Uncertainty principle and uncertainty relations
J. B. M. Uffink; J. Hilgevoord
1985-01-01
It is generally believed that the uncertainty relation q p1\\/2, where q and p are standard deviations, is the precise mathematical expression of the uncertainty principle for position and momentum in quantum mechanics. We show that actually it is not possible to derive from this relation two central claims of the uncertainty principle, namely, the impossibility of an arbitrarily sharp
Heisenberg's uncertainty principle
Paul Busch; Teiko Heinonen; Pekka Lahti
2007-01-01
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a condition ensuring that mutually exclusive experimental options can be reconciled if an appropriate trade-off is accepted. The uncertainty principle is shown to appear in three manifestations,
Generalized uncertainty principles
Ronny Machluf
2008-07-14
The phenomenon in the essence of classical uncertainty principles is well known since the thirties of the last century. We introduce a new phenomenon which is in the essence of a new notion that we introduce: "Generalized Uncertainty Principles". We show the relation between classical uncertainty principles and generalized uncertainty principles. We generalized "Landau-Pollak-Slepian" uncertainty principle. Our generalization relates the following two quantities and two scaling parameters: 1) The weighted time spreading $\\int_{-\\infty}^\\infty |f(x)|^2w_1(x)dx$, ($w_1(x)$ is a non-negative function). 2) The weighted frequency spreading $\\int_{-\\infty}^\\infty |\\hat{f}(\\omega)|^2w_2(\\omega)d\\omega$. 3) The time weight scale $a$, ${w_1}_a(x)=w_1(xa^{-1})$ and 4) The frequency weight scale $b$, ${w_2}_b(\\omega)=w_2(\\omega b^{-1})$. "Generalized Uncertainty Principle" is an inequality that summarizes the constraints on the relations between the two spreading quantities and two scaling parameters. For any two reasonable weights $w_1(x)$ and $w_2(\\omega)$, we introduced a three dimensional set in $R^3$ that is in the essence of many uncertainty principles. The set is called "possibility body". We showed that classical uncertainty principles (such as the Heiseneberg-Pauli-Weyl uncertainty principle) stem from lower bounds for different functions defined on the possibility body. We investigated qualitative properties of general uncertainty principles and possibility bodies. Using this approach we derived new (quantitative) uncertainty principles for Landau-Pollak-Slepian weights. We found the general uncertainty principles related to homogeneous weights, $w_1(x)=w_2(x)=x^k$, $k\\in N$, up to a constant.
Economic uncertainty principle? Alexander Harin
Paris-Sud XI, Université de
Economic uncertainty principle? Alexander Harin This preliminary paper presents a qualitative description of the economic principle of (hidden, latent) uncertainty. Mathematical expressions of principle. ....................................................................... 2 1. Economic uncertainty principle ........................................... 2 1.1. General
C. Y. Chen
2008-12-23
By examining two counterexamples to the existing theory, it is shown, with mathematical rigor, that as far as scattered particles are concerned the true distribution function is in principle not determinable (indeterminacy principle or uncertainty principle) while the average distribution function over each predetermined finite velocity solid-angle element can be calculated.
Heisenberg's Uncertainty Principle
P. Busch; T. Heinonen; P. Lahti
2007-10-30
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a condition ensuring that mutually exclusive experimental options can be reconciled if an appropriate trade-off is accepted. The uncertainty principle is shown to appear in three manifestations, in the form of uncertainty relations: for the widths of the position and momentum distributions in any quantum state; for the inaccuracies of any joint measurement of these quantities; and for the inaccuracy of a measurement of one of the quantities and the ensuing disturbance in the distribution of the other quantity. Whilst conceptually distinct, these three kinds of uncertainty relations are shown to be closely related formally. Finally, we survey models and experimental implementations of joint measurements of position and momentum and comment briefly on the status of experimental tests of the uncertainty principle.
Uncertainty Principles Sparse Representation in Overcomplete Dictionaries
Hirn, Matthew
Uncertainty Principles Sparse Representation in Overcomplete Dictionaries Uncertainty Principles November 8, 2007 Matthew J. Hirn Uncertainty Principles in Sparse Representation and Compressed Sensing #12;Uncertainty Principles Sparse Representation in Overcomplete Dictionaries Outline 1 Uncertainty Principles
Uncertainty principles and vector quantization
Yurii Lyubarskii; Roman Vershynin
2010-01-01
Abstract. An abstract form of the Uncertainty Principle set forth by Candes and Tao has found remarkable applications in the sparse approximation theory. This pa- per demonstates a new connection between the Uncertainty Principle and the vector quantization theory. We show that for frames in C, that satisfy the Uncertainty Principle, one can quickly convert every frame representation into a
Uncertainty Principle Respects Locality
Dongsheng Wang
2013-03-21
The notion of nonlocality implicitly implies there might be some kind of spooky action at a distance in nature, however, the validity of quantum mechanics has been well tested up to now. In this work it is argued that the notion of nonlocality is physically improper, the basic principle of locality in nature is well respected by quantum mechanics, namely, the uncertainty principle. We show that the quantum bound on the Clauser, Horne, Shimony, and Holt (CHSH) inequality can be recovered from the uncertainty relation in a multipartite setting, and the same bound exists classically which indicates that nonlocality does not capture the essence of quantum and then distinguish quantum mechanics and classical mechanics properly. We further argue that the super-quantum correlation demonstrated by the nonlocal box is not physically comparable with the quantum one, as the result, the physical foundation for the existence of nonlocality is falsified. The origin of the quantum structure of nature still remains to be explained, some post-quantum theory which is more complete in some sense than quantum mechanics is possible and might not necessarily be a hidden variable theory.
On Generalized Uncertainty Principle
Bhupendra Nath Tiwari
2011-09-20
We study generalized uncertainty principle through the basic concepts of limit and Fourier transformation and analyze both the quantum theory of gravity and string theory from the perspective of complex function theory. Motivated from the noncommutative nature of string theory, we have proposed a UV/IR mixing dependent function $ \\tilde{\\delta}(\\Delta x,\\Delta k, \\epsilon) $. For a given $ \\tilde{\\delta}(\\Delta x,\\Delta k, \\epsilon) $, we arrived at the string uncertainty principle from the analyticity condition of a complex function, which depends upon UV cut-off of the theory. This non trivially modifies the quantum measurements, black hole physics and short distance geometries. The present analysis is based on the postulate that the Planck scale is the minimal length scale in nature. Furthermore, our consideration is in perfect agreement with the existence of the maximum length scale in nature. Both of the above length scales rely only upon the analysis of $ \\tilde{\\delta}(\\Delta x,\\Delta k, \\epsilon) $ and do not directly make use of any specific structure of the theory or Hamiltonian. The Regge behavior of the string spectrum and the quantization of the horizon area of a black hole are natural consequences of the function $ \\tilde{\\delta}(\\Delta x,\\Delta k, \\epsilon) $. It is hereby anticipated that $ \\tilde{\\delta}(\\Delta x,\\Delta k, \\epsilon) $ contains all possible corrections operating in nature, and thus a promising possibility to reveal important clues towards the geometric origin of $M$-theory.
Uncertainty principle quantum estimation theory
Yamamoto, Hirosuke
Uncertainty principle in view of quantum estimation theory Keiji Matsumoto METR 97-08 October 1997 #12;Uncertainty principle in view of quantum estimation theory Keiji Matsumoto 1 Abstract Position-momentum uncertainty relation is examined in the light of quantum estimation theory, and some counterintuitive results
HARDY'S UNCERTAINTY PRINCIPLE ON CERTAIN LIE GROUPS
Cowling, Michael
HARDY'S UNCERTAINTY PRINCIPLE ON CERTAIN LIE. 1. Introduction The Uncertainty Principle states, roughly speaking, that a nonzero function f, considerable attention has been devoted to discovering forms of the* * Uncertainty Principle on Lie groups
Quantum Action Principle with Generalized Uncertainty Principle
Jie Gu
2013-11-01
One of the common features in all promising candidates of quantum gravity is the existence of a minimal length scale, which naturally emerges with a generalized uncertainty principle, or equivalently a modified commutation relation. Schwinger's quantum action principle was modified to incorporate this modification, and was applied to the calculation of the kernel of a free particle, partly recovering the result previously studied using path integral.
Gravity from the uncertainty principle
NASA Astrophysics Data System (ADS)
McCulloch, M. E.
2014-02-01
It is shown here that Newton's gravity law can be derived from the uncertainty principle. The idea is that as the distance between two bodies in mutual orbit decreases, their uncertainty of position decreases, so their momentum and hence the force on them must increase to satisfy the uncertainty principle. When this result is summed over all the possible interactions between the Planck masses in the two bodies, Newton's gravity law is obtained. This model predicts that masses less than the Planck mass will be unaffected by gravity and so it may be tested by looking for an abrupt decrease in the density of space dust, for masses above the Planck mass.
Uncertainty Relation from Holography Principle
Jia-Zhong Chen; Duoje Jia
2006-11-18
We propose that the information and entropy of an isolated system are two sides of one coin in the sense that they can convert into each other by measurement and evolution of the system while the sum of them is identically conserved. The holographic principle is reformulated in the way that this conserved sum is bounded by a quarter of the area A of system boundary. Uncertainty relation is derived from the holographic principle.
Uncertainty principle and kinetic equations
R. Alexandre; Y. Morimoto; S. Ukai; C.-J. Xu; T. Yang
2008-01-01
A large number of mathematical studies on the Boltzmann equation are based on the Grad's angular cutoff assumption. However, for particle interaction with inverse power law potentials, the associated cross-sections have a non-integrable singularity corresponding to the grazing collisions. Smoothing properties of solutions are then expected. On the other hand, the uncertainty principle, established by Heisenberg in 1927, has been
Entropy and the uncertainty principle
Rupert L. Frank; Elliott H. Lieb
2011-09-06
We generalize, improve and unify theorems of Rumin, and Maassen--Uffink about classical entropies associated to quantum density matrices. These theorems refer to the classical entropies of the diagonals of a density matrix in two different bases. Thus they provide a kind of uncertainty principle. Our inequalities are sharp because they are exact in the high-temperature or semi-classical limit.
Gerbes and Heisenberg's Uncertainty Principle
J. M. Isidro
2006-03-31
We prove that a gerbe with a connection can be defined on classical phase space, taking the U(1)-valued phase of certain Feynman path integrals as Cech 2-cocycles. A quantisation condition on the corresponding 3-form field strength is proved to be equivalent to Heisenberg's uncertainty principle.
On Gravity and the Uncertainty Principle
Ronald J. Adler; David I. Santiago
1999-01-01
Heisenberg showed in the early days of quantum theory that the uncertainty principle follows as a direct consequence of the quantization of electromagnetic radiation in the form of photons. As we show here the gravitational interaction of the photon and the particle being observed modifies the uncertainty principle with an additional term. From the modified or gravitational uncertainty principle it
Greedy Signal Recovery and Uniform Uncertainty Principles
Needell, Deanna
Greedy Signal Recovery and Uniform Uncertainty Principles SPIE - IE 2008 Deanna Needell Joint work with Roman Vershynin UC Davis, January 2008 Greedy Signal Recovery and Uniform Uncertainty Principles p.1 Uncertainty Principles p.3/24 #12;Setup · Consider v Rd , v 0 := | supp v| n d. · We call such signals n
Directional Uncertainty Principle for Quaternion Fourier Transform
Eckhard Hitzer
2013-06-06
This paper derives a new directional uncertainty principle for quaternion valued functions subject to the quaternion Fourier transformation. This can be generalized to establish directional uncertainty principles in Clifford geometric algebras with quaternion subalgebras. We demonstrate this with the example of a directional spacetime algebra function uncertainty principle related to multivector wave packets.
Greedy Signal Recovery and Uniform Uncertainty Principles
Needell, Deanna
Greedy Signal Recovery and Uniform Uncertainty Principles SIAM Deanna Needell Joint work with Roman Vershynin UC Davis, July 2008 Greedy Signal Recovery and Uniform Uncertainty Principles p.1/27 #12;Outline · Empirical Results · Improvements Greedy Signal Recovery and Uniform Uncertainty Principles p.2/27 #12
The uncertainty principle: A mathematical survey
Gerald B. Folland; Alladi Sitaram
1997-01-01
We survey various mathematical aspects of the uncertainty principle, including Heisenberg’s inequality and its variants, local\\u000a uncertainty inequalities, logarithmic uncertainty inequalities, results relating to Wigner distributions, qualitative uncertainty\\u000a principles, theorems on approximate concentration, and decompositions of phase space.
The Donoho-Stark Uncertainty Principle An Uncertainty Principle for Cyclic Groups of Prime Order
Hirn, Matthew
The Donoho-Stark Uncertainty Principle An Uncertainty Principle for Cyclic Groups of Prime Order Uncertainty Principles for Finite Abelian Groups Matthew J. Hirn Norbert Wiener Center University of Maryland September 20, 2007 Matthew J. Hirn Uncertainty Principles for Finite Abelian Groups #12;The Donoho
Uncertainty Principles for Compact Groups
Gorjan Alagic; Alexander Russell
2008-08-29
We establish an operator-theoretic uncertainty principle over arbitrary compact groups, generalizing several previous results. As a consequence, we show that if f is in L^2(G), then the product of the measures of the supports of f and its Fourier transform ^f is at least 1; here, the dual measure is given by the sum, over all irreducible representations V, of d_V rank(^f(V)). For finite groups, our principle implies the following: if P and R are projection operators on the group algebra C[G] such that P commutes with projection onto each group element, and R commutes with left multiplication, then the squared operator norm of PR is at most rank(P)rank(R)/|G|.
Quantum Mechanics and the Generalized Uncertainty Principle
Jang Young Bang; Micheal S. Berger
2006-11-30
The generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantum gravity. We consider a simple quantum mechanical model where the operator corresponding to position has discrete eigenvalues and show how the generalized uncertainty principle results for minimum uncertainty wave packets.
Quantum mechanics and the generalized uncertainty principle
Bang, Jang Young; Berger, Micheal S. [Physics Department, Indiana University, Bloomington, Indiana 47405 (United States)
2006-12-15
The generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantum gravity. We consider a simple quantum mechanical model where the operator corresponding to position has discrete eigenvalues and show how the generalized uncertainty principle results for minimum uncertainty wave packets.
Gamma-Ray Telescope and Uncertainty Principle
ERIC Educational Resources Information Center
Shivalingaswamy, T.; Kagali, B. A.
2012-01-01
Heisenberg's Uncertainty Principle is one of the important basic principles of quantum mechanics. In most of the books on quantum mechanics, this uncertainty principle is generally illustrated with the help of a gamma ray microscope, wherein neither the image formation criterion nor the lens properties are taken into account. Thus a better…
The Uncertainty Principle in Software Engineering
Hadar Ziv; Debra J. Richardson; René Klösch
1996-01-01
This paper makes two contributions to software engineering research. First, we observe that uncertainty permeates software development but is rarely captured explicitly in software models. We remedy this situation by presenting the Uncertainty Principle in Software Engineering (UPSE), which states that uncertainty is inherent and inevitable in software development processes and products. We substantiate UPSE by providing examples of uncertainty
Uncertainty Principles and Sum Complexes Roy Meshulam
Meshulam, Roy
Uncertainty Principles and Sum Complexes Roy Meshulam March 28, 2014 Abstract Let p be a prime@math.technion.ac.il . Supported by an ISF grant. 1 #12;of the Heisenberg quantum-mechanical uncertainty principle: If f L2 (R of the uncertainty principle. Let G be a finite abelian group and let F[G] be the group algebra of G over the field F
The Species Delimitation Uncertainty Principle
Adams, Byron J.
