a spacetime whose source is a massless scalar field that satisfies the general relativistic wave equation and the Einstein equations with minimal coupling. The spacetime is identified as one of a family of (2+1)-dimensional general relativistic spacetimes discovered by Cavaglià.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gergely, Laszlo A.

We study the possibility of brane-world generalization of the Einstein-Straus Swiss-cheese cosmological model. We find that the modifications induced by the brane-world scenario are excessively restrictive. At a first glance only the motion of the boundary is modified and the fluid in the exterior region is allowed to have pressure. The general relativistic Einstein-Straus model emerges in the low density limit. However by imposing that the central mass in the Schwarzschild voids is constant, a combination of the junction conditions and modified cosmological evolution leads to the conclusion that the brane is flat. Thus no generic Swiss-cheese universe can existmore » on the brane. The conclusion is not altered by the introduction of a cosmological constant in the FLRW regions. This shows that although allowed in the low density limit, the Einstein-Straus universe cannot emerge from cosmological evolution in the brane-world scenario.« less

Extrema of mass, first law of black hole mechanics, and a staticity theorem in Einstein-Maxwell-axion-dilaton gravity

NASA Astrophysics Data System (ADS)

Rogatko, Marek

1998-08-01

Using the ADM formulation of the Einstein-Maxwell axion-dilaton gravity we derive the formulas for the variation of mass and other asymptotic conserved quantities in the theory under consideration. Generalizing this kind of reasoning to the initial data for the manifold with an interior boundary we get the generalized first law of black hole mechanics. We consider an asymptotically flat solution to the Einstein-Maxwell axion-dilaton gravity describing a black hole with a Killing vector field timelike at infinity, the horizon of which comprises a bifurcate Killing horizon with a bifurcate surface. Supposing that the Killing vector field is asymptotically orthogonal to the static hypersurface with boundary S and a compact interior, we find that the solution is static in the exterior world, when the timelike vector field is normal to the horizon and has vanishing electric and axion-electric fields on static slices.

Quantification of topological changes of vorticity contours in two-dimensional Navier-Stokes flow.

PubMed

Ohkitani, Koji; Al Sulti, Fayeza

2010-06-01

A characterization of reconnection of vorticity contours is made by direct numerical simulations of the two-dimensional Navier-Stokes flow at a relatively low Reynolds number. We identify all the critical points of the vorticity field and classify them by solving an eigenvalue problem of its Hessian matrix on the basis of critical-point theory. The numbers of hyperbolic (saddles) and elliptic (minima and maxima) points are confirmed to satisfy Euler's index theorem numerically. Time evolution of these indices is studied for a simple initial condition. Generally speaking, we have found that the indices are found to decrease in number with time. This result is discussed in connection with related works on streamline topology, in particular, the relationship between stagnation points and the dissipation. Associated elementary procedures in physical space, the merging of vortices, are studied in detail for a number of snapshots. A similar analysis is also done using the stream function.

Measure-valued solutions to the complete Euler system revisited

NASA Astrophysics Data System (ADS)

Březina, Jan; Feireisl, Eduard

2018-06-01

We consider the complete Euler system describing the time evolution of a general inviscid compressible fluid. We introduce a new concept of measure-valued solution based on the total energy balance and entropy inequality for the physical entropy without any renormalization. This class of so-called dissipative measure-valued solutions is large enough to include the vanishing dissipation limits of the Navier-Stokes-Fourier system. Our main result states that any sequence of weak solutions to the Navier-Stokes-Fourier system with vanishing viscosity and heat conductivity coefficients generates a dissipative measure-valued solution of the Euler system under some physically grounded constitutive relations. Finally, we discuss the same asymptotic limit for the bi-velocity fluid model introduced by H.Brenner.

Determination of diffusion coefficient in disordered organic semiconductors

NASA Astrophysics Data System (ADS)

Rani, Varsha; Sharma, Akanksha; Ghosh, Subhasis

2016-05-01

Charge carrier transport in organic semiconductors is dominated by positional and energetic disorder in Gaussian density of states (GDOS) and is characterized by hopping through localized states. Due to the immobilization of charge carriers in these localized states, significant non-uniform carrier distribution exists, resulting diffusive transport. A simple, nevertheless powerful technique to determine diffusion coefficient D in disordered organic semiconductors has been presented. Diffusion coefficients of charge carriers in two technologically important organic molecular semiconductors, Pentacene and copper phthalocyanine (CuPc) have been measured from current-voltage (J-V) characteristics of Al/Pentacene/Au and Al/CuPc/Au based Schottky diodes. Ideality factor g and carrier mobility μ have been calculated from the exponential and space charge limited region respectively of J-V characteristics. Classical Einstein relation is not valid in organic semiconductors due to energetic disorders in DOS. Using generalized Einstein relation, diffusion coefficients have been obtained to be 1.31×10-6 and 1.73×10-7 cm2/s for Pentacene and CuPc respectively.

Inflation in Einstein-Cartan theory with energy-momentum tensor with spin

NASA Technical Reports Server (NTRS)

Fennelly, A. J.; Bradas, James C.; Smalley, Larry L.

1988-01-01

Generalized, or power-law, inflation is shown to necessarily exist for a simple, anisotropic (Bianchi Type I) cosmology in the Einstein-Cartan gravitational theory with the Ray-Smalley (RS) improved energy-momentum tensor with spin. Formal solution of the EC field equations with the fluid equations of motion explicitly shows inflation caused by the RS spin angular kinetic energy density.

A numerical approach to finding general stationary vacuum black holes

NASA Astrophysics Data System (ADS)

Adam, Alexander; Kitchen, Sam; Wiseman, Toby

2012-08-01

The Harmonic Einstein equation is the vacuum Einstein equation supplemented by a gauge fixing term which we take to be that of DeTurck. For static black holes analytically continued to Riemannian manifolds without boundary at the horizon, this equation has previously been shown to be elliptic, and Ricci flow and Newton’s method provide good numerical algorithms to solve it. Here we extend these techniques to the arbitrary cohomogeneity stationary case which must be treated in Lorentzian signature. For stationary spacetimes with globally timelike Killing vector the Harmonic Einstein equation is elliptic. In the presence of horizons and ergo-regions it is less obviously so. Motivated by the Rigidity theorem we study a class of stationary black hole spacetimes which is general enough to include many interesting higher dimensional solutions. We argue the Harmonic Einstein equation consistently truncates to this class of spacetimes giving an elliptic problem. The Killing horizons and axes of rotational symmetry are boundaries for this problem and we determine boundary conditions there. As a simple example we numerically construct 4D rotating black holes in a cavity using Anderson’s boundary conditions. We demonstrate both Newton’s method and Ricci flow to find these Lorentzian solutions.

Dynamic characteristics of a multi-wavelength Brillouin-Raman fiber laser assisted by multiple four-wave mixing processes in a ring cavity

NASA Astrophysics Data System (ADS)

Shirazi, M. R.; Mohamed Taib, J.; De La Rue, R. M.; Harun, S. W.; Ahmad, H.

2015-03-01

Dynamic characteristics of a multi-wavelength Brillouin-Raman fiber laser (MBRFL) assisted by four-wave mixing have been investigated through the development of Stokes and anti-Stokes lines under different combinations of Brillouin and Raman pump power levels and different Raman pumping schemes in a ring cavity. For a Stokes line of order higher than three, the threshold power was less than the saturation power of its last-order Stokes line. By increasing the Brillouin pump power, the nth order anti-Stokes and the (n+4)th order Stokes power levels were unexpectedly increased almost the same before the Stokes line threshold power. It was also found out that the SBS threshold reduction (SBSTR) depended linearly on the gain factor for the 1st and 2nd Stokes lines, as the first set. This relation for the 3rd and 4th Stokes lines as the second set, however, was almost linear with the same slope before SBSTR -6 dB, then, it approached to the linear relation in the first set when the gain factor was increased to 50 dB. Therefore, the threshold power levels of Stokes lines for a given Raman gain can be readily estimated only by knowing the threshold power levels in which there is no Raman amplification.

The Viking Relativity Experiment

NASA Technical Reports Server (NTRS)

Shapiro, I. I.; Reasenberg, R. D.; Macneil, P. E.; Goldstein, R. B.; Brenkle, J. P.; Cain, D. L.; Komarek, T.; Zygielbaum, A. I.; Cuddihy, W. F.; Michael, W. H., Jr.