2001-01-01
If, as Einstein said, "it is the theory which decides what we can observe," then "the species problem" could be solved by simply improving our theoretical definition of what a species is. However, because delimiting species entails predicting the historical fate of evolutionary lineages, species appear to behave according to the Heisenberg Uncertainty Principle, which states that the most philosophically satisfying definitions of species are the least operational, and as species concepts are modified to become more operational they tend to lose their philosophical integrity. Can species be delimited operationally without losing their philosophical rigor? To mitigate the contingent properties of species that tend to make them difficult for us to delimit, I advocate a set of operations that takes into account the prospective nature of delimiting species. Given the fundamental role of species in studies of evolution and biodiversity, I also suggest that species delimitation proceed within the context of explicit hypothesis testing, like other scientific endeavors. The real challenge is not so much the inherent fallibility of predicting the future but rather adequately sampling and interpreting the evidence available to us in the present. PMID:19265874
Disturbance, the uncertainty principle and quantum optics
NASA Technical Reports Server (NTRS)
Martens, Hans; Demuynck, Willem M.
1993-01-01
It is shown how a disturbance-type uncertainty principle can be derived from an uncertainty principle for joint measurements. To achieve this, we first clarify the meaning of 'inaccuracy' and 'disturbance' in quantum mechanical measurements. The case of photon number and phase is treated as an example, and it is applied to a quantum non-demolition measurement using the optical Kerr effect.
The Uncertainty Principle in Image Processing
Roland Wilson; Goesta H. Granlund
1984-01-01
The uncertainty principle is recognized as one of the fundamental results in signal processing. Its role in inference is, however, less well known outside of quantum mechanics. It is the aim of this paper to provide a unified approach to the problem of uncertainty in image processing. It is shown that uncertainty can be derived from the fundamental constraints on
Schrodinger equation from an exact uncertainty principle
Michael J. W. Hall; Marcel Reginatto
2001-01-01
An exact uncertainty principle, formulated as the assumption that a classical\\u000aensemble is subject to random momentum fluctuations of a strength which is\\u000adetermined by and scales inversely with uncertainty in position, leads from the\\u000aclassical equations of motion to the Schrodinger equation. Thus there is an\\u000aexact formulation of the uncertainty principle which precisely captures the\\u000aessence of what
Uncertainty Principle and the Standard Quantum Limits
Horace P. Yuen
2005-10-10
The role of the Uncertainty Principle is examined through the examples of squeezing, information capacity, and position monitoring. It is suggested that more attention should be directed to conceptual considerations in quantum information science and technology.
Noncommutativity, generalized uncertainty principle and FRW cosmology
A. Bina; K. Atazadeh; S. Jalalzadeh
2007-09-23
We consider the effects of noncommutativity and the generalized uncertainty principle on the FRW cosmology with a scalar field. We show that, the cosmological constant problem and removability of initial curvature singularity find natural solutions in this scenarios.
Uncertainty principles on certain Lie groups
A. Sitaram; M. Sundari; S. Thangavelu
1995-01-01
There are several ways of formulating the uncertainty principle for the Fourier transform on ?\\u000a n\\u000a . Roughly speaking, the uncertainty principle says that if a functionf is ‘concentrated’ then its Fourier transform\\u000a $$\\\\tilde f$$\\u000a cannot be ‘concentrated’ unlessf is identically zero. Of course, in the above, we should be precise about what we mean by ‘concentration’. There are several
Uncertainty principle and quantum Fisher information. II
Paolo Gibilisco; Daniele Imparato; Tommaso Isola
2007-01-01
Heisenberg and Schrödinger uncertainty principles give lower bounds for the product of variances Varrho(A)Varrho(B) if the observables A,B are not compatible, namely, if the commutator [A,B] is not zero. In this paper, we prove an uncertainty principle in Schrödinger form where the bound for the product of variances Varrho(A)Varrho(B) depends on the area spanned by the commutators i[rho,A] and i[rho,B
Curriculum in Art Education: The Uncertainty Principle.
ERIC Educational Resources Information Center
Sullivan, Graeme
1989-01-01
Identifies curriculum as the pivotal link between theory and practice, noting that all stages of curriculum research and development are characterized by elements of uncertainty. States that this uncertainty principle reflects the reality of practice as it mirrors the contradictory nature of art, the pluralism of schools and society, and the…
On the uncertainty principle in discrete signals
L. C. Calves; P. Vilbe
1992-01-01
It has recently been shown that the uncertainty principle holds true by appropriate definitions of the durations even if discrete signals are considered. A basic inequality was derived in the particular case where the Fourier transform is real. As an extension to this work, the authors prove the uncertainty relation in the general case of a complex Fourier transform and
Naturalistic Misunderstanding of the Heisenberg Uncertainty Principle.
ERIC Educational Resources Information Center
McKerrow, K. Kelly; McKerrow, Joan E.
1991-01-01
The Heisenberg Uncertainty Principle, which concerns the effect of observation upon what is observed, is proper to the field of quantum physics, but has been mistakenly adopted and wrongly applied in the realm of naturalistic observation. Discusses the misuse of the principle in the current literature on naturalistic research. (DM)
Uncertainty Principles and Optimality on Circles and Spheres
Martin, Ralph R.
Uncertainty Principles and Optimality on Circles and Spheres Tim N. T. Goodman and Say Song Goh Abstract. From a general uncertainty principle we derive uncertainty principles on spheres in any dimension which extend, for real-valued functions, known uncertainty principles on spheres in two and three
A revision of the Generalized Uncertainty Principle
Cosimo Bambi
2008-04-30
The Generalized Uncertainty Principle arises from the Heisenberg Uncertainty Principle when gravity is taken into account, so the leading order correction to the standard formula is expected to be proportional to the gravitational constant $G_N = L_{Pl}^2$. On the other hand, the emerging picture suggests a set of departures from the standard theory which demand a revision of all the arguments used to deduce heuristically the new rule. In particular, one can now argue that the leading order correction to the Heisenberg Uncertainty Principle is proportional to the first power of the Planck length $L_{Pl}$. If so, the departures from ordinary quantum mechanics would be much less suppressed than what is commonly thought.
An uncertainty principle for unimodular quantum groups
Crann, Jason [School of Mathematics and Statistics, Carleton University, Ottawa, Ontario K1S 5B6 (Canada); Université Lille 1 - Sciences et Technologies, UFR de Mathématiques, Laboratoire de Mathématiques Paul Painlevé - UMR CNRS 8524, 59655 Villeneuve d'Ascq Cédex (France); Kalantar, Mehrdad, E-mail: jason-crann@carleton.ca, E-mail: mkalanta@math.carleton.ca [School of Mathematics and Statistics, Carleton University, Ottawa, Ontario K1S 5B6 (Canada)
2014-08-15
We present a generalization of Hirschman's entropic uncertainty principle for locally compact Abelian groups to unimodular locally compact quantum groups. As a corollary, we strengthen a well-known uncertainty principle for compact groups, and generalize the relation to compact quantum groups of Kac type. We also establish the complementarity of finite-dimensional quantum group algebras. In the non-unimodular setting, we obtain an uncertainty relation for arbitrary locally compact groups using the relative entropy with respect to the Haar weight as the measure of uncertainty. We also show that when restricted to q-traces of discrete quantum groups, the relative entropy with respect to the Haar weight reduces to the canonical entropy of the random walk generated by the state.
An uncertainty principle for unimodular quantum groups
Jason Crann; Mehrdad Kalantar
2014-11-02
We present a generalization of Hirschman's entropic uncertainty principle for locally compact abelian groups to unimodular locally compact quantum groups. As a corollary, we strengthen a well-known uncertainty principle for compact groups, and generalize the relation to compact quantum groups of Kac type. We also establish the complementarity of finite-dimensional quantum group algebras. In the non-unimodular setting, we obtain an uncertainty relation for arbitrary locally compact groups using the relative entropy with respect to the Haar weight as the measure of uncertainty. We also show that when restricted to normal central states of discrete quantum groups, the relative entropy with respect to the Haar weight reduces to the canonical entropy of the random walk generated by the central state.
An uncertainty principle for unimodular quantum groups
NASA Astrophysics Data System (ADS)
Crann, Jason; Kalantar, Mehrdad
2014-08-01
We present a generalization of Hirschman's entropic uncertainty principle for locally compact Abelian groups to unimodular locally compact quantum groups. As a corollary, we strengthen a well-known uncertainty principle for compact groups, and generalize the relation to compact quantum groups of Kac type. We also establish the complementarity of finite-dimensional quantum group algebras. In the non-unimodular setting, we obtain an uncertainty relation for arbitrary locally compact groups using the relative entropy with respect to the Haar weight as the measure of uncertainty. We also show that when restricted to q-traces of discrete quantum groups, the relative entropy with respect to the Haar weight reduces to the canonical entropy of the random walk generated by the state.
An Uncertainty Principle for Ultraspherical Expansions
Margit Rösler; Michael Voit
1997-01-01
Motivated by Heisenberg–Weyl type uncertainty principles for the torusTand the sphereS2due to Breitenberger, Narowich, Ward, and others, we derive an uncertainty relation for radial functions on the spheresSn?Rn+1and, more generally, for ultraspherical expansions on [0,?]. In this setting, the “frequency variance” of aL2-function on [0,?] is defined by means of the ultraspherical differential operator, which plays the role of a
Generalized Uncertainty Principle and Dark Matter
Pisin Chen
2003-05-01
There have been proposals that primordial black hole remnants (BHRs) are the dark matter, but the idea is somewhat vague. Recently we argued that the generalized uncertainty principle (GUP) may prevent black holes from evaporating completely, in a similar way that the standard uncertainty principle prevents the hydrogen atom from collapsing. We further noted that the hybrid inflation model provides a plausible mechanism for production of large numbers of small black holes. Combining these we suggested that the dark matter might be composed of Planck-size BHRs. In this paper we briefly review these arguments, and discuss the reheating temperature as a result of black hole evaporation.
Generalized Uncertainty Principle and Dark Matter
Chen, P
2004-01-13
There have been proposals that primordial black hole remnants (BHRs) are the dark matter, but the idea is somewhat vague. Recently we argued that the generalized uncertainty principle (GUP) may prevent black holes from evaporating completely, in a similar way that the standard uncertainty principle prevents the hydrogen atom from collapsing. We further noted that the hybrid inflation model provides a plausible mechanism for production of large numbers of small black holes. Combining these we suggested that the dark matter might be composed of Planck-size BHRs. In this paper we briefly review these arguments, and discuss the reheating temperature as a result of black hole evaporation.
Uncertainty Principle and Quantum Fisher Information - II
P. Gibilisco; D. Imparato; T. Isola
2007-05-21
Heisenberg and Schr{\\"o}dinger uncertainty principles give lower bounds for the product of variances $Var_{\\rho}(A)\\cdot Var_{\\rho}(B)$, in a state $\\rho$, if the observables $A,B$ are not compatible, namely if the commutator $[A,B]$ is not zero. In this paper we prove an uncertainty principle in Schr{\\"o}dinger form where the bound for the product of variances $Var_{\\rho}(A)\\cdot Var_{\\rho}(B)$ depends on the area spanned by the commutators $[\\rho,A]$ and $[\\rho,B]$ with respect to an arbitrary quantum version of the Fisher information.
Harmonic Analysis and Qualitative Uncertainty Principle
Ji King
2010-08-09
This paper investigates the mathematical nature of qualitative uncertainty principle (QUP), which plays an important role in mathematics, physics and engineering fields. Consider a 3-tuple (K, H1, H2) that K: H1 -> H2 is an integral operator. Suppose a signal f in H1, {\\Omega}1 and {\\Omega}2 are domains on which f, Kf define respectively. Does this signal f vanish if |{\\Sigma}(f)|uncertainty principle, nonlinear method and sparse representation, are thus suggested. The notion of operator family is developed and is applied to understand remarkable performances of recent sparse representation.
Uncertainty principles as embeddings of modulation spaces
Yevgeniy V. Galperin; Karlheinz Gröchenig
2002-01-01
A class of new uncertainty principles is derived in the form of embeddings of Fourier–Lebesgue spaces into modulation spaces. These embeddings provide practical, sufficient conditions for a function to belong to a modulation space. Counterexamples based on the properties of Gabor expansions demonstrate that the embeddings are optimal.
A Principle of Uncertainty for Information Seeking.
ERIC Educational Resources Information Center
Kuhlthau, Carol C.
1993-01-01
Proposes an uncertainty principle for information seeking based on the results of a series of studies that investigated the user's perspective of the information search process. Constructivist theory is discussed as a conceptual framework for studying the user's perspective, and areas for further research are suggested. (Contains 44 references.)…
A generalized uncertainty principle in quantum gravity
Michele Maggiore
1993-01-01
We discuss a Gedanken experiment for the measurement of the area of the apparent horizon of a black hole in quantum gravity. Using rather general and model-independent considerations we find a generalized uncertainty principle which agrees with a similar result obtained in the framework of string theories. The result indicates that a minimum length of the order of the Planck
Interpretation of Electron Tunneling from Uncertainty Principle
Angik Sarkar; T. K. Bhattacharyya
2005-07-25
Beginners studying quantum mechanics are often baffled with electron tunneling.Hence an easy approach for comprehension of the topic is presented here on the basis of uncertainty principle.An estimate of the tunneling time is also derived from the same method.
Wave-particle Duality and the Uncertainty Principle Frank Rioux
Rioux, Frank
Wave-particle Duality and the Uncertainty Principle Frank Rioux CSB/SJU Nick Herbert, author) is shown below in atomic units (h = 2). It clearly illustrates the uncertainty principle because the wave of the uncertainty principle, the particle-like character of a quon is revealed only when there is uncertainty
A geometric formulation of uncertainty principle
G. M. Bosyk; T. M. Osán; P. W. Lamberti; M. Portesi
2013-10-11
A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a projector associated with an observable, and interpret it as the probability of obtaining the outcome corresponding to that projector. We make use of fidelity-based metrics such as angle, Bures and root-infidelity ones, to propose a measure of uncertainty. The triangle inequality allows us to derive a family of uncertainty relations. In the case of the angle metric, we re-obtain the Landau--Pollak inequality for pure states and show, in a natural way, how to extend it to the case of mixed states in arbitrary dimension. In addition, we derive and compare novel uncertainty relations when using other known fidelity-based metrics.
HEISENBERG'S UNCERTAINTY PRINCIPLE IN THE SENSE OF BEURLING HAAKAN HEDENMALM
Hedenmalm, Håkan
HEISENBERG'S UNCERTAINTY PRINCIPLE IN THE SENSE OF BEURLING HAAKAN HEDENMALM In memory of Boris Korenblum ABSTRACT. We shed new light on Heisenberg's uncertainty principle in the sense of Beurling principle. In general terms, Heisenberg's uncertainty principle asserts that a function and its Fourier
HEISENBERG'S UNCERTAINTY PRINCIPLE IN THE SENSE OF BEURLING
Hedenmalm, Håkan
HEISENBERG'S UNCERTAINTY PRINCIPLE IN THE SENSE OF BEURLING By HAAKAN HEDENMALM In memory of Boris Korenblum Abstract. We shed new light on Heisenberg's uncertainty principle in the sense of Beurling principle. In general terms, Heisenberg's uncertainty principle asserts that a function and its Fourier
THE UNCERTAINTY PRINCIPLE: A BRIEF SURVEY MATTHEW BEGUE
Johnson, Raymond L.
THE UNCERTAINTY PRINCIPLE: A BRIEF SURVEY MATTHEW BEGU´E Contents 1. Introduction 1 2. L2 (R The uncertainty principle is a cornerstone in quantum phsysics. However, its principles play an equally monumental of the uncertainty principle in harmonic analysis (Heisenberg's inequality). We then extend Heisenberg's inequality
Phenomenological Implications of the Generalized Uncertainty Principle
Saurya Das; Elias C. Vagenas
2009-01-13
Various theories of Quantum Gravity argue that near the Planck scale, the Heisenberg Uncertainty Principle should be replaced by the so called Generalized Uncertainty Principle (GUP). We show that the GUP gives rise to two additional terms in any quantum mechanical Hamiltonian, proportional to \\beta p^4 and \\beta^2 p^6 respectively, where \\beta \\sim 1/(M_{Pl}c)^2 is the GUP parameter. These terms become important at or above the Planck energy. Considering only the first of these, and treating it as a perturbation, we show that the GUP affects the Lamb shift, Landau levels, reflection and transmission coefficients of a potential step and potential barrier, and the current in a Scanning Tunnel Microscope (STM). Although these are too small to be measurable at present, we speculate on the possibility of extracting measurable predictions in the future.
Uncertainty principle and quantum Fisher information
Paolo Gibilisco; Tommaso Isola
2007-01-01
A family of inequalities, related to the uncertainty principle, has been recently proved by S. Luo, Z. Zhang, Q. Zhang, H.\\u000a Kosaki, K. Yanagi, S. Furuichi and K. Kuriyama. We show that the inequalities have a geometric interpretation in terms of\\u000a quantum Fisher information. Using this formulation one may naturally ask if this family of inequalities can be further extendend,
On a principle of cosmological uncertainty
Antonio Enea Romano
2012-07-18
We show that cosmological observations are subject to an intrinsic uncertainty which can be expressed in the form of an uncertainty relation similar to the Heisenberg principle. This is a consequence of the fact that the four dimensional space-time metric information is projected into the one-dimensional observational red-shift space, implying a limit on the amount of information which can be extracted about the underlying geometry. Since multiple space-time configurations can lead to the same red-shift, there is an unavoidable uncertainty about the determination of the space-time geometry. This suggests the existence of a limit about of the amount of information that cosmological observations can reveal about our Universe that no experiment could ever overcame, conceptually similar to what happens in quantum mechanics.
Generalized uncertainty principle: Approaches and applications
NASA Astrophysics Data System (ADS)
Tawfik, A.; Diab, A.
2014-11-01
In this paper, we review some highlights from the String theory, the black hole physics and the doubly special relativity and some thought experiments which were suggested to probe the shortest distances and/or maximum momentum at the Planck scale. Furthermore, all models developed in order to implement the minimal length scale and/or the maximum momentum in different physical systems are analyzed and compared. They entered the literature as the generalized uncertainty principle (GUP) assuming modified dispersion relation, and therefore are allowed for a wide range of applications in estimating, for example, the inflationary parameters, Lorentz invariance violation, black hole thermodynamics, Saleker-Wigner inequalities, entropic nature of gravitational laws, Friedmann equations, minimal time measurement and thermodynamics of the high-energy collisions. One of the higher-order GUP approaches gives predictions for the minimal length uncertainty. A second one predicts a maximum momentum and a minimal length uncertainty, simultaneously. An extensive comparison between the different GUP approaches is summarized. We also discuss the GUP impacts on the equivalence principles including the universality of the gravitational redshift and the free fall and law of reciprocal action and on the kinetic energy of composite system. The existence of a minimal length and a maximum momentum accuracy is preferred by various physical observations. The concern about the compatibility with the equivalence principles, the universality of gravitational redshift and the free fall and law of reciprocal action should be addressed. We conclude that the value of the GUP parameters remain a puzzle to be verified.
Generalized Uncertainty Principle: Approaches and Applications
Abdel Nasser Tawfik; Abdel Magied Diab
2014-11-23
We review highlights from string theory, black hole physics and doubly special relativity and some "thought" experiments which were suggested to probe the shortest distance and/or the maximum momentum at the Planck scale. The models which are designed to implement the minimal length scale and/or the maximum momentum in different physical systems are analysed entered the literature as the Generalized Uncertainty Principle (GUP). We compare between them. The existence of a minimal length and a maximum momentum accuracy is preferred by various physical observations. Furthermore, assuming modified dispersion relation allows for a wide range of applications in estimating, for example, the inflationary parameters, Lorentz invariance violation, black hole thermodynamics, Saleker-Wigner inequalities, entropic nature of the gravitational laws, Friedmann equations, minimal time measurement and thermodynamics of the high-energy collisions. One of the higher-order GUP approaches gives predictions for the minimal length uncertainty. Another one predicts a maximum momentum and a minimal length uncertainty, simultaneously. An extensive comparison between the different GUP approaches is summarized. We also discuss the GUP impacts on the equivalence principles including the universality of the gravitational redshift and the free fall and law of reciprocal action and on the kinetic energy of composite system. The concern about the compatibility with the equivalence principles, the universality of gravitational redshift and the free fall and law of reciprocal action should be addressed. We conclude that the value of the GUP parameters remain a puzzle to be verified.
"Moral Uncertainty and the Principle of Equity among Moral Theories"
Sepielli, Andrew
2008-01-01
Moral Uncertainty and the Principle of Equity among MoralUncertainty and Its Consequences, Ted Lockhart argues that intertheoretic comparisons of value differences are possible if we adopt a principle
A Robertson-type Uncertainty Principle and Quantum Fisher Information
Isola, Tommaso
A Robertson-type Uncertainty Principle and Quantum Fisher Information Paolo Gibilisco , Daniele and let be a density matrix. The Robertson uncertainty principle det {Cov(Ah, Aj)} det - i 2 Tr([Ah, Aj, uncertainty principle, operator monotone functions, matrix means, quantum Fisher information. 1 Introduction
UNCERTAINTY PRINCIPLE AND QUANTUM FISHER INFORMATION PAOLO GIBILISCO1
Isola, Tommaso
UNCERTAINTY PRINCIPLE AND QUANTUM FISHER INFORMATION PAOLO GIBILISCO1 AND TOMMASO ISOLA2 1. A family of inequalities, related to the uncertainty principle, has been recently proved by S. Luo, Z: Uncertainty principle, monotone metrics, quantum Fisher information, Wigner-Yanase-Dyson information. 1 #12
AN ENTROPIC UNCERTAINTY PRINCIPLE FOR POSITIVE OPERATOR VALUED MEASURES
Rumin, Michel
AN ENTROPIC UNCERTAINTY PRINCIPLE FOR POSITIVE OPERATOR VALUED MEASURES MICHEL RUMIN Abstract. Extending a recent result by Frank and Lieb, we show an entropic uncertainty principle for mixed states, uncertainty principle, homogeneous spaces, log-Sobolev. 1 #12;2 MICHEL RUMIN We shall see that when
Quantitative Robust Uncertainty Principles and Optimally Sparse Decompositions
Candes, Emmanuel J.
Quantitative Robust Uncertainty Principles and Optimally Sparse Decompositions Emmanuel J. Cand June 2005 & July 2006 Abstract In this paper, we develop a robust uncertainty principle for finite on . In fact, we can make the above uncertainty principle quantitative in the sense that if f is supported on T
EQUALITY CASES FOR THE UNCERTAINTY PRINCIPLE IN FINITE ABELIAN GROUPS
Paris-Sud XI, Université de
EQUALITY CASES FOR THE UNCERTAINTY PRINCIPLE IN FINITE ABELIAN GROUPS ALINE BONAMI & SAIFALLAH notation. Uncertainty principles show how small the support and the spectrum of a nonzero function f may by Matolcsi and Sz¨ucs in [6]. It is usually referred to as Stark-Donoho Uncertainty Principle and deals 1991
AN UNCERTAINTY PRINCIPLE FOR ULTRASPHERICAL EXPANSIONS Margit Rosler
Roesler, Margit
AN UNCERTAINTY PRINCIPLE FOR ULTRASPHERICAL EXPANSIONS Margit R¨osler Mathematisches Institut. Abstract Motivated by HeisenbergWeyl type uncertainty principles for the torus T and the sphere S 2 due'' on [0; ß] with the time t tending to 0 , we show that the bound of our uncertainty principle is optimal
Quantitative Robust Uncertainty Principles and Optimally Sparse Decompositions
Candes, Emmanuel J.
Quantitative Robust Uncertainty Principles and Optimally Sparse Decompositions Emmanuel J. Cand In this paper, we develop a robust uncertainty principle for finite signals in CN which states that for nearly (less than half, say) of ^f is concentrated on . As an application of this robust uncertainty principle
THE UNCERTAINTY PRINCIPLE FOR FOURIER TRANSFORMS ON THE REAL LINE
May, J. Peter
THE UNCERTAINTY PRINCIPLE FOR FOURIER TRANSFORMS ON THE REAL LINE MITCH HILL Abstract. This paper inversion theorem and use this to prove the classical uncertainty principle which shows that the spread. Fourier Inversion 8 5. The Uncertainty Principle 13 6. The Amrein-Berthier Theorem 15 Acknowledgments 17
UNCERTAINTY PRINCIPLES FOR INTEGRAL OPERATORS SAIFALLAH GHOBBER AND PHILIPPE JAMING
Paris-Sud XI, Université de
UNCERTAINTY PRINCIPLES FOR INTEGRAL OPERATORS SAIFALLAH GHOBBER AND PHILIPPE JAMING Abstract. The aim of this paper is to prove new uncertainty principles for an integral operator T with a bounded's local uncertainty principle which states that if a nonzero function f L2(Rd, µ) is highly localized
Quantitative Robust Uncertainty Principles and Optimally Sparse Decompositions
Soatto, Stefano
Quantitative Robust Uncertainty Principles and Optimally Sparse Decompositions Emmanuel J. Cand Abstract In this paper, we develop a robust uncertainty principle for finite signals in CN which states uncertainty principle quantitative in the sense that if f is supported on T, then only a small percentage
Uncertainty Principle and Quantum Fisher Information -II Paolo Gibilisco
Ceragioli, Francesca
Uncertainty Principle and Quantum Fisher Information - II Paolo Gibilisco , Daniele Imparato and Tommaso Isola April 20, 2007 Abstract Heisenberg and Schr¨odinger uncertainty principles give lower bounds [A, B] is not zero. In this paper we prove an uncertainty principle in Schr¨odinger form where
An uncertainty principle for the Dunkl transform Margit Rosler
Roesler, Margit
An uncertainty principle for the Dunkl transform Margit R¨osler Zentrum Mathematik, Technische@mathematik.tumuenchen.de Abstract This note presents an analogue of the classical HeisenbergWeyl uncertainty principle. Analogues of the classical variancebased WeylHeisenberg uncertainty principle for the Dunkl transform have
The Uncertainty Principle: Group Theoretic Approach, Possible Minimizers
Sochen, Nir
The Uncertainty Principle: Group Theoretic Approach, Possible Minimizers and Scale-Space Properties@ee.technion.ac.il Abstract. The uncertainty principle is a fundamental concept in the context of signal and image processing a formalism for finding functions which are the minimizers of the uncertainty principles. A general theorem
An Uncertainty Principle for Discrete Signals Sangnam Nam
Paris-Sud XI, Université de
An Uncertainty Principle for Discrete Signals Sangnam Nam Aix Marseille Universit´e, CNRS, Centrale-established by the Heisenberg's uncertainty principle when the time-frequency spread is measured in terms of the variance interpretation cannot become a reality; the well-known uncertainty principles expresse the idea
Uncertainty Principle and Quantum Fisher Information -II Paolo Gibilisco
Isola, Tommaso
Uncertainty Principle and Quantum Fisher Information - II Paolo Gibilisco , Daniele Imparato and Tommaso Isola May 21, 2007 Abstract Heisenberg and Schr¨odinger uncertainty principles give lower bounds [A, B] is not zero. In this paper we prove an uncertainty principle in Schr¨odinger form where
Heisenberg Uncertainty Principle for the q-Bessel Fourier transform
Paris-Sud XI, Université de
Heisenberg Uncertainty Principle for the q-Bessel Fourier transform Lazhar Dhaouadi Abstract further variant of Heisen- bergs uncertainty principle. Let f be the Fourier transform of f defined by f is defined by V [g] = R x2 g(x)dx. The Heisenberg uncertainty principle can be stated as follows V [|f|2 ]V
UNCERTAINTY PRINCIPLES AND ASYMPTOTIC BEHAVIOR SAY SONG GOH yz
Martin, Ralph R.
UNCERTAINTY PRINCIPLES AND ASYMPTOTIC BEHAVIOR SAY SONG GOH yz DEPARTMENT OF MATHEMATICS NATIONAL AND TIM N. T. GOODMAN Abstract Various uncertainty principles for univariate functions are studied also establish a general uncertainty principle for n pairs of operators on a Hilbert space, n = 2; 3
THE UNCERTAINTY PRINCIPLE IN HARMONIC ANALYSIS BLAINE TALBUT
May, J. Peter
THE UNCERTAINTY PRINCIPLE IN HARMONIC ANALYSIS BLAINE TALBUT Abstract. We present several uncertainty principle results from Fourier anal- ysis. The results we present are formally unrelated to one transform simultaneously. Contents 1. Introduction 1 2. Heisenberg's Uncertainty Principle 2 3. Complex
Optimal Functions for a Periodic Uncertainty Principle and Multiresolution Analysisy
Prestin, Jürgen
Optimal Functions for a Periodic Uncertainty Principle and Multiresolution Analysisy Dedicated frequency uncertainty principle described by Breitenberger in 3]. These extremal functions give rise by the Heisenberg uncertainty principle, and it is well known that the Gaussian functions serve as extremal
EQUALITY CASES FOR THE UNCERTAINTY PRINCIPLE IN FINITE ABELIAN GROUPS
Paris-Sud XI, Université de
EQUALITY CASES FOR THE UNCERTAINTY PRINCIPLE IN FINITE ABELIAN GROUPS ALINE BONAMI & SAIFALLAH will write Zn := Z/nZ to simplify notation. Uncertainty principles show how small the support]. It is usually referred to as Donoho-Stark Uncertainty Principle and deals 1991 Mathematics Subject
The uncertainty principle and quantum chaos
NASA Technical Reports Server (NTRS)
Chirikov, Boris V.