1977-01-01

Measurements of the round-trip time of flight of radio signals transmitted from the earth to the Viking spacecraft are being analyzed to test the predictions of Einstein's theory of general relativity. According to this theory the signals will be delayed by up to approximately 250 microsec owing to the direct effect of solar gravity on the propagation. A very preliminary qualitative analysis of the Viking data obtained near the 1976 superior conjunction of Mars indicates agreement with the predictions to within the estimated uncertainty of 0.5%.

How black holes saved relativity

NASA Astrophysics Data System (ADS)

Prescod-Weinstein, Chanda

2016-02-01

While there have been many popular-science books on the historical and scientific legacy of Albert Einstein's general theory of relativity, a gap exists in the literature for a definitive, accessible history of the theory's most famous offshoot: black holes. In Black Hole, the science writer Marcia Bartusiak aims for a discursive middle ground, writing solely about black holes at a level suitable for both high-school students and more mature readers while also giving some broader scientific context for black-hole research.

Toward an explicit analysis of generalization: A stimulus control interpretation

PubMed Central

Kirby, Kimberly C.; Bickel, Warren K.

1988-01-01

Producing generality of treatment effects to new settings has been a critical concern for applied behavior analysts, but a systematic and reliable means of producing generality has yet to be provided. We argue that the principles of stimulus control and reinforcement underlie the production of most generalized effects; therefore, we suggest interpreting generalization programming in terms of stimulus control. The generalization programming procedures identified by Stokes and Baer (1977) are discussed in terms of both the stimulus control tactics explicitly identified and those that may be operating but are not explicitly identified. Our interpretation clarifies the critical components of Stokes and Baer's procedures and places greater emphasis on planning for generalization as a part of training procedures. PMID:22478006

Relativity experiment on Helios - A status report

NASA Technical Reports Server (NTRS)

Anderson, J. D.; Melbourne, W. G.; Cain, D. L.; Lau, E. K.; Wong, S. K.; Kundt, W.

1975-01-01

The relativity experiment on Helios (Experiment 11) uses S-band and Doppler data, and spacecraft-solar-orbital data to measure the effects of general relativity in the solar system and the quadrupole moment in the solar gravitational field. Specifically, Experiment 11 is converned with measuring the following effects: (1) relativistic orbital corrections described by two parameters of the space-time metric which are both equal to unity in Einstein's theory; (2) orbital perturbations caused by a finite quadrupole moment of an oblate sun, described by zonal harmonics in the solar gravitational field.

Testing Einstein in Space: The Gravity Probe B Relativity Mission

NASA Astrophysics Data System (ADS)

Mester, John

The Gravity Probe B Relativity Mission was successfully launched on April 20, 2004 from Vandenberg Air Force Base in California, a culmination of 40 years of collaborative development at Stanford University and NASA. The goal of the GP-B experiment is to perform precision tests of two independent predictions of general relativity, the geodetic effect and frame dragging. On-orbit cryogenic operations lasted 17.3 months, exceeding requirements. Analysis of the science data is now in progress with a planned announcement of results scheduled for December 2007.

The Gravity-Probe-B relativity gyroscope experiment - Development of the prototype flight instrument

NASA Technical Reports Server (NTRS)

Turneaure, J. P.; Everitt, C. W. F.; Parkinson, B. W.; Bardas, D.; Breakwell, J. V.

1989-01-01

The Gravity-Probe-B relativity gyroscope experiment (GP-B) will measure the geodetic and frame-dragging precession rates of gyroscopes in a 650 km high polar orbit about the earth. The goal is to measure these two effects, which are predicted by Einstein's General Theory of Relativity, to 0.01 percent (geodetic) and 1 percent (frame-dragging). This paper presents the development progress for full-size prototype flight hardware including the gyroscopes, gyro readout and magnetic shielding system, and an integrated ground test instrument.

Comparing numerical and analytic approximate gravitational waveforms

NASA Astrophysics Data System (ADS)

Afshari, Nousha; Lovelace, Geoffrey; SXS Collaboration

2016-03-01

A direct observation of gravitational waves will test Einstein's theory of general relativity under the most extreme conditions. The Laser Interferometer Gravitational-Wave Observatory, or LIGO, began searching for gravitational waves in September 2015 with three times the sensitivity of initial LIGO. To help Advanced LIGO detect as many gravitational waves as possible, a major research effort is underway to accurately predict the expected waves. In this poster, I will explore how the gravitational waveform produced by a long binary-black-hole inspiral, merger, and ringdown is affected by how fast the larger black hole spins. In particular, I will present results from simulations of merging black holes, completed using the Spectral Einstein Code (black-holes.org/SpEC.html), including some new, long simulations designed to mimic black hole-neutron star mergers. I will present comparisons of the numerical waveforms with analytic approximations.

Fragments of Science: Festschrift for Mendel Sachs

NASA Astrophysics Data System (ADS)

Ram, Michael

1999-11-01

The Table of Contents for the full book PDF is as follows: * Preface * Sketches at a Symposium * For Mendel Sachs * The Constancy of an Angular Point of View * Information-Theoretic Logic and Transformation-Theoretic Logic * The Invention of the Transistor and the Realization of the Hole * Mach's Principle, Newtonian Gravitation, Absolute Space, and Einstein * The Sun, Our Variable Star * The Inconstant Sun: Symbiosis of Time Variations of Sunspots, Atmospheric Radiocarbon, Aurorae, and Tree Ring Growth * Other Worlds * Super-Classical Quantum Mechanics * A Probabilistic Approach to the Phase Problem of X-Ray Crystallography * A Nonlinear Twist on Inertia Gives Unified Electroweak Gravitation * Neutrino Oscillations * On an Incompleteness in the General-Relativistic Description of Gravitation * All Truth is One * Ideas of Physics: Correspondence between Colleagues * The Influence of the Physics and Philosophy of Einstein's Relativity on My Attitudes in Science: An Autobiography

Gravitational waves — A review on the theoretical foundations of gravitational radiation

NASA Astrophysics Data System (ADS)

Dirkes, Alain

2018-05-01

In this paper, we review the theoretical foundations of gravitational waves in the framework of Albert Einstein’s theory of general relativity. Following Einstein’s early efforts, we first derive the linearized Einstein field equations and work out the corresponding gravitational wave equation. Moreover, we present the gravitational potentials in the far away wave zone field point approximation obtained from the relaxed Einstein field equations. We close this review by taking a closer look on the radiative losses of gravitating n-body systems and present some aspects of the current interferometric gravitational waves detectors. Each section has a separate appendix contribution where further computational details are displayed. To conclude, we summarize the main results and present a brief outlook in terms of current ongoing efforts to build a spaced-based gravitational wave observatory.

A Conceptual Derivation of Einstein's Postulates of Special Relativity.

ERIC Educational Resources Information Center

Bearden, Thomas E.

This document presents a discussion and conceptual derivation of Einstein's postulates of special relativity. The perceptron approach appears to be a fundamentally new manner of regarding physical phenomena and it is hoped that physicists will interest themselves in the concept. (Author)

General Navier–Stokes-like momentum and mass-energy equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Monreal, Jorge, E-mail: jmonreal@mail.usf.edu

2015-03-15

A new system of general Navier–Stokes-like equations is proposed to model electromagnetic flow utilizing analogues of hydrodynamic conservation equations. Such equations are intended to provide a different perspective and, potentially, a better understanding of electromagnetic mass, energy and momentum behaviour. Under such a new framework additional insights into electromagnetism could be gained. To that end, we propose a system of momentum and mass-energy conservation equations coupled through both momentum density and velocity vectors.

Spatial and velocity statistics of inertial particles in turbulent flows

NASA Astrophysics Data System (ADS)

Bec, J.; Biferale, L.; Cencini, M.; Lanotte, A. S.; Toschi, F.

2011-12-01

Spatial and velocity statistics of heavy point-like particles in incompressible, homogeneous, and isotropic three-dimensional turbulence is studied by means of direct numerical simulations at two values of the Taylor-scale Reynolds number Reλ ~ 200 and Reλ ~ 400, corresponding to resolutions of 5123 and 20483 grid points, respectively. Particles Stokes number values range from St ≈ 0.2 to 70. Stationary small-scale particle distribution is shown to display a singular -multifractal- measure, characterized by a set of generalized fractal dimensions with a strong sensitivity on the Stokes number and a possible, small Reynolds number dependency. Velocity increments between two inertial particles depend on the relative weight between smooth events - where particle velocity is approximately the same of the fluid velocity-, and caustic contributions - when two close particles have very different velocities. The latter events lead to a non-differentiable small-scale behaviour for the relative velocity. The relative weight of these two contributions changes at varying the importance of inertia. We show that moments of the velocity difference display a quasi bi-fractal-behavior and that the scaling properties of velocity increments for not too small Stokes number are in good agreement with a recent theoretical prediction made by K. Gustavsson and B. Mehlig arXiv: 1012.1789v1 [physics.flu-dyn], connecting the saturation of velocity scaling exponents with the fractal dimension of particle clustering.

Transport properties of glass-forming liquids suggest that dynamic crossover temperature is as important as the glass transition temperature.

PubMed

Mallamace, Francesco; Branca, Caterina; Corsaro, Carmelo; Leone, Nancy; Spooren, Jeroen; Chen, Sow-Hsin; Stanley, H Eugene

2010-12-28

It is becoming common practice to partition glass-forming liquids into two classes based on the dependence of the shear viscosity η on temperature T. In an Arrhenius plot, ln η vs 1/T, a strong liquid shows linear behavior whereas a fragile liquid exhibits an upward curvature [super-Arrhenius (SA) behavior], a situation customarily described by using the Vogel-Fulcher-Tammann law. Here we analyze existing data of the transport coefficients of 84 glass-forming liquids. We show the data are consistent, on decreasing temperature, with the onset of a well-defined dynamical crossover η(×), where η(×) has the same value, η(×) ≈ 10(3) Poise, for all 84 liquids. The crossover temperature, T(×), located well above the calorimetric glass transition temperature T(g), marks significant variations in the system thermodynamics, evidenced by the change of the SA-like T dependence above T(×) to Arrhenius behavior below T(×). We also show that below T(×) the familiar Stokes-Einstein relation D/T ∼ η(-1) breaks down and is replaced by a fractional form D/T ∼ η(-ζ), with ζ ≈ 0.85.

Atomic structure and transport properties of Cu50Zr45Al5 metallic liquids and glasses: Molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Zhang, Y.; Mattern, N.; Eckert, J.

2011-11-01

We have simulated the atomic structure and the transport properties of Cu50Zr45Al5 metallic liquids and glasses within a wide cooling temperature range from 2000 to 300 K, using molecular dynamics simulations. High fractions of Cu- and Al-centered full icosahedra and Zr-centered icosahedra-like clusters have been detected in both supercooled liquids and glasses. The heat capacity and linear thermal expansion coefficients of both liquids and glasses are also calculated, which have not been reported for this off-eutectic composition previously. The critical temperature (Tc) of Cu50Zr45Al5 liquids is determined to be 874.7 K by investigating the self-diffusivity using the mode coupling theory. A dynamics cross-over is detected in the vicinity of Tc, which can be reflected by different diffusion mechanisms and a remarkable deviation from the Einstein-Stokes relation. The results further suggest a fragile to strong transition of Cu50Zr45Al5 liquids between 1500 K and 1300 K upon cooling, which may result from a drastic increase of stable clusters within this temperature range.

Nuclear quantum dynamics in dense hydrogen

PubMed Central

Kang, Dongdong; Sun, Huayang; Dai, Jiayu; Chen, Wenbo; Zhao, Zengxiu; Hou, Yong; Zeng, Jiaolong; Yuan, Jianmin

2014-01-01

Nuclear dynamics in dense hydrogen, which is determined by the key physics of large-angle scattering or many-body collisions between particles, is crucial for the dynamics of planet's evolution and hydrodynamical processes in inertial confinement confusion. Here, using improved ab initio path-integral molecular dynamics simulations, we investigated the nuclear quantum dynamics regarding transport behaviors of dense hydrogen up to the temperatures of 1 eV. With the inclusion of nuclear quantum effects (NQEs), the ionic diffusions are largely higher than the classical treatment by the magnitude from 20% to 146% as the temperature is decreased from 1 eV to 0.3 eV at 10 g/cm3, meanwhile, electrical and thermal conductivities are significantly lowered. In particular, the ionic diffusion is found much larger than that without NQEs even when both the ionic distributions are the same at 1 eV. The significant quantum delocalization of ions introduces remarkably different scattering cross section between protons compared with classical particle treatments, which explains the large difference of transport properties induced by NQEs. The Stokes-Einstein relation, Wiedemann-Franz law, and isotope effects are re-examined, showing different behaviors in nuclear quantum dynamics. PMID:24968754

Fluorescence correlation spectroscopy to measure the metabolism of high-density lipoprotein

NASA Astrophysics Data System (ADS)

Deitrick, Russell; Gibson, Emily; Razzaghi, Hamid

2009-10-01

High-density lipoprotein (HDL), referred to as the ``good cholesterol'', carries free cholesterol to the liver to be filtered from the bloodstream and is important to our understanding of atherosclerosis. HDL is metabolized in part by the enzyme Endothelial Lipase (EL). With this project we will use fluorescence correlation spectroscopy (FCS) to study the metabolism of HDL by EL comparing wild type with different genetic mutations. FCS is an advanced microscopy technique in which we record fluctuations in the fluorescence of dye-labeled molecules (in this case, HDL labeled with Nile Red) as they freely diffuse through a small focal volume. This data can be analyzed mathematically using the cross-correlation function, from which we can ultimately ascertain much information. In our case, we are interested in the diffusion coefficient which, via the Stokes-Einstein relation for a sphere, we can determine the size of HDL as it undergoes the process of metabolism. Preliminary results seem to indicate that the metabolic process occurs very quickly, that the final size of HDL depends primarily on the concentration of EL, and that the wild and mutant variants of EL have a similar effectiveness. In following experiments, we hope to investigate these relationships further.

Evaluation of the detachment energy of hydrated phosphate anion over a wide range of cluster size and revisiting solvent-berg model: a theoretical study

NASA Astrophysics Data System (ADS)

Pathak, Arup Kumar

2014-12-01

An explicit analytical expression has been obtained for vertical detachment energy (VDE) that can be used to calculate the same over a wide range (both stable and unstable regions) of cluster sizes including the bulk from the knowledge of VDE for a finite number of stable clusters (n = 16-23). The calculated VDE for the bulk is found to be very good in agreement (within 1%) with the available experimental result and the domain of instability lies between n = 0 and n = 15 for the hydrated clusters, PO3 -4 . nH2O. The minimum number (n0) of water molecules needed to stabilise the phosphate anion is 16. We are able to explain the origin of solvent-berg model and anomalous conductivity from the knowledge of first stable cluster. We have also provided a scheme to calculate the radius of the solvent-berg for phosphate anion. The calculated conductivity using Stokes-Einstein relation and the radius of solvent-berg is found to be very good in agreement (within 4%) with the available experimental results.

NMR and molecular dynamics study of the size, shape, and composition of reverse micelles in a cetyltrimethylammonium bromide (CTAB)/n-hexane/pentanol/water microemulsion.

PubMed

Mills, Amanda J; Wilkie, John; Britton, Melanie M

2014-09-11

The size, shape, and composition of reverse micelles (RMs) in a cetyltrimethylammonium bromide (CTAB)/pentanol/n-hexane/water microemulsion were investigated using pulsed gradient stimulated echo (PGSTE) nuclear magnetic resonance (NMR) measurements and molecular modeling. PGSTE data were collected at observation times (Δ) of 10, 40, and 450 ms. At long observation times, CTAB and pentanol exhibited single diffusion coefficients. However, at short (Δ ≤ 40 ms) observation times both CTAB and pentanol exhibited slow and fast diffusion coefficients. These NMR data indicate that both CTAB and pentanol molecules reside in different environments within the microemulsion and that there is exchange between regions on the millisecond time scale. Molecular dynamic simulations of the CTAB RM, in a solvent box containing n-hexane and pentanol, produced an ellipsoid shaped RM. Using structural parameters from these simulations and the Stokes-Einstein relation, the structure factor and dimensions of the reverse micelle were determined. Analysis of the composition of the interphase also showed that there was a variation in the ratio of surfactant to cosurfactant molecules depending on the curvature of the interphase.