1993-01-01
The conception of quantum chaos is described in some detail. The most striking feature of this novel phenomenon is that all the properties of classical dynamical chaos persist here but, typically, on the finite and different time scales only. The ultimate origin of such a universal quantum stability is in the fundamental uncertainty principle which makes discrete the phase space and, hence, the spectrum of bounded quantum motion. Reformulation of the ergodic theory, as a part of the general theory of dynamical systems, is briefly discussed.
Quantum randomness certified by the uncertainty principle
NASA Astrophysics Data System (ADS)
Vallone, Giuseppe; Marangon, Davide G.; Tomasin, Marco; Villoresi, Paolo
2014-11-01
We present an efficient method to extract the amount of true randomness that can be obtained by a quantum random number generator (QRNG). By repeating the measurements of a quantum system and by swapping between two mutually unbiased bases, a lower bound of the achievable true randomness can be evaluated. The bound is obtained thanks to the uncertainty principle of complementary measurements applied to min-entropy and max-entropy. We tested our method with two different QRNGs by using a train of qubits or ququart and demonstrated the scalability toward practical applications.
Dilaton cosmology, noncommutativity, and generalized uncertainty principle
Vakili, Babak [Department of Physics, Shahid Beheshti University, Evin, Tehran 19839 (Iran, Islamic Republic of)
2008-02-15
The effects of noncommutativity and of the existence of a minimal length on the phase space of a dilatonic cosmological model are investigated. The existence of a minimum length results in the generalized uncertainty principle (GUP), which is a deformed Heisenberg algebra between the minisuperspace variables and their momenta operators. I extend these deformed commutating relations to the corresponding deformed Poisson algebra. For an exponential dilaton potential, the exact classical and quantum solutions in the commutative and noncommutative cases, and some approximate analytical solutions in the case of GUP, are presented and compared.
Least uncertainty principle in deformation quantization
Gerstenhaber, Murray [Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6395 (United States)
2007-02-15
Deformation quantization generally produces families of cohomologically equivalent quantizations of a single physical system. We conjecture that the physically meaningful ones (i) allow enough observable energy distributions, i.e., ones for which no pure quantum state has negative probability, and (ii) reduce the uncertainty in the probability distribution of the resulting quantum states. For the simple harmonic oscillator this principle selects the classic Groenewold-Moyal (or Weyl) product on phase space while for the free particle, in which there is no real quantization, all cohomologically equivalent quantizations are equally good.
Quantum Randomness Certified by the Uncertainty Principle
G. Vallone; D. Marangon; M. Tomasin; P. Villoresi
2014-12-22
We present an efficient method to extract the amount of true randomness that can be obtained by a Quantum Random Number Generator (QRNG). By repeating the measurements of a quantum system and by swapping between two mutually unbiased bases, a lower bound of the achievable true randomness can be evaluated. The bound is obtained thanks to the uncertainty principle of complementary measurements applied to min- and max- entropies. We tested our method with two different QRNGs, using a train of qubits or ququart, demonstrating the scalability toward practical applications.
Robertson-Schrödinger formulation of Ozawa's Uncertainty Principle
Catarina Bastos; A. E. Bernardini; O. Bertolami; N. C. Dias; J. N. Prata
2014-11-08
A more general measurement disturbance uncertainty principle is presented in a Robertson-Schr\\"odinger formulation. It is shown that it is stronger and having nicer properties than Ozawa's uncertainty relations. In particular is invariant under symplectic transformations. One shows also that there are states of the probe (measuring device) that saturate the matrix formulation of measurement disturbance uncertainty principle.
UNCERTAINTY PRINCIPLES IN HILBERT SPACES SAY SONG GOH y
Martin, Ralph R.
UNCERTAINTY PRINCIPLES IN HILBERT SPACES SAY SONG GOH y DEPARTMENT OF MATHEMATICS NATIONAL identi#12;ed. The third idea that we explore here is rooted in the uncertainty principles arising from the commutator of two linear operators acting on a Hilbert space which relate to the Heisenberg uncertainty
Experimental investigation of the entanglement-assisted entropic uncertainty principle
Chuan-Feng Li; Jin-Shi Xu; Xiao-Ye Xu; Ke Li; Guang-Can Guo
2012-04-23
The uncertainty principle, which bounds the uncertainties involved in obtaining precise outcomes for two complementary variables defining a quantum particle, is a crucial aspect in quantum mechanics. Recently, the uncertainty principle in terms of entropy has been extended to the case involving quantum entanglement. With previously obtained quantum information for the particle of interest, the outcomes of both non-commuting observables can be predicted precisely, which greatly generalises the uncertainty relation. Here, we experimentally investigated the entanglement-assisted entropic uncertainty principle for an entirely optical setup. The uncertainty is shown to be near zero in the presence of quasi-maximal entanglement. The new uncertainty relation is further used to witness entanglement. The verified entropic uncertainty relation provides an intriguing perspective in that it implies the uncertainty principle is not only observable-dependent but is also observer-dependent.
Black hole thermodynamics with generalized uncertainty principle
Li Xiang; X. Q. Wen
2009-03-18
In the standard viewpoint, the temperature of a stationary black hole is proportional to its surface gravity, $T_H=\\hbar\\kappa/2\\pi$. This is a semiclassical result and the quantum gravity effects are not taken into consideration. This Letter explores a unified expression for the black hole temperature in the sense of a generalized uncertainty principle(GUP). Our discussion involves a heuristic analysis of a particle which is absorbed by the black hole. Besides a class of static and spherically symmetric black holes, an axially symmetric Kerr-Newman black hole is considered. Different from the existing literature, we suggest that the black hole's irreducible mass represent the characteristic size in the absorption process. The information capacity of a remnant is also discussed by Bousso's D-bound in de Sitter spacetime.
Heisenberg's Uncertainty Principle and Interpretive Research in Science Education.
ERIC Educational Resources Information Center
Roth, Wolff-Michael
1993-01-01
Heisenberg's uncertainty principle and the derivative notions of interdeterminacy, uncertainty, precision, and observer-observed interaction are discussed and their applications to social science research examined. Implications are drawn for research in science education. (PR)
Incorporation of Generalized Uncertainty Principle into Lifshitz Field Theories
Mir Faizal; Barun Majumder
2015-03-23
In this paper, we will incorporation the generalized uncertainty principle into field theories with Lifshitz scaling. We will first construct both bososnic and fermionic theories with Lifshitz scaling based on generalized uncertainty principle. After that we will incorporate the generalized uncertainty principle into an non-abelian gauge theory with Lifshitz scaling. We will observe that even though the action for this theory is non-local, it is invariant under local gauge transformations. We will also perform the stochastic quantization of this Lifshitz fermionic theory based generalized uncertainty principle.
Lorentz Invariance Violation and Generalized Uncertainty Principle
A. Tawfik; H. Magdy; A. Farag Ali
2012-05-27
Recent approaches for quantum gravity are conjectured to give predictions for a minimum measurable length, a maximum observable momentum and an essential generalization for the Heisenberg uncertainty principle (GUP). The latter is based on a momentum-dependent modification in the standard dispersion relation and leads to Lorentz invariance violation (LIV). The main features of the controversial OPERA measurements on the faster-than-light muon neutrino anomaly are used to calculate the time of flight delays $\\Delta t$ and the relative change $\\Delta v$ in the speed of neutrino in dependence on the redshift $z$. The results are compared with the OPERA measurements. We find that the measurements are too large to be interpreted as LIV. Depending on the rest mass, the propagation of high-energy muon neutrino can be superluminal. The comparison with the ultra high energy cosmic rays seems to reveals an essential ingredient of the approach combining string theory, loop quantum gravity, black hole physics and doubly spacial relativity and the one assuming a pertubative departure from exact Lorentz invariance.
Nonlocal and generalized uncertainty principle black holes
Piero Nicolini
2012-02-21
In this paper we study the issue of the role of nonlocality as a possible ingredient to solve long standing problems in the physics of black holes. To achieve this goal we analytically derive new black hole metrics improved by corrections from nonlocal gravity actions with an entire function of the order 1/2 and lower than 1/2, the latter corresponding to generalized uncertainty principle corrections. This lets us extend our previous findings about noncommutative geometry inspired black holes recently recognized as nonlocal black holes due to an entire function of order higher than 1/2. As a result we show that irrespective of the order of the function, nonlocality leads to the following properties for black hole spacetimes: i) horizon extremization also in the neutral, non rotating case; ii) black hole phase transition from a Schwarzschild phase to a positive heat capacity cooling down phase; iii) zero temperature remnant formation at the end of the evaporation process; iv) negligible quantum back reaction due to the presence of an upper bound for the Hawking temperature. Finally we show that, in agreement with the general theory of cut off functions, a regular deSitter core accounting for the energy density of virtual gravitons replaces the curvature singularity only in the case of entire functions of order 1/2 or higher.
Quantum groups, gravity, and the generalized uncertainty principle
Michele Maggiore
1994-01-01
We investigate the relationship between the generalized uncertainty principle in quantum gravity and the quantum deformation of the Poincaré algebra. We find that a deformed Newton-Wigner position operator and the generators of spatial translations and rotations of the deformed Poincaré algebra obey a deformed Heisenberg algebra from which the generalized uncertainty principle follows. The result indicates that in the kappa-deformed
Nondivergent classical response functions from uncertainty principle: Quasiperiodic systems
Cao, Jianshu
Nondivergent classical response functions from uncertainty principle: Quasiperiodic systems Maksym the quantized uncertainty volume O( n ) around the microcanonical energy surface. For a quasiperiodic system's correspondence principle: each matrix element u (t) v corresponds to the (u v)th Fourier component of (t
The algebraic structure of the generalized uncertainty principle
Michele Maggiore
1993-01-01
We show that a deformation of the Heisenberg algebra which depends on a dimensionful parameter kappa is the algebraic structure which underlies the generalized uncertainty principle in quantum gravity. The deformed algebra and therefore the form of the generalized uncertainty principle are fixed uniquely by rather simple assumptions. The string theory result is reproduced expanding our result at first order
An entropic uncertainty principle for positive operator valued measures
Michel Rumin
2011-10-25
Extending a recent result by Frank and Lieb, we show an entropic uncertainty principle for mixed states in a Hilbert space relatively to pairs of positive operator valued measures that are independent in some sense. This yields spatial-spectral uncertainty principles and log-Sobolev inequalities for invariant operators on homogeneous spaces, which are sharp in the compact case.
Privacy Amplification, Private States, and the Uncertainty Principle
Joseph M. Renes; Jean-Christian Boileau
2007-02-19
We show that three principle means of treating privacy amplification in quantum key distribution, private state distillation, classical privacy amplification, and via the uncertainty principle, are equivalent and interchangeable. By adapting the security proof based on the uncertainty principle, we construct a new protocol for private state distillation which we prove is identical to standard classical privacy amplification. Underlying this approach is a new characterization of private states, related to their standard formulation by the uncertainty principle, which gives a more physical understanding of security in quantum key distribution.
Thermodynamics of black holes and the symmetric generalized uncertainty principle
Abhijit Dutta; Sunandan Gangopadhyay
2014-08-23
In this paper, we have investigated the thermodynamics of Schwarzschild black holes using the symmetric generalized uncertainty principle which contains correction terms involving momentum and position uncertainty. We obtain the mass-temperature relation and the heat capacity of the black hole using which we compute the critical and remnant masses. The entropy is found to satisfy the area law upto leading order corrections from the symmetric generalized uncertainty principle.
String Theory and Space-Time Uncertainty Principle
Tamiaki Yoneya
2000-01-01
The notion of a space-time uncertainty principle in string theory is clarified and further developed. The motivation and the derivation of the principle are first reviewed in a reasonably self-contained way. It is then shown that the nonperturbative (Borel summed) high-energy and high-momentum transfer behavior of string scattering is consistent with the space-time uncertainty principle. It is also shown that,
Chemical Principles Revisited: Perspectives on the Uncertainty Principle and Quantum Reality.
ERIC Educational Resources Information Center
Bartell, Lawrence S.
1985-01-01
Explicates an approach that not only makes the uncertainty seem more useful to introductory students but also helps convey the real meaning of the term "uncertainty." General topic areas addressed include probability amplitudes, rationale behind the uncertainty principle, applications of uncertainty relations, and quantum processes. (JN)
HARDY'S UNCERTAINTY PRINCIPLE ON SEMISIMPLE GROUPS M. COWLING, A. SITARAM, AND M. SUNDARI
Cowling, Michael
HARDY'S UNCERTAINTY PRINCIPLE ON SEMISIMPLE GROUPS M. COWLING, A described in the abstract is due* * to Hardy [3]; we call it Hardy's Uncertainty Principle. Considerable] generalis* *ed Hardy's Uncertainty Principle to connected semisimple Lie groups with one conjugacy cla
An uncertainty principle, Wegner estimates and localization near fluctuation boundaries
Anne Boutet de Monvel; Daniel Lenz; Peter Stollmann
2009-05-18
We prove a simple uncertainty principle and show that it can be applied to prove Wegner estimates near fluctuation boundaries. This gives new classes of models for which localization at low energies can be proven.
Tests of Quantum Gravity via Generalized Uncertainty Principle
Yumi Ko; Sunggeun Lee; Soonkeon Nam
2006-08-03
In this paper we propose a way of determining the subleading corrections to the Bekenstein-Hawking black hole entropy by considering a modified generalized uncertainty principle with two parameters. In the context of modified generalized uncertainty principle, coefficients of the correction terms of black hole entropy are written in terms of combination of the parameters. We also calculate corrections to the Stefan-Boltzman law of Hawking radiation corresponding to modified generalized uncertainty principle. By comparing the entropy with one from black holes in string theory compactified on a Calabi-Yau manifold, we point out that the topological information of the compactified space can not easily be related to the parameters in modified generalized uncertainty principle.
Quantization of fields based on Generalized Uncertainty Principle
Toshihiro Matsuo; Yuuichirou Shibusa
2006-06-14
We construct a quantum theory of free scalar field in 1+1 dimensions based on a `Generalized Uncertainty Principle'. Both canonical and path integral formalism are employed. Higher dimensional extension is easily performed in the path integral formalism.
The Generalized Uncertainty Principle and Quantum Gravity Phenomenology
Ahmed Farag Ali; Saurya Das; Elias C. Vagenas
2010-01-18
In this article we examine a Generalized Uncertainty Principle which differs from the Heisenberg Uncertainty Principle by terms linear and quadratic in particle momenta, as proposed by the authors in an earlier paper. We show that this affects all Hamiltonians, and in particular those which describe low energy experiments. We discuss possible observational consequences. Further, we also show that this indicates that space may be discrete at the fundamental level.