Dynamical, structural and chemical heterogeneities in a binary metallic glass-forming liquid

NASA Astrophysics Data System (ADS)

Puosi, F.; Jakse, N.; Pasturel, A.

2018-04-01

As it approaches the glass transition, particle motion in liquids becomes highly heterogeneous and regions with virtually no mobility coexist with liquid-like domains. This complex dynamic is believed to be responsible for different phenomena including non-exponential relaxation and the breakdown of the Stokes-Einstein relation. Understanding the relationships between dynamical heterogeneities and local structure in metallic liquids and glasses is a major scientific challenge. Here we use classical molecular dynamics simulations to study the atomic dynamics and microscopic structure of Cu50Zr50 alloy in the supercooling regime. Dynamical heterogeneities are identified via an isoconfigurational analysis. We demonstrate the transition from isolated to clustering low mobility with decreasing temperature. These slow clusters, whose sizes grow upon cooling, are also associated with concentration fluctuations, characterized by a Zr-enriched phase, with a composition CuZr2 . In addition, a structural analysis of slow clusters based on Voronoi tessellation evidences an increase with respect of the bulk system of the fraction of Cu atoms having a local icosahedral order. These results are in agreement with the consolidated scenario of the relevant role played by icosahedral order in the dynamic slowing-down in supercooled metal alloys.

Infrared lessons for ultraviolet gravity: the case of massive gravity and Born-Infeld

NASA Astrophysics Data System (ADS)

Beltrán Jiménez, Jose; Heisenberg, Lavinia; Olmo, Gonzalo J.

2014-11-01

We generalize the ultraviolet sector of gravitation via a Born-Infeld action using lessons from massive gravity. The theory contains all of the elementary symmetric polynomials and is treated in the Palatini formalism. We show how the connection can be solved algebraically to be the Levi-Civita connection of an effective metric. The non-linearity of the algebraic equations yields several branches, one of which always reduces to General Relativity at low curvatures. We explore in detail a minimal version of the theory, for which we study solutions in the presence of a perfect fluid with special attention to the cosmological evolution. In vacuum we recover Ricci-flat solutions, but also an additional physical solution corresponding to an Einstein space. The existence of two physical branches remains for non-vacuum solutions and, in addition, the branch that connects to the Einstein space in vacuum is not very sensitive to the specific value of the energy density. For the branch that connects to the General Relativity limit we generically find three behaviours for the Hubble function depending on the equation of state of the fluid, namely: either there is a maximum value for the energy density that connects continuously with vacuum, or the energy density can be arbitrarily large but the Hubble function saturates and remains constant at high energy densities, or the energy density is unbounded and the Hubble function grows faster than in General Relativity. The second case is particularly interesting because it could offer an interesting inflationary epoch even in the presence of a dust component. Finally, we discuss the possibility of avoiding certain types of singularities within the minimal model.

Quasi-topological Ricci polynomial gravities

NASA Astrophysics Data System (ADS)

Li, Yue-Zhou; Liu, Hai-Shan; Lü, H.

2018-02-01

Quasi-topological terms in gravity can be viewed as those that give no contribution to the equations of motion for a special subclass of metric ansätze. They therefore play no rôle in constructing these solutions, but can affect the general perturbations. We consider Einstein gravity extended with Ricci tensor polynomial invariants, which admits Einstein metrics with appropriate effective cosmological constants as its vacuum solutions. We construct three types of quasi-topological gravities. The first type is for the most general static metrics with spherical, toroidal or hyperbolic isometries. The second type is for the special static metrics where g tt g rr is constant. The third type is the linearized quasitopological gravities on the Einstein metrics. We construct and classify results that are either dependent on or independent of dimensions, up to the tenth order. We then consider a subset of these three types and obtain Lovelock-like quasi-topological gravities, that are independent of the dimensions. The linearized gravities on Einstein metrics on all dimensions are simply Einstein and hence ghost free. The theories become quasi-topological on static metrics in one specific dimension, but non-trivial in others. We also focus on the quasi-topological Ricci cubic invariant in four dimensions as a specific example to study its effect on holography, including shear viscosity, thermoelectric DC conductivities and butterfly velocity. In particular, we find that the holographic diffusivity bounds can be violated by the quasi-topological terms, which can induce an extra massive mode that yields a butterfly velocity unbound above.

Homogeneous, anisotropic three-manifolds of topologically massive gravity

NASA Astrophysics Data System (ADS)

Nutku, Y.; Baekler, P.

1989-10-01

We present a new class of exact solutions of Deser, Jackiw, and Templeton's theory (DJT) of topologically massive gravity which consists of homogeneous, anisotropic manifolds. In these solutions the coframe is given by the left-invariant 1-forms of 3-dimensional Lie algebras up to constant scale factors. These factors are fixed in terms of the DJT coupling constant μ which is the constant of proportionality between the Einstein and Cotton tensors in 3-dimensions. Differences between the scale factors result in anisotropy which is a common feature of topologically massive 3-manifolds. We have found that only Bianchi Types VI, VIII, and IX lead to nontrivial solutions. Among these, a Bianchi Type IX, squashed 3-sphere solution of the Euclideanized DJT theory has finite action. Bianchi Type VIII, IX solutions can variously be embedded in the de Sitter/anti-de Sitter space. That is, some DJT 3-manifolds that we shall present here can be regarded as the basic constituent of anti-de Sitter space which is the ground state solution in higher dimensional generalization of Einstein's general relativity.

Homogeneous, anisotropic three-manifolds of topologically massive gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nutku, Y.; Baekler, P.

1989-10-01

We present a new class of exact solutions of Deser, Jackiw, and Templeton's theory (DJT) of topologically massive gravity which consists of homogeneous, anisotropic manifolds. In these solutions the coframe is given by the left-invariant 1-forms of 3-dimensional Lie algebras up to constant scale factors. These factors are fixed in terms of the DJT coupling constant {mu}m which is the constant of proportionality between the Einstein and Cotton tensors in 3-dimensions. Differences between the scale factors result in anisotropy which is a common feature of topologically massive 3-manifolds. We have found that only Bianchi Types VI, VIII, and IX leadmore » to nontrivial solutions. Among these, a Bianchi Type IX, squashed 3-sphere solution of the Euclideanized DJT theory has finite action, Bianchi Type VIII, IX solutions can variously be embedded in the de Sitter/anti-de Sitter space. That is, some DJT 3-manifolds that we shall present here can be regarded as the basic constitent of anti-de Sitter space which is the ground state solution in higher dimensional generalizations of Einstein's general relativity. {copyright} 1989 Academic Press, Inc.« less

Einstein's 1919 View

NASA Astrophysics Data System (ADS)

Goradia, Shantilal

2012-10-01

When Rutherford discovered the nuclear force in 1919, he felt the force he discovered reflected some deviation of Newtonian gravity. Einstein too in his 1919 paper published the failure of the general relativity and Newtonian gravity to explain nuclear force and, in his concluding remarks, he retracted his earlier introduction of the cosmological constant. Consistent with his genius, we modify Newtonian gravity as probabilistic gravity using natural Planck units for a realistic study of nature. The result is capable of expressing both (1) nuclear force [strong coupling], and (2) Newtonian gravity in one equation, implying in general, in layman's words, that gravity is the cumulative effect of all quantum mechanical forces which are impossible to measure at long distances. Non discovery of graviton and quantum gravity silently support our findings. Continuing to climb on the shoulders of the giants enables us to see horizons otherwise unseen, as reflected in our book: ``Quantum Consciousness - The Road to Reality,'' and physics/0210040, where we derive the fine structure constant as a function of the age of the universe in Planck times consistent with Gamow's hint, using natural logarithm consistent with Feynman's hint.

The turning point for Einstein's Annus mirabilis

NASA Astrophysics Data System (ADS)

Rynasiewicz, Robert; Renn, Jürgen

The year 1905 has been called Einstein's Annus mirabilis because of three ground-breaking works completed over the span of a few months-the light-quantum paper, the Brownian motion paper, and the paper on the electrodynamics of moving bodies introducing the special theory of relativity. There are prima facie reasons for thinking that the origins of these papers cannot be understood in isolation from one another. Due to space limitations, we concentrate primarily on the light quantum paper, since, in key respects, it marks the turning point for the Annus mirabilis. The task is to probe, not just how the idea of the light quantum might have occurred to Einstein, but, more importantly, what convinced him that the idea was not just a quixotic hypothesis, but an unavoidable and demonstrable feature of radiation. The crucial development, we suggest, arose from comparing the energy fluctuations that follow rigorously from the Stefan-Boltzmann law, as well as from Wien's distribution formula for blackbody radiation, with what it is reasonable to expect from Maxwell's electromagnetic theory of light. A special case of this is addressed in Einstein's one paper from 1904, "Zur allgemeinen molekularen Theorie der Wärme". Annalen der Physik, 14, 355-362 (Also in CPAE, Vol. 2, Doc. 5)]. The outcome for the general case leads naturally to the central theoretical argument of the light quantum paper, the expectation of Brownian-like motion, and several of the key results for the electrodynamics of moving bodies.

On the existence of the field line solutions of the Einstein-Maxwell equations

NASA Astrophysics Data System (ADS)

Vancea, Ion V.

The main result of this paper is the proof that there are local electric and magnetic field configurations expressed in terms of field lines on an arbitrary hyperbolic manifold. This electromagnetic field is described by (dual) solutions of the Maxwell’s equations of the Einstein-Maxwell theory. These solutions have the following important properties: (i) they are general, in the sense that the knot solutions are particular cases of them and (ii) they reduce to the electromagnetic fields in the field line representation in the flat space-time. Also, we discuss briefly the real representation of these electromagnetic configurations and write down the corresponding Einstein equations.

Gravitomagnetism: From Einstein's 1912 Paper to the Satellites LAGEOS and Gravity Probe B

NASA Astrophysics Data System (ADS)

Pfister, Herbert

The first concrete calculations of (linear) gravitomagnetic effects were performed by Einstein in 1912-1913. Einstein also directly and decisively contributed to the "famous" papers by Thirring (and Lense) from 1918. Generalizations to strong fields were performed not earlier than in 1966 by Brill and Cohen. Extensions to higher orders of the angular velocity ω by Pfister and Braun (1985-1989) led to a solution of the centrifugal force problem and to a quasiglobal principle of equivalence. The difficulties but also the recent successes to measure gravitomagnetic effects are reviewed, and cosmological and Machian aspects of gravitomagnetism are discussed.

Book Review: Book review

NASA Astrophysics Data System (ADS)

Wegener, Daan

Writing a biography of a complex personality and mastermind like Albert Einstein is a daunting task for any historian of science. Yet the sheer temptation of writing his biography has apparently helped to overcome scholarly scruples, as biographies of Einstein have appeared quite regularly on the market. One of them is Einstein: his Life and Universe by journalist Walter Isaacson. It is a best-seller, which is one of the reasons the book deserves a critical evaluation. Isaacson is a man of considerable repute: he has been the chairman of CNN and managing editor of Time magazine. Isaacson's Einstein is written in a style that is accessible to a wide audience. Scholars who are already familiar with Einstein's physics may still enjoy the parts of the book that deal with the relation between Einstein and the press. Indeed, the breadth of its scope is the book's major merit, as it connects the personal, scientific, public and political dimensions of Einstein's life. In this review, I discuss Isaacson's treatment of these dimensions one-by-one.

Clustering and relative velocity of heavy particles under gravitational settling in isotropic turbulent flows

NASA Astrophysics Data System (ADS)

Jin, Guodong; He, Guo-Wei

2015-11-01

Clustering and intermittency in radial relative velocity (RRV) of heavy particles of same size settling in turbulent flows can be remarkably changed due to gravity. Clustering is monotonically reduced at Stokes number less than 1 under gravity due to the disability of the centrifugal mechanism, however it is non-monotonically enhanced at Stokes number greater than 1 due to the multiplicative amplification in the case that the proposed effective Kubo number is less than 1. Although gravity causes monotonical reduction in the rms of RRV of particles at a given Stokes number with decreasing Froude number, the variation tendency in the tails of standardized PDF of RRV versus Froude number is obviously different: the tails become narrower at a small Stokes number, while they become broader at a large Stokes number. The mechanism of this variation stems from the compromise between the following two competing factors. The mitigation of correlation of particle positions and the regions of high strain rate which are more intermittent reduces the intermittency in RRV at small Stokes numbers, while the significant reduction in the backward-in-time relative separations will make particle pairs see small-scale structures, leading to a higher intermittency in RRV at large Stokes numbers. NSAF of China (grant number U1230126); NSFC (grant numbers 11072247 and 11232011).

Divergence identities in curved space-time a resolution of the stress-energy problem

NASA Astrophysics Data System (ADS)

Yilmaz, Hüseyin

1989-03-01

It is noted that the joint use of two basic differential identities in curved space-time, namely, 1) the Einstein-Hilbert identity (1915), and 2) the identity of P. Freud (1939), permits a viable alternative to general relativity and a resolution of the "field stress-energy" problem of the gravitational theory. (A tribute to Eugene P. Wigner's 1957 presidential address to the APS)

What is Gravitational Lensing?(LBNL Summer Lecture Series)

ScienceCinema

Alexie, Leauthaud; Reiko, Nakajima [Berkeley Center for Cosmological Physics, Berkely, California, United States

2017-12-09

July 28, 2009 Berkeley Lab summer lecture: Gravitational lensing is explained by Einstein's general theory of relativity: galaxies and clusters of galaxies, which are very massive objects, act on spacetime by causing it to become curved. Alexie Leauthaud and Reiko Nakajima, astrophysicists with the Berkeley Center for Cosmological Physics, will discuss how scientists use gravitational lensing to investigate the nature of dark energy and dark matter in the universe.

Explained in 60 Seconds: A collaboration with Symmetry Magazine, a Fermilab/SLAC publication

NASA Astrophysics Data System (ADS)

Trodden, M.

2011-07-01

The Big Bang refers to the start of the rapid expansion of our Universe. Edwin Hubble discovered this expansion in the 1920s through observations of faraway galaxies, showing that the distances between them are growing as time passes. This stunning discovery is beautifully explained by general relativity — Einstein's theory of gravity — augmented by two new concepts, dark matter and dark energy.

Gambling with the Universe

NASA Astrophysics Data System (ADS)

Hawking, Stephen

2002-05-01

This is an excerpt from Stephen Hawking's book The Universe in a Nutshell. Roger Penrose and Stephen Hawking, Lucasian Professor of Mathematics at the University of Cambridge, were able to show that Einstein's General Theory of Relativity implied that the universe and time itself must have had a beginning in a tremendous explosion. The discovery of the expansion of the universe is one of the great intellectual revolutions of the twentieth century.

The equivalence of Darmois-Israel and distributional method for thin shells in general relativity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mansouri, R.; Khorrami, M.

1996-11-01

A distributional method to solve the Einstein{close_quote}s field equations for thin shells is formulated. The familiar field equations and jump conditions of Darmois-Israel formalism are derived. A careful analysis of the Bianchi identities shows that, for cases under consideration, they make sense as distributions and lead to jump conditions of Darmois-Israel formalism. {copyright} {ital 1996 American Institute of Physics.}

Cosmological constant implementing Mach principle in general relativity

NASA Astrophysics Data System (ADS)

Namavarian, Nadereh; Farhoudi, Mehrdad

2016-10-01

We consider the fact that noticing on the operational meaning of the physical concepts played an impetus role in the appearance of general relativity (GR). Thus, we have paid more attention to the operational definition of the gravitational coupling constant in this theory as a dimensional constant which is gained through an experiment. However, as all available experiments just provide the value of this constant locally, this coupling constant can operationally be meaningful only in a local area. Regarding this point, to obtain an extension of GR for the large scale, we replace it by a conformal invariant model and then, reduce this model to a theory for the cosmological scale via breaking down the conformal symmetry through singling out a specific conformal frame which is characterized by the large scale characteristics of the universe. Finally, we come to the same field equations that historically were proposed by Einstein for the cosmological scale (GR plus the cosmological constant) as the result of his endeavor for making GR consistent with the Mach principle. However, we declare that the obtained field equations in this alternative approach do not carry the problem of the field equations proposed by Einstein for being consistent with Mach's principle (i.e., the existence of de Sitter solution), and can also be considered compatible with this principle in the Sciama view.

Relativity time-delay experiments utilizing 'Mariner' spacecraft

NASA Technical Reports Server (NTRS)

Esposito, P. B.; Anderson, J. D.