Supersymmetric Field Theory Based on Generalized Uncertainty Principle
Yuuichirou Shibusa
2007-04-12
We construct a quantum theory of free fermion field based on the generalized uncertainty principle using supersymmetry as a guiding principle. A supersymmetric field theory with a real scalar field and a Majorana fermion field is given explicitly and we also find that the supersymmetry algebra is deformed from an usual one.
Microscopic black hole stabilization via the uncertainty principle
NASA Astrophysics Data System (ADS)
Vayenas, Constantinos G.; Grigoriou, Dimitrios
2015-01-01
Due to the Heisenberg uncertainty principle, gravitational confinement of two- or three-rotating particle systems can lead to microscopic Planckian or sub-Planckian black holes with a size of order their Compton wavelength. Some properties of such states are discussed in terms of the Schwarzschild geodesics of general relativity and compared with properties computed via the combination of special relativity, equivalence principle, Newton's gravitational law and Compton wavelength. It is shown that the generalized uncertainty principle (GUP) provides a satisfactory fit of the Schwarzschild radius and Compton wavelength of such microscopic, particle-like, black holes.
The Uncertainty Principle in the Presence of Quantum Memory
Mario Berta; Matthias Christandl; Roger Colbeck; Joseph M. Renes; Renato Renner
2011-03-01
The uncertainty principle, originally formulated by Heisenberg, dramatically illustrates the difference between classical and quantum mechanics. The principle bounds the uncertainties about the outcomes of two incompatible measurements, such as position and momentum, on a particle. It implies that one cannot predict the outcomes for both possible choices of measurement to arbitrary precision, even if information about the preparation of the particle is available in a classical memory. However, if the particle is prepared entangled with a quantum memory, a device which is likely to soon be available, it is possible to predict the outcomes for both measurement choices precisely. In this work we strengthen the uncertainty principle to incorporate this case, providing a lower bound on the uncertainties which depends on the amount of entanglement between the particle and the quantum memory. We detail the application of our result to witnessing entanglement and to quantum key distribution.
The Entropic Uncertainty Principle for Decaying Systems and CP violation
Beatrix C. Hiesmayr
2011-03-17
Employing an effective formalism for decaying system we are able to investigate Heisenberg's uncertainty relation for observables measured at accelerator facilities. In particular we investigate the neutral K--meson system and show that, firstly, due to the time evolution an uncertainty between strangeness measurements at different times is introduced and, secondly, due to the imbalance of matter and antimatter (CP violation) an uncertainty in the evolution of the eigenstates of the effective Hamiltonian of the system. Consequently, the existence of CP violation is linked to uncertainties of observables, i.e. the outcomes cannot be predicted even in principle to arbitrary precisions.
Path detection and the uncertainty principle
Pippa Storey; Sze Tan; Matthew Collett; Daniel Walls
1994-01-01
QUANTUM mechanics predicts that any detector capable of determining the path taken by a particle through a double slit will destroy the interference. This follows from the principle of complementarity formulated by Niels Bohr: simultaneous observation of wave and particle behaviour is prohibited. But such a description makes no reference to the physical mechanism by which the interference is lost.
M. Athans; R. Ku; S. Gershwin
1977-01-01
This note shows that the optimal control of dynamic systems with uncertain parameters has certain limitations. In particular, by means of a simple scalar linear-quadratic optimal control example, it is shown that the infinite horizon solution does not exist if the parameter uncertainty exceeds a certain quantifiable threshold; we call this the uncertainty threshold principle. The philosophical and design implications
Applications of the uncertainty principle for finite abelian groups to communications engineering
Pfander, Götz
Applications of the uncertainty principle for finite abelian groups to communications engineering, Germany We obtain uncertainty principles for finite abelian groups relating the cardinality of the support their applications. These uncertainty principles are based on well-established uncertainty principles for the Fourier
Generalized Uncertainty Principle and Self-dual Black Holes
Bernard Carr; Leonardo Modesto; Isabeau Prémont-Schwarz
2011-07-04
The Generalized Uncertainty Principle suggests corrections to the Uncertainty Principle as the energy increases towards the Planck value. It provides a natural transition between the expressions for the Compton wavelength below the Planck mass and the black hole event horizon size above this mass. It also suggests corrections to the the event horizon size as the black hole mass falls towards the Planck value, leading to the concept of a Generalized Event Horizon. Extrapolating below the Planck mass suggests the existence of a new class of black holes, whose size is of order the Compton wavelength for their mass. Such sub-Planckian black holes have recently been discovered in the context of loop quantum gravity and it is possible that this applies more generally. This suggests an intriguing connection between black holes, the Uncertainty Principle and quantum gravity.
Uniform Uncertainty Principle for Bernoulli and Subgaussian Ensembles
Shahar Mendelson; Alain Pajor; Nicole Tomczak-Jaegermann
2008-01-01
The paper considers random matrices with independent subgaussian columns and provides a new elementary proof of the Uniform\\u000a Uncertainty Principle for such matrices. The Principle was introduced by Candes, Romberg and Tao in 2004; for subgaussian\\u000a random matrices it was carlier proved by the present authors, as a consequence of a general result based on a generic chaining\\u000a method of
The generalized uncertainty principle as quantum gravitational friction
NASA Astrophysics Data System (ADS)
Bargueño, Pedro
2015-01-01
In this article we present a dissipative Schrodinger-Langevin-like Hamiltonian which incorporates implicitly the deformed commutation relations which are linear in particle momenta due to a generalized uncertainty principle. This result is based on interpreting the deformation parameter as quantum gravitational friction on the configuration space.
Single-Slit Diffraction and the Uncertainty Principle
ERIC Educational Resources Information Center
Rioux, Frank
2005-01-01
A theoretical analysis of single-slit diffraction based on the Fourier transform between coordinate and momentum space is presented. The transform between position and momentum is used to illuminate the intimate relationship between single-slit diffraction and uncertainty principle.
The Uncertainty Principle, Virtual Particles and Real Forces
ERIC Educational Resources Information Center
Jones, Goronwy Tudor
2002-01-01
This article provides a simple practical introduction to wave-particle duality, including the energy-time version of the Heisenberg Uncertainty Principle. It has been successful in leading students to an intuitive appreciation of "virtual particles" and the role they play in describing the way ordinary particles, like electrons and protons, exert…
The optimal transform for the discrete Hirschman uncertainty principle
Tomasz Przebinda; Victor E. Debrunner; Murad Özaydin
2001-01-01
We determine all signals giving equality for the discrete Hirschman uncertainty principle. We single out the case where the entropies of the time signal and its Fourier transform are equal. These signals (up to scalar multiples) form an orthonormal basis giving an orthogonal transform that optimally packs a finite-duration discrete-time signal. The transform may be computed via a fast algorithm
Uniform uncertainty principle for Bernoulli and subgaussian ensembles
Shahar Mendelson; Alain Pajor; Nicole Tomczak-Jaegermann
2006-01-01
We present a simple solution to a question posed by Candes, Romberg and Tao on the uniform uncertainty principle for Bernoulli random matrices. More precisely, we show that a rectangular k*n random subgaussian matrix (with k < n) has the property that by arbitrarily extracting any m (with m < k) columns, the resulting submatrices are arbitrarily close to (multiples
Non-commutative space–time and the uncertainty principle
Eric Carlen; R. Vilela Mendesb
2001-01-01
The full algebra of relativistic quantum mechanics (Lorentz plus Heisenberg) is unstable. Stabilization by deformation leads to a new deformation parameter ??2, ? being a length and ? a ± sign. The implications of the deformed algebras for the uncertainty principle and the density of states are worked out and compared with the results of past analysis following from gravity
Generalized Uncertainty Principle, Modified Dispersion Relations and Early Universe Thermodynamics
Kourosh Nozari; Behnaz Fazlpour
2006-06-17
In this paper, we study the effects of Generalized Uncertainty Principle(GUP) and Modified Dispersion Relations(MDRs) on the thermodynamics of ultra-relativistic particles in early universe. We show that limitations imposed by GUP and particle horizon on the measurement processes, lead to certain modifications of early universe thermodynamics.
Heisenberg's uncertainty principle in the sense of Beurling
Haakan Hedenmalm
2012-04-05
We shed new light on Heisenberg's uncertainty principle in the sense of Beurling, by offering an essentially different proof which permits us to weaken the assumptions substantially, and examples show that the result is sharp. The proof involves Fourier and Mellin transforms. We alo extend to a setting of two functions. A higher-dimensional analogue is considered as well.
Effects of the Modified Uncertainty Principle on the Inflation Parameters
Barun Majumder
2012-02-24
In this Letter we study the effects of the Modified Uncertainty Principle as proposed in [8] on the inflationary dynamics of the early universe in both standard and Randall-Sundrum type II scenarios. We find that the quantum gravitational effect increase the amplitude of density fluctuation, which is oscillatory in nature, with an increase in the tensor-to-scalar ratio.
Uncertainty Principles for the Fourier Transforms in Quantum Calculus
Neji Bettaibi; Ahmed Fitouhi; Wafa Binous
2006-02-28
Some properties of the $q$-Fourier-sine transform are studied and $q$-analogues of the Heisenberg uncertainty principle is derived for the $q$-Fourier-cosine transform studied in \\cite{FB} and for the $q$-Fourier-sine transform.
Gauge Theories under Incorporation of a Generalized Uncertainty Principle
Martin Kober
2011-12-05
There is considered an extension of gauge theories according to the assumption of a generalized uncertainty principle which implies a minimal length scale. A modification of the usual uncertainty principle implies an extended shape of matter field equations like the Dirac equation. If there is postulated invariance of such a generalized field equation under local gauge transformations, the usual covariant derivative containing the gauge potential has to be replaced by a generalized covariant derivative. This leads to a generalized interaction between the matter field and the gauge field as well as to an additional self interaction of the gauge field. Since the existence of a minimal length scale seems to be a necessary assumption of any consistent quantum theory of gravity, the gauge principle is a constitutive ingredient of the standard model and even gravity can be described as gauge theory of local translations or Lorentz transformations, the presented extension of gauge theories appears as a very important consideration.
Gauge theories under incorporation of a generalized uncertainty principle
Kober, Martin [Frankfurt Institute for Advanced Studies (FIAS), Institut fuer Theoretische Physik, Johann Wolfgang Goethe-Universitaet, Ruth-Moufang-Strasse 1, 60438 Frankfurt am Main (Germany)
2010-10-15
There is considered an extension of gauge theories according to the assumption of a generalized uncertainty principle which implies a minimal length scale. A modification of the usual uncertainty principle implies an extended shape of matter field equations like the Dirac equation. If there is postulated invariance of such a generalized field equation under local gauge transformations, the usual covariant derivative containing the gauge potential has to be replaced by a generalized covariant derivative. This leads to a generalized interaction between the matter field and the gauge field as well as to an additional self-interaction of the gauge field. Since the existence of a minimal length scale seems to be a necessary assumption of any consistent quantum theory of gravity, the gauge principle is a constitutive ingredient of the standard model, and even gravity can be described as gauge theory of local translations or Lorentz transformations, the presented extension of gauge theories appears as a very important consideration.
arXiv:math.FA/0701207v17Jan2007 WEAK UNCERTAINTY PRINCIPLE FOR FRACTALS, GRAPHS
Teplyaev, Alexander
arXiv:math.FA/0701207v17Jan2007 WEAK UNCERTAINTY PRINCIPLE FOR FRACTALS, GRAPHS AND METRIC MEASURE and manifolds. Contents 1. Introduction 1 2. Main results 3 2.1. Weak uncertainty principle and effective resistance metric 3 2.2. Weak uncertainty principle and Poincar´e-type inequality 5 2.3. Weak uncertainty
A volume inequality for quantum Fisher information and the uncertainty principle
Isola, Tommaso
A volume inequality for quantum Fisher information and the uncertainty principle Paolo Gibilisco-adjoint matrices and let be a density matrix. The Robertson uncertainty principle det {Cov(Ah, Aj)} det - i 2 Tr.2) the "standard" uncertainty principle to distinguish it from other inequalities like the "entropic" uncertainty
NASA Technical Reports Server (NTRS)
Athans, M.; Ku, R.; Gershwin, S. B.
1977-01-01
This note shows that the optimal control of dynamic systems with uncertain parameters has certain limitations. In particular, by means of a simple scalar linear-quadratic optimal control example, it is shown that the infinite horizon solution does not exist if the parameter uncertainty exceeds a certain quantifiable threshold; we call this the uncertainty threshold principle. The philosophical and design implications of this result are discussed.
Coherent States of Harmonic Oscillator and Generalized Uncertainty Principle
Kourosh Nozari; Tahereh Azizi
2005-04-20
In this paper dynamics and quantum mechanical coherent states of a simple harmonic oscillator are considered in the framework of Generalized Uncertainty Principle(GUP). Equations of motion for simple harmonic oscillator are derived and some of their new implications are discussed. Then coherent states of harmonic oscillator in the case of GUP are compared with relative situation in ordinary quantum mechanics. It is shown that in the framework of GUP there is no considerable difference in definition of coherent states relative to ordinary quantum mechanics. But, considering expectation values and variances of some operators, based on quantum gravitational arguments one concludes that although it is possible to have complete coherency and vanishing broadening in usual quantum mechanics, gravitational induced uncertainty destroys complete coherency in quantum gravity and it is not possible to have a monochromatic ray in principle.
Quantum black hole in the generalized uncertainty principle framework
Bina, A.; Moslehi, A. [Department of Physics, Faculty of Science, Arak University, Arak 879 (Iran, Islamic Republic of); Jalalzadeh, S. [Department of Physics, Shahid Beheshti University G.C., Evin, Tehran 19839 (Iran, Islamic Republic of); Research Institute for Astronomy and Astrophysics of Maragha (RIAAM) Maragha, Iran, P. O. Box: 55134-441 (Iran, Islamic Republic of)
2010-01-15
In this paper we study the effects of the generalized uncertainty principle (GUP) on canonical quantum gravity of black holes. Through the use of modified partition function that involves the effects of the GUP, we obtain the thermodynamical properties of the Schwarzschild black hole. We also calculate the Hawking temperature and entropy for the modification of the Schwarzschild black hole in the presence of the GUP.
Optimal Functions for a Periodic Uncertainty Principle and Multiresolution Analysis
Ewald Quak; Jurgen Prestin
1995-01-01
. In this paper, it is shown that certain Theta functions are asymptoticallyoptimal for the periodic time frequency uncertainty principle described by Breitenbergerin [3]. These extremal functions give rise to a periodic multiresolution analysis wherethe corresponding wavelets also show similar localization properties.Subject Classification. Primary 42A16, Secondary 26D05, 26D10, 26D15.x1. IntroductionA fundamental result on time and frequency localization of square-integrable functions...
Uncertainty principle for Gabor systems and the Zak transform
Czaja, Wojciech; Zienkiewicz, Jacek [Institute of Mathematics, University of Wrodaw, Plac Grunwaldzki 2/4, 50-384 Wrodaw (Poland)
2006-12-15
We show that if g(set-membership sign)L{sup 2}(R) is a generator of a Gabor orthonormal basis with the lattice ZxZ, then its Zak transform Z(g) satisfies {nabla}Z(g)(negated-set-membership sign)L{sup 2}([0,1){sup 2}). This is a generalization and extension of the Balian-Low uncertainty principle.
Uncertainty principles for magnetic structures on certain coadjoint orbits
Ingrid Beltita; Daniel Beltita
2009-06-08
By building on our earlier work, we establish uncertainty principles in terms of Heisenberg inequalities and of the ambiguity functions associated with magnetic structures on certain coadjoint orbits of infinite-dimensional Lie groups. These infinite-dimensional Lie groups are semidirect products of nilpotent Lie groups and invariant function spaces thereon. The recently developed magnetic Weyl calculus is recovered in the special case of function spaces on abelian Lie groups.
Born-Jordan Quantization and the Uncertainty Principle
Maurice A. de Gosson
2013-03-11
The Weyl correspondence and the related Wigner formalism lie at the core of traditional quantum mechanics. We discuss here an alternative quantization scheme, whose idea goes back to Born and Jordan, and which has recently been revived in another context, namely time-frequency analysis. We show that in particular the uncertainty principle does not enjoy full symplectic covariance properties in the Born and Jordan scheme, as opposed to what happens in the Weyl quantization.
Simple security proof of quantum key distribution via uncertainty principle
Masato Koashi
2005-05-14
We present an approach to the unconditional security of quantum key distribution protocols based on the uncertainty principle. The approach applies to every case that has been treated via the argument by Shor and Preskill, and relieve them from the constraints of finding quantum error correcting codes. It can also treat the cases with uncharacterized apparatuses. We derive a secure key rate for the Bennett-Brassard-1984 protocol with an arbitrary source characterized only by a single parameter representing the basis dependence.
New agegraphic dark energy model with generalized uncertainty principle
Yong-Wan Kim; Hyung Won Lee; Yun Soo Myung; Mu-In Park
2008-08-07
We investigate the new agegraphic dark energy models with generalized uncertainty principle (GUP). It turns out that although the GUP affects the early universe, it does not change the current and future dark energy-dominated universe significantly. Furthermore, this model could describe the matter-dominated universe in the past only when the parameter $n$ is chosen to be $n>n_c$, where the critical value determined to be $n_c=2.799531478$.
"Stringy" Coherent States Inspired By Generalized Uncertainty Principle
Subir Ghosh; Pinaki Roy
2012-04-16
In this Letter we have explicitly constructed Generalized Coherent States for the Non-Commutative Harmonic Oscillator that directly satisfy the Generalized Uncertainty Principle (GUP). Our results have a smooth commutative limit. The states show fractional revival which provides an independent bound on the GUP parameter. Using this and similar bounds we derive the largest possible value of the (GUP induced) minimum length scale. Mandel parameter analysis shows that the statistics is Sub-Poissionian.
Generalized uncertainty principle and Ho?ava-Lifshitz gravity
Yun Soo Myung
2009-08-13
We explore a connection between generalized uncertainty principle (GUP) and modified Ho\\v{r}ava-Lifshitz (HL) gravity. The GUP density function may be replaced by the cutoff function for the renormalization group of modified Ho\\v{r}ava-Lifshitz gravity. We find the GUP-corrected graviton propagators and compare these with tensor propagators in the HL gravity. Two are qualitatively similar, but the $p^5$-term arisen from Cotton tensor is missed in the GUP-corrected graviton propagator.
Remarks on Generalized Uncertainty Principle Induced from Constraint System
NASA Astrophysics Data System (ADS)
Eune, Myungseok; Kim, Wontae
2014-12-01
The extended commutation relations for generalized uncertainty principle (GUP) have been based on the assumption of the minimal length in position. Instead of this assumption, we start with a constrained Hamiltonian system described by the conventional Poisson algebra and then impose appropriate second class constraints to this system. Consequently, we can show that the consistent Dirac brackets for this system are nothing, but the extended commutation relations describing the GUP.
Generalized Uncertainty Principle: Implications for Black Hole Complementarity
Pisin Chen; Yen Chin Ong; Dong-han Yeom
2014-12-10
At the heart of the black hole information loss paradox and the firewall controversy lies the conflict between quantum mechanics and general relativity. Much has been said about quantum corrections to general relativity, but much less in the opposite direction. It is therefore crucial to examine possible corrections to quantum mechanics due to gravity. Indeed, the Heisenberg Uncertainty Principle is one profound feature of quantum mechanics, which nevertheless may receive correction when gravitational effects become important. Such generalized uncertainty principle [GUP] has been motivated from not only quite general considerations of quantum mechanics and gravity, but also string theoretic arguments. We examine the role of GUP in the context of black hole complementarity. We find that while complementarity can be violated by large N rescaling if one assumes only the Heisenberg's Uncertainty Principle, the application of GUP may save complementarity, but only if certain N-dependence is also assumed. This raises two important questions beyond the scope of this work, i.e., whether GUP really has the proposed form of N-dependence, and whether black hole complementarity is indeed correct.
Generalized uncertainty principle: implications for black hole complementarity
NASA Astrophysics Data System (ADS)
Chen, Pisin; Ong, Yen Chin; Yeom, Dong-han
2014-12-01
At the heart of the black hole information loss paradox and the firewall controversy lies the conflict between quantum mechanics and general relativity. Much has been said about quantum corrections to general relativity, but much less in the opposite direction. It is therefore crucial to examine possible corrections to quantum mechanics due to gravity. Indeed, the Heisenberg Uncertainty Principle is one profound feature of quantum mechanics, which nevertheless may receive correction when gravitational effects become important. Such generalized uncertainty principle [GUP] has been motivated from not only quite general considerations of quantum mechanics and gravity, but also string theoretic arguments. We examine the role of GUP in the context of black hole complementarity. We find that while complementarity can be violated by large N rescaling if one assumes only the Heisenberg's Uncertainty Principle, the application of GUP may save complementarity, but only if certain N -dependence is also assumed. This raises two important questions beyond the scope of this work, i.e., whether GUP really has the proposed form of N -dependence, and whether black hole complementarity is indeed correct.
Atomic and Molecular Quantum Theory Course Number: C561 14 The Heisenberg's Uncertainty Principle
Iyengar, Srinivasan S.
Atomic and Molecular Quantum Theory Course Number: C561 14 The Heisenberg's Uncertainty Principle Now we are ready to find out what the Heisenberg's Uncertainty Principle really is, in all its glory.15) Equation (14.15) is called the Heisenberg uncertainty principle. This equation suggests that one cannot
Rioux, Frank
the Uncertainty Principle Frank Rioux|SJU The uncertainty principle is revealed by a comparison of the coordinate and momentum wave functions for the hydrogen atom (z=1) and helium ion (z=2) clearly illustrate the uncertainty principle. 0 2 4 6 r 2 1 r
Rioux, Frank
to Illustrate the Uncertainty Principle Frank Rioux Diffraction has a simple quantum mechanical interpretation the uncertainty principle. A screen with a single slit of width, w, is illuminated with a coherent photon position, it localizes the incident beam in the xdirection. According to the uncertainty principle, because
HARDY-POINCARE, RELLICH AND UNCERTAINTY PRINCIPLE INEQUALITIES ON RIEMANNIAN MANIFOLDS
HARDY-POINCAR´E, RELLICH AND UNCERTAINTY PRINCIPLE INEQUALITIES ON RIEMANNIAN MANIFOLDS ISMAIL and Uncertainty principle inequalities on a Riemannian manifold M, started in [16]. In the present paper we prove new weighted Hardy-Poincar´e, Rellich and Uncertainty principle inequalities and their improved
PostDoc position available: Uncertainty Principles in Signal Processing, and Applications to
Feichtinger, Hans Georg
PostDoc position available: Uncertainty Principles in Signal Processing, and Applications to Audio Commission within the FET programme), whose aim is to investigate Uncertainty Principles and their impact. In the framework of the UNLocX project2 , these problems are addressed in connection with uncertainty principles
ccsd-00005822,version1-4Jul2005 HERMITE FUNCTIONS AND UNCERTAINTY PRINCIPLES FOR THE
Paris-Sud XI, Université de
ccsd-00005822,version1-4Jul2005 HERMITE FUNCTIONS AND UNCERTAINTY PRINCIPLES FOR THE FOURIER an uncertainty principle due to Beurling into a characterization of Hermite functions. More precisely, all for this transform. 1. Introduction and Notations. Uncertainty principles state that a function and its Fourier
UNCERTAINTY PRINCIPLE By reanalysing the experiment on Heisenberg Gamma-Ray
Groppi, Christopher
1 UNCERTAINTY PRINCIPLE IS UNTENABLE By reanalysing the experiment on Heisenberg Gamma-Ray Microscope and one of ideal experiment from which uncertainty principle is derived , it is found that actually uncertainty principle can not be obtained from these two ideal experiments . And it is found
The Uncertainty Principle in the Presence of Quantum Memory Mario Berta,1, 2
The Uncertainty Principle in the Presence of Quantum Memory Mario Berta,1, 2 Matthias Christandl,1: 26th July 2010) The uncertainty principle [1] lies at the heart of quantum theory, illuminating a dramatic dif- ference with classical mechanics. The principle bounds the uncertainties of the outcomes
The Multi-Dimensional Hardy Uncertainty Principle and its Interpretation in Terms of the
Feichtinger, Hans Georg
The Multi-Dimensional Hardy Uncertainty Principle and its Interpretation in Terms of the Wigner 15, AT-1090 Wien February 1, 2008 Abstract We extend Hardy's uncertainty principle for a square. We use this extension to show that Hardy's uncertainty principle is equivalent to a statement
ON UNCERTAINTY PRINCIPLES IN THE FINITE DIMENSIONAL SAIFALLAH GHOBBER AND PHILIPPE JAMING
Paris-Sud XI, Université de
ON UNCERTAINTY PRINCIPLES IN THE FINITE DIMENSIONAL SETTING SAIFALLAH GHOBBER AND PHILIPPE JAMING Abstract. The aim of this paper is to prove an uncertainty principle for the representation of a vector in two bases. Our result extends previously known "qualitative" uncertainty principles into more
A dynamical uncertainty principle in von Neumann algebras by operator monotone functions
Isola, Tommaso
A dynamical uncertainty principle in von Neumann algebras by operator monotone functions Paolo matrices) and is a state (density matrix). In this case the standard uncertainty principle, provedL30, 46L60. Key words and phrases. Uncertainty principle, operator monotone function, quantum Fisher
Optimal Functions for a Periodic Uncertainty Principle and Multiresolution Analysis y
Prestin, Jürgen
Optimal Functions for a Periodic Uncertainty Principle and Multiresolution Analysis y Dedicated frequency uncertainty principle described by Breitenberger in [3]. These extremal functions give rise by the Heisenberg uncertainty principle, and it is well known that the Gaussian functions serve as extremal
arXiv:0801.3402v2 On Generalized Uncertainty Principle
########### arXiv:0801.3402v2 [hepth] 20 Sep 2011 On Generalized Uncertainty Principle Bhupendra We study generalized uncertainty principle through the basic concepts of limit and Fourier at the string uncertainty principle from the analytic- ity condition of a complex function, which depends upon
hal-00080459,version2-13Dec2006 UNCERTAINTY PRINCIPLES FOR RADAR AMBIGUITY FUNCTIONS AND
Paris-Sud XI, Université de
hal-00080459,version2-13Dec2006 UNCERTAINTY PRINCIPLES FOR RADAR AMBIGUITY FUNCTIONS AND MOMENTS is not achievable because of the so-called "ambiguity uncertainty principle", that is the constraint R2 |A(u)(x, y are given by various versions of the uncertainty principle for the ambiguity function, see e.g. [BDJ, De, Gr
WEAK UNCERTAINTY PRINCIPLES ON FRACTALS KASSO A. OKOUDJOU AND ROBERT S. STRICHARTZ
Okoudjou, Kasso A.
WEAK UNCERTAINTY PRINCIPLES ON FRACTALS KASSO A. OKOUDJOU AND ROBERT S. STRICHARTZ #3; Abstract. We eigenfunctions on some of these fractals precludes an uncertainty principle in the vein of Heisenberg's in of pcf fractals, thereby obtaining an uncertainty principle on a particular type of non-pcf fractal. 1
Fabio Scardigli; Roberto Casadio
2007-11-23
It has been recently debated whether a class of generalized uncertainty principles that include gravitational sources of error are compatible with the holographic principle in models with extra spatial dimensions. We had in fact shown elsewhere that the holographic scaling is lost when more than four space-time dimensions are present. However, we shall show here that the validity of the holographic counting can be maintained also in models with extra spatial dimensions, but at the intriguing price that the equivalence principle for a point-like source be violated and the inertial mass differ from the gravitational mass in a specific non-trivial way.
NASA Technical Reports Server (NTRS)
Athans, M.; Ku, R.; Gershwin, S. B.
1976-01-01
The fundamental limitations of the optimal control of dynamic systems with random parameters are analyzed by studying a scalar linear-quadratic optimal control example. It is demonstrated that optimum long-range decision making is possible only if the dynamic uncertainty (quantified by the means and covariances of the random parameters) is below a certain threshold. If this threshold is exceeded, there do not exist optimum decision rules. This phenomenon is called the 'uncertainty threshold principle'. The implications of this phenomenon to the field of modelling, identification, and adaptive control are discussed.
Universal Uncertainty Principle in the Measurement Operator Formalism
Masanao Ozawa
2005-10-27
Heisenberg's uncertainty principle has been understood to set a limitation on measurements; however, the long-standing mathematical formulation established by Heisenberg, Kennard, and Robertson does not allow such an interpretation. Recently, a new relation was found to give a universally valid relation between noise and disturbance in general quantum measurements, and it has become clear that the new relation plays a role of the first principle to derive various quantum limits on measurement and information processing in a unified treatment. This paper examines the above development on the noise-disturbance uncertainty principle in the model-independent approach based on the measurement operator formalism, which is widely accepted to describe a class of generalized measurements in the field of quantum information. We obtain explicit formulas for the noise and disturbance of measurements given by the measurement operators, and show that projective measurements do not satisfy the Heisenberg-type noise-disturbance relation that is typical in the gamma-ray microscope thought experiments. We also show that the disturbance on a Pauli operator of a projective measurement of another Pauli operator constantly equals the square root of 2, and examine how this measurement violates the Heisenberg-type relation but satisfies the new noise-disturbance relation.
Nonequilibrium fluctuation-dissipation inequality and nonequilibrium uncertainty principle.