1974-01-01

Relativity predicts that the transit time of a signal propagated from the earth to a spacecraft and retransmitted back to earth ought to exhibit an additional, variable time delay. The present work describes some of the analytical techniques employed in experiments using Mariner spacecraft designed to test the accuracy of this prediction. Two types of data are analyzed in these relativity experiments; these include phase-coherent, two-way Doppler shift and round-trip, transit-time measurements. Results of Mariner 6 and 7 relativistic time-delay experiments are in agreement with Einstein's theory of general relativity with an uncertainty of 3%.

Numerical modeling of the interaction of liquid drops and jets with shock waves and gas jets

NASA Astrophysics Data System (ADS)

Surov, V. S.

1993-02-01

The motion of a liquid drop (jet) and of the ambient gas is described, in the general case, by Navier-Stokes equations. An approximate solution to the interaction of a plane shock wave with a single liquid drop is presented. Based on the analysis, the general system of Navier-Stokes equations is reduced to two groups of equations, Euler equations for gas and Navier-Stokes equations for liquid; solutions to these equations are presented. The discussion also covers the modeling of the interaction of a shock wave with a drop screen, interaction of a liquid jet with a counterpropagating supersonic gas flow, and modeling of processes in a shock layer during the impact of a drop against an obstacle in gas flow.

A precise extragalactic test of General Relativity.

PubMed

Collett, Thomas E; Oldham, Lindsay J; Smith, Russell J; Auger, Matthew W; Westfall, Kyle B; Bacon, David; Nichol, Robert C; Masters, Karen L; Koyama, Kazuya; van den Bosch, Remco

2018-06-22

Einstein's theory of gravity, General Relativity, has been precisely tested on Solar System scales, but the long-range nature of gravity is still poorly constrained. The nearby strong gravitational lens ESO 325-G004 provides a laboratory to probe the weak-field regime of gravity and measure the spatial curvature generated per unit mass, γ. By reconstructing the observed light profile of the lensed arcs and the observed spatially resolved stellar kinematics with a single self-consistent model, we conclude that γ = 0.97 ± 0.09 at 68% confidence. Our result is consistent with the prediction of 1 from General Relativity and provides a strong extragalactic constraint on the weak-field metric of gravity. Copyright © 2018 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.

Development of a time-dependent incompressible Navier-Stokes solver based on a fractional-step method

NASA Technical Reports Server (NTRS)

Rosenfeld, Moshe

1990-01-01

The development, validation and application of a fractional step solution method of the time-dependent incompressible Navier-Stokes equations in generalized coordinate systems are discussed. A solution method that combines a finite-volume discretization with a novel choice of the dependent variables and a fractional step splitting to obtain accurate solutions in arbitrary geometries was previously developed for fixed-grids. In the present research effort, this solution method is extended to include more general situations, including cases with moving grids. The numerical techniques are enhanced to gain efficiency and generality.

CMB B-mode auto-bispectrum produced by primordial gravitational waves

NASA Astrophysics Data System (ADS)

Tahara, Hiroaki W. H.; Yokoyama, Jun'ichi

2018-01-01

Gravitational waves from inflation induce polarization patterns in the cosmic microwave background (CMB). It is known that there are only two types of non-Gaussianities of the gravitational waves in the most general covariant scalar field theory having second-order field equations, namely, generalized G-inflation. One originates from the inherent non-Gaussianity in general relativity, and the other from a derivative coupling between the Einstein tensor and the scalar field. We calculate polarization bispectra induced by these non-Gaussianities by transforming them into separable forms by virtue of the Laplace transformation. It is shown that future experiments can constrain the new one but cannot detect the general relativistic one.

Regulative feedback in pattern formation: towards a general relativistic theory of positional information.

PubMed

Jaeger, Johannes; Irons, David; Monk, Nick

2008-10-01

Positional specification by morphogen gradients is traditionally viewed as a two-step process. A gradient is formed and then interpreted, providing a spatial metric independent of the target tissue, similar to the concept of space in classical mechanics. However, the formation and interpretation of gradients are coupled, dynamic processes. We introduce a conceptual framework for positional specification in which cellular activity feeds back on positional information encoded by gradients, analogous to the feedback between mass-energy distribution and the geometry of space-time in Einstein's general theory of relativity. We discuss how such general relativistic positional information (GRPI) can guide systems-level approaches to pattern formation.

A particle-particle collision strategy for arbitrarily shaped particles at low Stokes numbers

NASA Astrophysics Data System (ADS)

Daghooghi, Mohsen; Borazjani, Iman

2016-11-01

We present a collision strategy for particles with any general shape at low Stokes numbers. Conventional collision strategies rely upon a short -range repulsion force along particles centerline, which is a suitable choice for spherical particles and may not work for complex-shaped particles. In the present method, upon the collision of two particles, kinematics of particles are modified so that particles have zero relative velocity toward each other along the direction in which they have the minimum distance. The advantage of this novel technique is that it guaranties to prevent particles from overlapping without unrealistic bounce back at low Stokes numbers, which may occur if repulsive forces are used. This model is used to simulate sedimentation of many particles in a vertical channel and suspensions of non-spherical particles under simple shear flow. This work was supported by the American Chemical Society (ACS) Petroleum Research Fund (PRF) Grant Number 53099-DNI9. The computational resources were partly provided by the Center for Computational Research (CCR) at the University at Buffalo.

A molecular dynamics examination of the relationship between self-diffusion and viscosity in liquid metals.

PubMed

Lü, Yongjun; Cheng, Hao; Chen, Min

2012-06-07

The self-diffusion coefficients D and the viscosities η of elemental Ni, Cu, and Ni-Si alloys have been calculated over a wide temperature range by molecular dynamics simulations. For elemental Ni and Cu, Arrhenius-law variations of D and η with temperature dominate. The temperature dependence of Dη can be approximated by a linear relation, whereas the Stokes-Einstein relation is violated. The calculations of D and η are extended to the regions close to the crystallization of Ni(95)Si(5), Ni(90)Si(10), and the glass transitions of Ni(80)Si(20) and Ni(75)Si(25). The results show that both D and η strongly deviate from the Arrhenius law in the vicinity of phase transitions, exhibiting a power-law divergence. We find a decoupling of diffusion and viscous flow just above the crystallization of Ni(95)Si(5) and Ni(90)Si(10). For the two glass-forming alloys, Ni(80)Si(20) and Ni(75)Si(25), the relation Dη = const is obeyed as the glass transition is approached, indicating a dynamic coupling as predicted by the mode-coupling theory. This coupling is enhanced with increasing Si composition and at 25%, Si spans a wide temperature range through the melting point. The decoupling is found to be related to the distribution of local ordered structure in the melts. The power-law governing the growth of solid-like clusters prior to crystallization creates a dynamic heterogeneity responsible for decoupling.

A molecular dynamics examination of the relationship between self-diffusion and viscosity in liquid metals

NASA Astrophysics Data System (ADS)

Lü, Yongjun; Cheng, Hao; Chen, Min

2012-06-01

The self-diffusion coefficients D and the viscosities η of elemental Ni, Cu, and Ni-Si alloys have been calculated over a wide temperature range by molecular dynamics simulations. For elemental Ni and Cu, Arrhenius-law variations of D and η with temperature dominate. The temperature dependence of Dη can be approximated by a linear relation, whereas the Stokes-Einstein relation is violated. The calculations of D and η are extended to the regions close to the crystallization of Ni95Si5, Ni90Si10, and the glass transitions of Ni80Si20 and Ni75Si25. The results show that both D and η strongly deviate from the Arrhenius law in the vicinity of phase transitions, exhibiting a power-law divergence. We find a decoupling of diffusion and viscous flow just above the crystallization of Ni95Si5 and Ni90Si10. For the two glass-forming alloys, Ni80Si20 and Ni75Si25, the relation Dη = const is obeyed as the glass transition is approached, indicating a dynamic coupling as predicted by the mode-coupling theory. This coupling is enhanced with increasing Si composition and at 25%, Si spans a wide temperature range through the melting point. The decoupling is found to be related to the distribution of local ordered structure in the melts. The power-law governing the growth of solid-like clusters prior to crystallization creates a dynamic heterogeneity responsible for decoupling.

Left-invariant Einstein metrics on S3 ×S3

NASA Astrophysics Data System (ADS)

Belgun, Florin; Cortés, Vicente; Haupt, Alexander S.; Lindemann, David

2018-06-01

The classification of homogeneous compact Einstein manifolds in dimension six is an open problem. We consider the remaining open case, namely left-invariant Einstein metrics g on G = SU(2) × SU(2) =S3 ×S3. Einstein metrics are critical points of the total scalar curvature functional for fixed volume. The scalar curvature S of a left-invariant metric g is constant and can be expressed as a rational function in the parameters determining the metric. The critical points of S, subject to the volume constraint, are given by the zero locus of a system of polynomials in the parameters. In general, however, the determination of the zero locus is apparently out of reach. Instead, we consider the case where the isotropy group K of g in the group of motions is non-trivial. When K ≇Z2 we prove that the Einstein metrics on G are given by (up to homothety) either the standard metric or the nearly Kähler metric, based on representation-theoretic arguments and computer algebra. For the remaining case K ≅Z2 we present partial results.

The Einstein database of IPC x-ray observations of optically selected and radio-selected quasars, 1.

NASA Technical Reports Server (NTRS)

Wilkes, Belinda J.; Tananbaum, Harvey; Worrall, D. M.; Avni, Yoram; Oey, M. S.; Flanagan, Joan

1994-01-01

We present the first volume of the Einstein quasar database. The database includes estimates of the X-ray count rates, fluxes, and luminosities for 514 quasars and Seyfert 1 galaxies observed with the Imaging Proportional Counter (IPC) aboard the Einstein Observatory. All were previously known optically selected or radio-selected objects, and most were the targets of the X-ray observations. The X-ray properties of the Active Galactic Nuclei (AGNs) have been derived by reanalyzing the IPC data in a systematic manner to provide a uniform database for general use by the astronomical community. We use the database to extend earlier quasar luminosity studies which were made using only a subset of the currently available data. The database can be accessed on internet via the SAO Einstein on-line system ('Einline') and is available in ASCII format on magnetic tape and DOS diskette.

Quasi-local conserved charges in the Einstein-Maxwell theory

NASA Astrophysics Data System (ADS)

Setare, M. R.; Adami, H.

2017-05-01

In this paper we consider the Einstein-Maxwell theory and define a combined transformation composed of diffeomorphism and U(1) gauge transformation. For generality, we assume that the generator χ of such transformation is field-dependent. We define the extended off-shell ADT current and then off-shell ADT charge such that they are conserved off-shell for the asymptotically field-dependent symmetry generator χ. Then, we define the conserved charge corresponding to the asymptotically field-dependent symmetry generator χ. We apply the presented method to find the conserved charges of the asymptotically AdS3 spacetimes in the context of the Einstein-Maxwell theory in three dimensions. Although the usual proposal for the quasi local charges provides divergent global charges for the Einstein-Maxwell theory with negative cosmological constant in three dimensions, here we avoid this problem by introducing proposed combined transformation χ

Radiating black hole solutions in Einstein-Gauss-Bonnet gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dominguez, Alfredo E.; Instituto Universitario Aeronautico, Avenida Fuerza Aerea km 6.5.; Gallo, Emanuel

2006-03-15

In this paper, we find some new exact solutions to the Einstein-Gauss-Bonnet equations. First, we prove a theorem which allows us to find a large family of solutions to the Einstein-Gauss-Bonnet gravity in n-dimensions. This family of solutions represents dynamic black holes and contains, as particular cases, not only the recently found Vaidya-Einstein-Gauss-Bonnet black hole, but also other physical solutions that we think are new, such as the Gauss-Bonnet versions of the Bonnor-Vaidya (de Sitter/anti-de Sitter) solution, a global monopole, and the Husain black holes. We also present a more general version of this theorem in which less restrictive conditionsmore » on the energy-momentum tensor are imposed. As an application of this theorem, we present the exact solution describing a black hole radiating a charged null fluid in a Born-Infeld nonlinear electrodynamics.« less

Interpretation of Mössbauer experiment in a rotating system: A new proof for general relativity

NASA Astrophysics Data System (ADS)

Corda, Christian

2015-04-01

A historical experiment by Kündig on the transverse Doppler shift in a rotating system measured with the Mössbauer effect (Mössbauer rotor experiment) has been recently first re-analyzed and then replied by an experimental research group. The results of re-analyzing the experiment have shown that a correct re-processing of Kündig's experimental data gives an interesting deviation of a relative redshift between emission and absorption resonant lines from the standard prediction based on the relativistic dilatation of time. That prediction gives a redshift ∇E/E ≃ -1/2 v2/c2 where v is the tangential velocity of the absorber of resonant radiation, c is the velocity of light in vacuum and the result is given to the accuracy of first-order in v2/c2. Data re-processing gave ∇E/E ≃ - kv2/c2 with k = 0.596 ± 0.006. Subsequent new experimental results by the reply of Kündig experiment have shown a redshift with k = 0.68 ± 0.03 instead. By using Einstein Equivalence Principle, which states the equivalence between the gravitational "force" and the pseudo-force experienced by an observer in a non-inertial frame of reference (included a rotating frame of reference) here we re-analyze the theoretical framework of Mössbauer rotor experiments directly in the rotating frame of reference by using a general relativistic treatment. It will be shown that previous analyses missed an important effect of clock synchronization and that the correct general relativistic prevision in the rotating frame gives k ≃ 2/3 in perfect agreement with the new experimental results. Such an effect of clock synchronization has been missed in various papers in the literature with some subsequent claim of invalidity of relativity theory and/or some attempts to explain the experimental results through "exotic" effects. Our general relativistic interpretation shows, instead, that the new experimental results of the Mössbauer rotor experiment are a new, strong and independent, proof of Einstein general relativity. In the final section of the paper we discuss an analogy with the use of General Relativity in Global Positioning Systems.

Effects of aspect ratio of multi-walled carbon nanotubes on coal washery waste water treatment.

PubMed

Aliyu, Ahmed; Kariim, Ishaq; Abdulkareem, Saka Ambali

2017-11-01

The dependency of adsorption behaviour on the aspect ratio of multi-walled carbon nanotubes (MWCNTs) has been explored. In this study, effect of growth temperature on yield and aspect ratio of MWCNTs by catalytic chemical vapour deposition (CCVD) method is reported. The result revealed that yield and aspect ratio of synthesised MWCNTs strongly depend on the growth temperature during CCVD operation. The resulting MWCNTs were characterized by High Resolution Transmission Electron Microscope (HRTEM), Dynamic Light Scattering (DLS) and X-ray diffraction (XRD) techniques to determine it diameter, hydrodynamic diameter and crystallinity respectively. Aspect ratio and length of the grown MWCNTs were determined from the HRTEM images with the hydrodynamic diameter using the modified Navier-Stokes and Stokes-Einstein equations. The effect of the prepared MWCNTs dosage were investigated on the Turbidity, Iron (Fe) and Lead (Pb) removal efficiency of coal washery effluent. The MWCNTs with higher length (58.17 μm) and diameter (71 nm) tend to show high turbidity and Fe removal, while MWCNTs with lower length (38.87 μm) and diameter (45 nm) tend to show high removal of Pb. Hence, the growth temperature during CCVD operation shows a great effluence on the aspect ratio of MWCNTs which determines it area of applications. Copyright © 2017 Elsevier Ltd. All rights reserved.

Raman analysis of phonon modes in a short period AlN/GaN superlattice

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sarkar, Ketaki; Datta, Debopam; Gosztola, David J.