Fleming, C H; Hu, B L; Roura, Albert
2013-07-01
The fluctuation-dissipation relation is usually formulated for a system interacting with a heat bath at finite temperature, and often in the context of linear response theory, where only small deviations from the mean are considered. We show that for an open quantum system interacting with a nonequilibrium environment, where temperature is no longer a valid notion, a fluctuation-dissipation inequality exists. Instead of being proportional, quantum fluctuations are bounded below by quantum dissipation, whereas classically the fluctuations vanish at zero temperature. The lower bound of this inequality is exactly satisfied by (zero-temperature) quantum noise and is in accord with the Heisenberg uncertainty principle, in both its microscopic origins and its influence upon systems. Moreover, it is shown that there is a coupling-dependent nonequilibrium fluctuation-dissipation relation that determines the nonequilibrium uncertainty relation of linear systems in the weak-damping limit. PMID:23944409
Minisuperspace dynamics in a generalized uncertainty principle framework
Battisti, Marco Valerio [ICRA-International Center for Relativistic Astrophysics Dipartimento di Fisica (G9), Universita di Roma 'La Sapienza' P.le A. Moro 5, 00185 Rome (Italy); Montani, Giovanni [ICRA-International Center for Relativistic Astrophysics Dipartimento di Fisica (G9), Universita di Roma 'La Sapienza' P.le A. Moro 5, 00185 Rome (Italy); ENEA C.R. Frascati (Dipartimento F.P.N.), Via Enrico Fermi 45, 00044 Frascati, Rome (Italy); ICRANET C.C. Pescara, P.le della Repubblica 10, 65100 Pescara (Italy)
2008-01-03
The minisuperspace dynamics of the Friedmann-Robertson-Walker (FRW) and of the Taub Universes in the context of a Generalized Uncertainty Principle is analyzed in detail. In particular, the motion of the wave packets is investigated and, in both the models, the classical singularity appear to be probabilistic suppressed. Moreover, the FRW wave packets approach the Planckian region in a stationary way and no evidences for a Big-Bounce, as predicted in Loop Quantum Cosmology, appear. On the other hand, the Taub wave packets provide the right behavior in predicting an isotropic Universe.
Effects of the Generalized Uncertainty Principle on the Inflation Parameters
Kourosh Nozari; Siamak Akhshabi
2009-10-19
We investigate the effects of the generalized uncertainty principle on the inflationary dynamics of the early universe in both standard and braneworld viewpoint. We choose the Randall-Sundrum II model as our underlying braneworld scenario. We find that the quantum gravitational effects lead to a spectral index which is not scale invariant. Also, the amplitude of density fluctuations is reduced by increasing the strength of quantum gravitational corrections. However, the tensor-to-scalar ratio increases by incorporation of these quantum gravity effects. We outline possible manifestations of these quantum gravity effects in the recent and future observations.
An inequality related to uncertainty principle in von Neumann algebras
Paolo Gibilisco; Tommaso Isola
2008-04-16
Recently Kosaki proved an inequality for matrices that can be seen as a kind of new uncertainty principle. Independently, the same result was proved by Yanagi, Furuichi and Kuriyama. The new bound is given in terms of Wigner-Yanase-Dyson informations. Kosaki himself asked if this inequality can be proved in the setting of von Neumann algebras. In this paper we provide a positive answer to that question and moreover we show how the inequality can be generalized to an arbitrary operator monotone function.
Hawking temperature for various kinds of black holes from Heisenberg uncertainty principle
Fabio Scardigli
2006-07-04
Hawking temperature is computed for a large class of black holes (with spherical, toroidal and hyperboloidal topologies) using only laws of classical physics plus the "classical" Heisenberg Uncertainty Principle. This principle is shown to be fully sufficient to get the result, and there is no need to this scope of a Generalized Uncertainty Principle.
Constraints on the Generalized Uncertainty Principle from Black Hole Thermodynamics
Gangopadhyay, Sunandan; Faizal, Mir
2015-01-01
In this paper, we calculate the modification to the thermodynamics of a Schwarzschild black hole in higher dimensions because of Generalized Uncertainty Principle (GUP). We use the fact that the leading order corrections to the entropy of a black hole has to be logarithmic in nature to restrict the form of GUP. We observe that in six dimensions, the usual GUP produces the correct form for the leading order corrections to the entropy of a black hole. However, in five and seven dimensions a linear GUP, which is obtained by a combination of DSR with the usual GUP, is needed to produce the correct form of the corrections to the entropy of a black hole. Finally, we demonstrate that in five dimensions, a new form of GUP containing quadratic and cubic powers of the momentum also produces the correct form for the leading order corrections to the entropy of a black hole.
The generalized uncertainty principle in the presence of extra dimensions
Benrong Mu; Houwen Wu; Haitang Yang
2009-09-24
We argue that in the Generalized Uncertainty Principle (GUP) model, the parameter $\\beta_0$ whose square root, multiplied by Planck length $\\ell_p$, approximates the minimum measurable distance, varies with energy scales. Since minimal measurable length and extra dimensions are both suggested by quantum gravity theories, we investigate models based on GUP and one extra dimension, compactified with radius $\\rho$. We obtain an inspiring relation $\\sqrt{\\beta_0} \\ell_p/\\rho \\sim {\\cal O}(1)$. This relation is also consistent with predictions at Planck scale and usual quantum mechanics scale. We also make estimations on the application range of the GUP model. It turns out that the minimum measurable length is exactly the compactification radius of the extra dimension.
A Robertson-type Uncertainty Principle and Quantum Fisher Information
Paolo Gibilisco; Daniele Imparato; Tommaso Isola
2007-07-09
Let $A_1,...,A_N$ be complex selfadjoint matrices and let $\\rho$ be a density matrix. The Robertson uncertainty principle $$ det (Cov_\\rho(A_h,A_j)) \\geq det (- \\frac{i}{2} Tr (\\rho [A_h,A_j])) $$ gives a bound for the quantum generalized covariance in terms of the commutators $ [A_h,A_j]$. The right side matrix is antisymmetric and therefore the bound is trivial (equal to zero) in the odd case $N=2m+1$. Let $f$ be an arbitrary normalized symmetric operator monotone function and let $_{\\rho,f}$ be the associated quantum Fisher information. In this paper we prove the inequality $$ det (Cov_\\rho (A_h,A_j)) \\geq det (\\frac{f(0)}{2} _{\\rho,f}) $$ that gives a non-trivial bound for any $N \\in {\\mathbb N}$ using the commutators $[\\rho,A_h]$.
Extended uncertainty principle and the geometry of (anti)-de Sitter space
S. Mignemi
2009-10-12
It has been proposed that on (anti)-de Sitter background, the Heisenberg uncertainty principle should be modified by the introduction of a term proportional to the cosmological constant. We show that this modification of the uncertainty principle can be derived straightforwardly from the geometric properties of (anti)-de Sitter spacetime. We also discuss the connection between the so-called extended generalized uncertainty principle and triply special relativity.
Effect of the Generalized Uncertainty Principle on post-inflation preheating
Chemissany, Wissam [Instituut voor Theoretische Fysica, Katholieke Universiteit Leuven, Celestijnenlaan 200D, B-3001 Leuven (Belgium); Das, Saurya; Ali, Ahmed Farag [Theoretical Physics Group, Department of Physics and Astronomy, University of Lethbridge, 4401 University Drive, Lethbridge, Alberta, T1K 3M4 Canada (Canada); Vagenas, Elias C., E-mail: wissam@itf.fys.kuleuven.be, E-mail: saurya.das@uleth.ca, E-mail: ahmed.ali@uleth.ca, E-mail: evagenas@academyofathens.gr [Research Center for Astronomy and Applied Mathematics, Academy of Athens, Soranou Efessiou 4, GR-11527, Athens (Greece)
2011-12-01
We examine effects of the Generalized Uncertainty Principle, predicted by various theories of quantum gravity to replace the Heisenberg's uncertainty principle near the Planck scale, on post inflation preheating in cosmology, and show that it can predict either an increase or a decrease in parametric resonance and a corresponding change in particle production. Possible implications are considered.
Cao, Jianshu
and the uncertainty principle Jianlan Wu and Jianshu Caoa) Department of Chemistry, Massachusetts Institute the linear divergence in the corresponding classical response function. On the basis of the uncertainty principle, the classical divergence is removed by phase-space averaging around the microcanonical energy
Corrections to the Cardy-Verlinde formula from the generalized uncertainty principle
Setare, M.R. [Physics Department, Institute for Studies in Theological Physics and Mathematics (IPM), P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of)
2004-10-15
In this Letter, we compute the corrections to the Cardy-Verlinde formula of the d-dimensional Schwarzschild black hole. These corrections stem from the generalized uncertainty principle. Then we show one can take into account the generalized uncertainty principle corrections of the Cardy-Verlinde entropy formula by just redefining the Virasoro operator L{sub 0} and the central charge c.
Effect of the Generalized Uncertainty Principle on Post-Inflation Preheating
Wissam Chemissany; Saurya Das; Ahmed Farag Ali; Elias C. Vagenas
2011-12-20
We examine effects of the Generalized Uncertainty Principle, predicted by various theories of quantum gravity to replace the Heisenberg's uncertainty principle near the Planck scale, on post inflation preheating in cosmology, and show that it can predict either an increase or a decrease in parametric resonance and a corresponding change in particle production. Possible implications are considered.
Uncertainty principle for Wigner-Yanase-Dyson information in semifinite von Neumann algebras
Paolo Gibilisco; Tommaso Isola
2008-04-16
Recently Kosaki proved an uncertainty principle for matrices, related to Wigner-Yanase-Dyson information, and asked if a similar inequality could be proved in the von Neumann algebra setting. In this paper we prove such an uncertainty principle in the semifinite case.
Remarks on the Fact that the Uncertainty Principle Does Not Determine the Quantum State
Maurice de Gosson; Franz Luef
2007-03-07
We discuss the relation between density matrices and the uncertainty principle; this allows us to justify and explain a recent statement by Man'ko et al. We thereafter use Hardy's uncertainty principle to prove a new result for Wigner distributions dominated by a Gaussian and we relate this result to the coarse-graining of phase-space by "quantum blobs".
Scientific and technological uncertainty, the precautionary principle, scenarios and risk management
Michael D. Rogers
2001-01-01
Uncertainty, the precautionary principle and scenario are three important concepts in current regulatory debates concerned with risk management. In this paper, each concept is described in relation to its regulatory context and a linkage between the three concepts is established. Three scenarios relating to increasing scientific and technical uncertainty are presented. The most obvious regulatory approach to uncertainty is to
Verification of the Uncertainty Principle by Using Diffraction of Light Waves
ERIC Educational Resources Information Center
Nikolic, D.; Nesic, Lj
2011-01-01
We described a simple idea for experimental verification of the uncertainty principle for light waves. We used a single-slit diffraction of a laser beam for measuring the angular width of zero-order diffraction maximum and obtained the corresponding wave number uncertainty. We will assume that the uncertainty in position is the slit width. For the…
Violation of the Robertson-Schrödinger uncertainty principle and non-commutative quantum mechanics
Catarina Bastos; Orfeu Bertolami; Nuno Costa Dias; João Nuno Prata
2012-11-26
We show that a possible violation of the Robertson-Schr\\"odinger uncertainty principle may signal the existence of a deformation of the Heisenberg-Weyl algebra. More precisely, we prove that any Gaussian in phase-space (even if it violates the Robertson-Schr\\"odinger uncertainty principle) is always a quantum state of an appropriate non-commutative extension of quantum mechanics. Conversely, all canonical non-commutative extensions of quantum mechanics display states that violate the Robertson-Schr\\"odinger uncertainty principle.
Relative entropy derivation of the uncertainty principle with quantum side information
Patrick J. Coles; Li Yu; Michael Zwolak
2011-12-07
We give a simple proof of the uncertainty principle with quantum side information, as in [Berta et al. Nature Physics 6, 659 (2010)], invoking the monotonicity of the relative entropy. Our proof shows that the entropic uncertainty principle can be viewed as a data-processing inequality, a special case of the notion that information cannot increase due to evolution in time. This leads to a systematic method for finding the minimum uncertainty states of various entropic uncertainty relations; interestingly such states are intimately connected with the reversibility of time evolution.
Rioux, Frank
to Illustrate the Uncertainty Principle Frank Rioux Department of chemistry College of St. Benedict and St. John. Or we could say diffraction is an excellent way to illustrate the uncertainty principle. A screen, it localizes the incident beam in the x-direction. Accoring to the uncertainty principle, because position
DOI 10.1007/s00209-010-0756-8 Mathematische Zeitschrift An uncertainty principle, Wegner estimates
Stollmann, P.
Math. Z. DOI 10.1007/s00209-010-0756-8 Mathematische Zeitschrift An uncertainty principle, Wegner uncertainty principle and show that it can be applied to prove Wegner estimates near fluctuation boundaries call "uncertainty principle" (see below for further discussion). The solution to the above mentioned
Durrani, Salman
CONCENTRATION UNCERTAINTY PRINCIPLES FOR SIGNALS ON THE UNIT SPHERE Zubair Khalid, Salman Durrani.kennedy}@anu.edu.au ABSTRACT The uncertainty principle is an important and powerful tool, with many applications in signal processing. This paper presents two concentration uncertainty principles for signals on the sphere which
d'Orléans, Université
´e no XV. Uncertainty principles for orthonormal bases Philippe JAMING Abstract : In this survey, we interpretation of the uncertainty principles as a statement about the time-frequency localiza- tion of elements dissipation property. Keywords : Uncertainty principles; orthonormal bases AMS subject class : 42B10 1
PUBLISHED ONLINE: 25 JULY 2010 | DOI: 10.1038/NPHYS1734 The uncertainty principle in the presence of
Loss, Daniel
LETTERS PUBLISHED ONLINE: 25 JULY 2010 | DOI: 10.1038/NPHYS1734 The uncertainty principle and Renato Renner1 The uncertainty principle, originally formulated by Heisenberg1 , clearly illustrates the difference between classical and quan- tum mechanics. The principle bounds the uncertainties about
Quantum-memory-assisted entropic uncertainty principle under noise
Z. Y. Xu; W. L. Yang; M. Feng
2012-03-15
The measurement outcomes of two incompatible observables on a particle can be precisely predicted when it is maximally entangled with a quantum memory, as quantified recently [Nature Phys. 6, 659 (2010)]. We explore the behavior of the uncertainty relation under the influence of local unital and nonunital noisy channels. While the unital noises only increase the amount of uncertainty, the amplitude-damping nonunital noises may amazingly reduce the amount of uncertainty in the long-time limit. This counterintuitive phenomenon could be justified by different competitive mechanisms between quantum correlations and the minimal missing information after local measurement.
A Computational Model of Limb Impedance Control Based on Principles of Internal Model Uncertainty
Mitrovic, Djordje; Klanke, Stefan; Osu, Rieko; Kawato, Mitsuo; Vijayakumar, Sethu
-known impedance control phenomena naturally emerge from the first principles of a stochastic optimization process that minimizes for internal model prediction uncertainties, along with energy and accuracy demands. The insights from this computational model could...
Forough Nasseri
2005-06-15
In this letter we compute the corrections to the fine structure constant in D-dimensional space. These corrections stem from the generalized uncertainty principle. We also discuss in three-space dimension.
The Affine uncertainty principle in one and two dimensions
P. Maass
1995-01-01
In this paper, we construct families of wavelets that minimize an uncertainty relation associated with square integrable representations of some canonical groups. Especially, we obtain a new interpretation of the Mexican hat function.