AlN/GaN-based optoelectronic devices have been the subject of intense research underlying the commercialization of efficient devices. Areas of considerable interest are the study of their lattice dynamics, phonon transport, and electron-phonon interactions specific to the interface of these heterostructures which results in additional optical phonon modes known as interface phonon modes. In this study, the framework of the dielectric continuum model (DCM) has been used to compare and analyze the optical phonon modes obtained from experimental Raman scattering measurements on AlN/GaN short-period superlattices. We have observed the localized E2(high), A1(LO) and the E1(TO) modes in superlattice measurements at frequencies shiftedmore » from their bulk values. To the best of our knowledge, the nanostructures used in these studies are among the smallest yielding useful Raman signatures for the interface modes. In addition, we have also identified an additional spread of interface phonon modes in the TO range resulting from the superlattice periodicity. The Raman signature contribution from the underlying AlxGa1-xN ternary has also been observed and analyzed. A temperature calibrationwas done based on Stokes/anti-Stokes ratio of A1(LO) using Raman spectroscopy in a broad operating temperature range. Good agreement between the experimental results and theoretically calculated calibration plot predicted using Bose-Einstein statistics was obtained.« less

Raman analysis of phonon modes in a short period AlN/GaN superlattice

NASA Astrophysics Data System (ADS)

Sarkar, Ketaki; Datta, Debopam; Gosztola, David J.; Shi, Fengyuan; Nicholls, Alan; Stroscio, Michael A.; Dutta, Mitra

2018-03-01

AlN/GaN-based optoelectronic devices have been the subject of intense research underlying the commercialization of efficient devices. Areas of considerable interest are the study of their lattice dynamics, phonon transport, and electron-phonon interactions specific to the interface of these heterostructures which results in additional optical phonon modes known as interface phonon modes. In this study, the framework of the dielectric continuum model (DCM) has been used to compare and analyze the optical phonon modes obtained from experimental Raman scattering measurements on AlN/GaN short-period superlattices. We have observed the localized E2(high), A1(LO) and the E1(TO) modes in superlattice measurements at frequencies shifted from their bulk values. To the best of our knowledge, the nanostructures used in these studies are among the smallest yielding useful Raman signatures for the interface modes. In addition, we have also identified an additional spread of interface phonon modes in the TO range resulting from the superlattice periodicity. The Raman signature contribution from the underlying AlxGa1-xN ternary has also been observed and analyzed. A temperature calibration was done based on Stokes/anti-Stokes ratio of A1(LO) using Raman spectroscopy in a broad operating temperature range. Good agreement between the experimental results and theoretically calculated calibration plot predicted using Bose-Einstein statistics was obtained.

Einstein's Theory Fights off Challengers

NASA Astrophysics Data System (ADS)

2010-04-01

Two new and independent studies have put Einstein's General Theory of Relativity to the test like never before. These results, made using NASA's Chandra X-ray Observatory, show Einstein's theory is still the best game in town. Each team of scientists took advantage of extensive Chandra observations of galaxy clusters, the largest objects in the Universe bound together by gravity. One result undercuts a rival gravity model to General Relativity, while the other shows that Einstein's theory works over a vast range of times and distances across the cosmos. The first finding significantly weakens a competitor to General Relativity known as "f(R) gravity". "If General Relativity were the heavyweight boxing champion, this other theory was hoping to be the upstart contender," said Fabian Schmidt of the California Institute of Technology in Pasadena, who led the study. "Our work shows that the chances of its upsetting the champ are very slim." In recent years, physicists have turned their attention to competing theories to General Relativity as a possible explanation for the accelerated expansion of the universe. Currently, the most popular explanation for the acceleration is the so-called cosmological constant, which can be understood as energy that exists in empty space. This energy is referred to as dark energy to emphasize that it cannot be directly detected. In the f(R) theory, the cosmic acceleration comes not from an exotic form of energy but from a modification of the gravitational force. The modified force also affects the rate at which small enhancements of matter can grow over the eons to become massive clusters of galaxies, opening up the possibility of a sensitive test of the theory. Schmidt and colleagues used mass estimates of 49 galaxy clusters in the local universe from Chandra observations, and compared them with theoretical model predictions and studies of supernovas, the cosmic microwave background, and the large-scale distribution of galaxies. They found no evidence that gravity is different from General Relativity on scales larger than 130 million light years. This limit corresponds to a hundred-fold improvement on the bounds of the modified gravitational force's range that can be set without using the cluster data. "This is the strongest ever constraint set on an alternative to General Relativity on such large distance scales," said Schmidt. "Our results show that we can probe gravity stringently on cosmological scales by using observations of galaxy clusters." The reason for this dramatic improvement in constraints can be traced to the greatly enhanced gravitational forces acting in clusters as opposed to the universal background expansion of the universe. The cluster-growth technique also promises to be a good probe of other modified gravity scenarios, such as models motivated by higher-dimensional theories and string theory. A second, independent study also bolsters General Relativity by directly testing it across cosmological distances and times. Up until now, General Relativity had been verified only using experiments from laboratory to Solar System scales, leaving the door open to the possibility that General Relativity breaks down on much larger scales. To probe this question, a group at Stanford University compared Chandra observations of how rapidly galaxy clusters have grown over time to the predictions of General Relativity. The result is nearly complete agreement between observation and theory. "Einstein's theory succeeds again, this time in calculating how many massive clusters have formed under gravity's pull over the last five billion years," said David Rapetti of the Kavli Institute for Particle Astrophysics and Cosmology (KIPAC) at Stanford University and SLAC National Accelerator Laboratory, who led the new study. "Excitingly and reassuringly, our results are the most robust consistency test of General Relativity yet carried out on cosmological scales." Rapetti and his colleagues based their results on a sample of 238 clusters detected across the whole sky by the now-defunct ROSAT X-ray telescope. These data were enhanced by detailed mass measurements for 71 distant clusters using Chandra, and 23 relatively nearby clusters using ROSAT, and combined with studies of supernovas, the cosmic microwave background, the distribution of galaxies and distance estimates to galaxy clusters. Galaxy clusters are important objects in the quest to understand the Universe as a whole. Because the observations of the masses of galaxy clusters are directly sensitive to the properties of gravity, they provide crucial information. Other techniques such as observations of supernovas or the distribution of galaxies measure cosmic distances, which depend only on the expansion rate of the universe. In contrast, the cluster technique used by Rapetti and his colleagues measure in addition the growth rate of the cosmic structure, as driven by gravity. "Cosmic acceleration represents a great challenge to our modern understanding of physics," said Rapetti's co-author Adam Mantz of NASA's Goddard Space Flight Center in Maryland. "Measurements of acceleration have highlighted how little we know about gravity at cosmic scales, but we're now starting to push back our ignorance." The paper by Fabian Schmidt was published in Physics Review D, Volume 80 in October 2009 and is co-authored by Alexey Vikhlinin of the Harvard-Smithsonian Center for Astrophysics in Cambridge, Massachusetts, and Wayne Hu of the University of Chicago, Illinois. The paper by David Rapetti was recently accepted for publication in the Monthly Notices of the Royal Astronomical Society and is co-authored by Mantz, Steve Allen of KIPAC at Stanford and Harald Ebeling of the Institute for Astronomy in Hawaii. NASA's Marshall Space Flight Center in Huntsville, Ala., manages the Chandra program for NASA's Science Mission Directorate in Washington. The Smithsonian Astrophysical Observatory controls Chandra's science and flight operations from Cambridge, Mass. More information, including images and other multimedia, can be found at: http://chandra.harvard.edu and http://chandra.nasa.gov

Conserved Quantities in General Relativity: From the Quasi-Local Level to Spatial Infinity

NASA Astrophysics Data System (ADS)

Chen, Po-Ning; Wang, Mu-Tao; Yau, Shing-Tung

2015-08-01

We define quasi-local conserved quantities in general relativity by using the optimal isometric embedding in Wang and Yau (Commun Math Phys 288(3):919-942, 2009) to transplant Killing fields in the Minkowski spacetime back to the 2-surface of interest in a physical spacetime. To each optimal isometric embedding, a dual element of the Lie algebra of the Lorentz group is assigned. Quasi-local angular momentum and quasi-local center of mass correspond to pairing this element with rotation Killing fields and boost Killing fields, respectively. They obey classical transformation laws under the action of the Poincaré group. We further justify these definitions by considering their limits as the total angular momentum and the total center of mass of an isolated system. These expressions were derived from the Hamilton-Jacobi analysis of the gravitational action and thus satisfy conservation laws. As a result, we obtained an invariant total angular momentum theorem in the Kerr spacetime. For a vacuum asymptotically flat initial data set of order 1, it is shown that the limits are always finite without any extra assumptions. We also study these total conserved quantities on a family of asymptotically flat initial data sets evolving by the vacuum Einstein evolution equation. It is shown that the total angular momentum is conserved under the evolution. For the total center of mass, the classical dynamical formula relating the center of mass, energy, and linear momentum is recovered, in the nonlinear context of initial data sets evolving by the vacuum Einstein evolution equation. The definition of quasi-local angular momentum provides an answer to the second problem in classical general relativity on Penrose's list (Proc R Soc Lond Ser A 381(1780):53-63, 1982).