Maria Luisa Dalla Chiara
2010-01-01
In contemporary science uncertainty is often represented as an intrinsic feature of natural and of human phenomena. As an example we need only think of two important conceptual revolutions that occurred\\u000a in physics and logic during the first half of the twentieth century: (1) the discovery of Heisenberg’s uncertainty principle in quantum mechanics; (2) the emergence of many-valued logical reasoning,
Maria Luisa Dalla Chiara
In contemporary science uncertainty is often represented as an intrinsic feature of natural and of human phenomena. As an example we need only think of two important conceptual revolutions occurred in physics\\u000a and in logic during the first half of the twentieth century: (a) the discovery of Heisenberg’s uncertainty principle in quantum mechanics; (b) the emergence of the many-valued logical
Hermite functions and uncertainty principles for the Fourier and the windowed Fourier transforms
Aline Bonami; Bruno Demange; Philippe Jaming
2001-01-01
We extend an uncertainty principle due to Beurling into a characterization of Hermite functions. More precisely, all functions $f$ on $\\\\R^d$ which may be written as $P(x)\\\\exp (Ax,x)$, with $A$ a real symmetric definite positive matrix, are characterized by integrability conditions on the product $f(x)\\\\hat{f}(y)$. We also give the best constant in uncertainty principles of Gelf'and Shilov type. We then
Entropy of the Randall-Sundrum brane world with the generalized uncertainty principle
Kim, Wontae; Park, Young-Jai [Department of Physics and Center for Quantum Spacetime, Sogang University, Seoul 121-742 (Korea, Republic of); Kim, Yong-Wan [National Creative Research Initiative Center for Controlling Optical Chaos, Pai-Chai University, Daejeon 302-735 (Korea, Republic of)
2006-11-15
By introducing the generalized uncertainty principle, we calculate the entropy of the bulk scalar field on the Randall-Sundrum brane background without any cutoff. We obtain the entropy of the massive scalar field proportional to the horizon area. Here, we observe that the mass contribution to the entropy exists in contrast to all previous results of the usual black hole cases with the generalized uncertainty principle.
Semiclassical corrections to black hole entropy and the generalized uncertainty principle
NASA Astrophysics Data System (ADS)
Bargueño, Pedro; Vagenas, Elias C.
2015-03-01
In this paper, employing the path integral method in the framework of a canonical description of a Schwarzschild black hole, we obtain the corrected inverse temperature and entropy of the black hole. The corrections are those coming from the quantum effects as well as from the Generalized Uncertainty Principle effects. Furthermore, an equivalence between the polymer quantization and the Generalized Uncertainty Principle description is shown provided the parameters characterizing these two descriptions are proportional.
Semiclassical corrections to black hole entropy and the generalized uncertainty principle
Bargueño, Pedro
2015-01-01
In this paper, employing the path integral method in the framework of a canonical description of a Schwarzschild black hole, we obtain the corrected inverse temperature and entropy of the black hole. The corrections are those coming from the quantum effects as well as from the Generalized Uncertainty Principle effects. Furthermore, an equivalence between the polymer quantization and the Generalized Uncertainty Principle description is shown provided the parameters characterizing these two descriptions are proportional.
Entropy of the Randall-Sundrum brane world with the generalized uncertainty principle
Wontae Kim; Yong-Wan Kim; Young-Jai Park
2006-11-02
By introducing the generalized uncertainty principle, we calculate the entropy of the bulk scalar field on the Randall-Sundrum brane background without any cutoff. We obtain the entropy of the massive scalar field proportional to the horizon area. Here, we observe that the mass contribution to the entropy exists in contrast to all previous results, which is independent of the mass of the scalar field, of the usual black hole cases with the generalized uncertainty principle.
Entropy bound of local quantum field theory with generalized uncertainty principle
Yong-Wan Kim; Hyung Won Lee; Yun Soo Myung
2009-02-25
We study the entropy bound for local quantum field theory (LQFT) with generalized uncertainty principle. The generalized uncertainty principle provides naturally a UV cutoff to the LQFT as gravity effects. Imposing the non-gravitational collapse condition as the UV-IR relation, we find that the maximal entropy of a bosonic field is limited by the entropy bound $A^{3/4}$ rather than $A$ with $A$ the boundary area.
Semiclassical corrections to black hole entropy and the generalized uncertainty principle
Pedro Bargueño; Elias C. Vagenas
2015-01-14
In this paper, employing the path integral method in the framework of a canonical description of a Schwarzschild black hole, we obtain the corrected inverse temperature and entropy of the black hole. The corrections are those coming from the quantum effects as well as from the Generalized Uncertainty Principle effects. Furthermore, an equivalence between the polymer quantization and the Generalized Uncertainty Principle description is shown provided the parameters characterizing these two descriptions are proportional.
A Discussion on Heisenberg Uncertainty Principle in the Picture of Special Relativity
Luca Nanni
2015-01-09
In this note the formulation of the Heisenberg uncertainty principle (HUP) in the picture of the special relativity is given. The inequality shows that the product of quantum conjugate variables uncertainties is greater than an amount that is not more a constant but depends on the speed of the system on which the measurement is taken.
van Asselt, M B A; Vos, E
2005-01-01
This article explores the use of the precautionary principle in situations of intermingled uncertainty and risk. It analyses how the so-called uncertainty paradox works out by examining the Pfizer case. It reveals regulatory complexities that result from contradictions in precautionary thinking. In conclusion, a plea is made for embedment of uncertainty information, while stressing the need to rethink regulatory reform in the broader sense. PMID:16304932
Uncertainty Principle--Limited Experiments: Fact or Academic Pipe-Dream?
ERIC Educational Resources Information Center
Albergotti, J. Clifton
1973-01-01
The question of whether modern experiments are limited by the uncertainty principle or by the instruments used to perform the experiments is discussed. Several key experiments show that the instruments limit our knowledge and the principle remains of strictly academic concern. (DF)
Generalized uncertainty principle and the conformally coupled scalar field quantum cosmology
NASA Astrophysics Data System (ADS)
Pedram, Pouria
2015-03-01
We exactly solve the Wheeler-DeWitt equation for the closed homogeneous and isotropic quantum cosmology in the presence of a conformally coupled scalar field and in the context of the generalized uncertainty principle. This form of generalized uncertainty principle is motivated by the black hole physics and it predicts a minimal length uncertainty proportional to the Planck length. We construct wave packets in momentum minisuperspace which closely follow classical trajectories and strongly peak on them upon choosing appropriate initial conditions. Moreover, based on the DeWitt criterion, we obtain wave packets that exhibit singularity-free behavior.
Generalized uncertainty principle and the conformally coupled scalar field quantum cosmology
Pedram, Pouria
2015-01-01
We exactly solve the Wheeler-DeWitt equation for the closed homogeneous and isotropic quantum cosmology in the presence of a conformally coupled scalar field and in the context of the generalized uncertainty principle. This form of generalized uncertainty principle is motivated by the black hole physics and it predicts a minimal length uncertainty proportional to the Planck length. We construct wave packets in momentum minisuperspace which closely follow classical trajectories and strongly peak on them upon choosing appropriate initial conditions. Moreover, based on the DeWitt criterion, we obtain wave packets that exhibit singularity-free behavior.
Generalized uncertainty principle and the conformally coupled scalar field quantum cosmology
Pouria Pedram
2015-02-25
We exactly solve the Wheeler-DeWitt equation for the closed homogeneous and isotropic quantum cosmology in the presence of a conformally coupled scalar field and in the context of the generalized uncertainty principle. This form of generalized uncertainty principle is motivated by the black hole physics and it predicts a minimal length uncertainty proportional to the Planck length. We construct wave packets in momentum minisuperspace which closely follow classical trajectories and strongly peak on them upon choosing appropriate initial conditions. Moreover, based on the DeWitt criterion, we obtain wave packets that exhibit singularity-free behavior.
Ming-Liang Hu; Heng Fan
2012-09-24
We relate the principle of quantum-memory-assisted entropic uncertainty to quantum teleportation and show geometrically that any two-qubit state which lowers the upper bound of this uncertainty relation is useful for teleportation. We also explore the efficiency of this entropic uncertainty principle on witnessing entanglement in a general class of bosonic structured reservoirs. The entanglement regions witnessed by different estimates are determined, which may have no relation with the explicit form of the spectral density of the reservoir for certain special chosen sets of the initial states.
Experimental Realization of Popper's Experiment: Violation of the Uncertainty Principle?
Yoon-Ho Kim; Yanhua Shih
1999-01-01
An entangled pair of photons (1 and 2) are emitted in opposite directions. A narrow slit is placed in the path of photon 1 to provide the precise knowledge of its position on the y-axis and this also determines the precise y-position of its twin, photon 2, due to quantum entanglement. Is photon 2 going to experience a greater uncertainty
Quantum covariance, quantum Fisher information and the uncertainty principle
Paolo Gibilisco; Fumio Hiai; Denes Petz
2007-12-07
In this paper the relation between quantum covariances and quantum Fisher informations are studied. This study is applied to generalize a recently proved uncertainty relation based on quantum Fisher information. The proof given hereconsiderably simplifies the previously proposed proofs and leads to more general inequalities.
The uncertainty principle determines the non-locality of quantum mechanics
Jonathan Oppenheim; Stephanie Wehner
2010-11-19
Two central concepts of quantum mechanics are Heisenberg's uncertainty principle, and a subtle form of non-locality that Einstein famously called ``spooky action at a distance''. These two fundamental features have thus far been distinct concepts. Here we show that they are inextricably and quantitatively linked. Quantum mechanics cannot be more non-local with measurements that respect the uncertainty principle. In fact, the link between uncertainty and non-locality holds for all physical theories.More specifically, the degree of non-locality of any theory is determined by two factors -- the strength of the uncertainty principle, and the strength of a property called ``steering'', which determines which states can be prepared at one location given a measurement at another.
Microscopic black hole and uncertainty principle with minimal length and momentum
M. M. Stetsko
2013-03-21
We investigate a microscopic black hole in case of modified generalized uncertainty principle with a minimal uncertainty in position as well as in momentum. We calculate thermodynamical functions of a Schwarzschild black hole such as temperature, entropy and heat capacity. It is shown that incorporation of minimal uncertainty in momentum leads to minimal temperature of a black hole similarly as we have for Schwarzschschild-AdS black hole without minimal uncertainty. Minimal temperature gives rise to Hawking-Page phase transition. Emission rate equation and black hole lifetime are also obtained.
Path Integral for Dirac oscillator with generalized uncertainty principle
Benzair, H. [Laboratoire LRPPS, Universite de Kasdi Merbah-Ouargla, BP 511, Route Ghardaia, 30000 Ouargla (Algeria); Laboratoire de Physique Theorique, Universite de Jijel BP98 Ouled Aissa, 18000 Jijel (Algeria); Boudjedaa, T. [Laboratoire de Physique Theorique, Universite de Jijel BP98 Ouled Aissa, 18000 Jijel (Algeria); Merad, M. [Laboratoire (L.S.D.C), Universite de Oum El Bouaghi, 04000 Oum El Bouaghi (Algeria)
2012-12-15
The propagator for Dirac oscillator in (1+1) dimension, with deformed commutation relation of the Heisenberg principle, is calculated using path integral in quadri-momentum representation. As the mass is related to momentum, we then adapt the space-time transformation method to evaluate quantum corrections and this latter is dependent from the point discretization interval.
Presilla, Carlo
PHYSICAL REVIEW B VOLUME 45, NUMBER 7 15 FEBRUARY 1992-I Uncertainty-principle noise in vacuum uncertainty principle for the position and momen- tum of a test mass monitored by the transducer through-quantized description of electron tunneling through a barrier to find an expression for the uncertainty in the width
NASA Astrophysics Data System (ADS)
Ayene, Mengesha; Kriek, Jeanne; Damtie, Baylie
2011-12-01
Quantum mechanics is often thought to be a difficult subject to understand, not only in the complexity of its mathematics but also in its conceptual foundation. In this paper we emphasize students’ depictions of the uncertainty principle and wave-particle duality of quantum events, phenomena that could serve as a foundation in building an understanding of quantum mechanics. A phenomenographic study was carried out to categorize a picture of students’ descriptions of these key quantum concepts. Data for this study were obtained from a semistructured in-depth interview conducted with undergraduate physics students (N=25) from Bahir Dar, Ethiopia. The phenomenographic data analysis revealed that it is possible to construct three qualitatively different categories to map students’ depictions of the concept wave-particle duality, namely, (1) classical description, (2) mixed classical-quantum description, and (3) quasiquantum description. Similarly, it is proposed that students’ depictions of the concept uncertainty can be described with four different categories of description, which are (1) uncertainty as an extrinsic property of measurement, (2) uncertainty principle as measurement error or uncertainty, (3) uncertainty as measurement disturbance, and (4) uncertainty as a quantum mechanics uncertainty principle. Overall, we found students are more likely to prefer a classical picture of interpretations of quantum mechanics. However, few students in the quasiquantum category applied typical wave phenomena such as interference and diffraction that cannot be explained within the framework classical physics for depicting the wavelike properties of quantum entities. Despite inhospitable conceptions of the uncertainty principle and wave- and particlelike properties of quantum entities in our investigation, the findings presented in this paper are highly consistent with those reported in previous studies. New findings and some implications for instruction and the curricula are discussed.
Marcelo A Marchiolli; Maurizio Ruzzi
2011-06-13
Generalized uncertainty principle and breakdown of the spacetime continuum certainly represent two important results derived of various approaches related to quantum gravity and black hole physics near the well-known Planck scale. The discreteness of space suggests, in particular, that all measurable lengths are quantized in units of a fundamental scale (in this case, the Planck length). Here, we propose a self-consistent theoretical framework for an important class of physical systems characterized by a finite space of states, and show that such a framework enlarges previous knowledge about generalized uncertainty principles, as topological effects in finite-dimensional discrete phase spaces come into play. Besides, we also investigate under what circumstances the generalized uncertainty principle (GUP) works out well and its inherent limitations.
Experimental Realization of Popper's Experiment: Violation of Uncertainty Principle?
NASA Astrophysics Data System (ADS)
Kim, Yoon-Ho; Yu, Rong; Shih, Yanhua
An entangled pair of photon 1 and 2 are emitted in opposite directions along the positive and negative x-axis. A narrow slit is placed in the path of photon 1 which provides precise knowledge about its position along the y-axis and because of the quantum entanglement this in turn provides precise knowledge of the position y of its twin, photon 2. Does photon 2 experience a greater uncertainty in its momentum, i.e., a greater ?py, due to the precise knowledge of its position y? This is the historical thought experiment of Sir Karl Popper which was aimed to undermine the Copenhagen interpretation in favor of a realistic viewpoint of quantum mechanics. Thispaper reports an experimental realization of the Popper's experiment. One may not agree with Popper's position on quantum mechanics; however, it calls for a correct understanding and interpretation of the experimental results.
NASA Technical Reports Server (NTRS)
Athans, M.; Ku, R.; Gershwin, S. B.
1977-01-01
This note shows that the optimal control of dynamic systems with uncertain parameters has certain limitations. In particular, by means of a simple scalar linear-quadratic optimal control example, it is shown that the infinite horizon solution does not exist if the parameter uncertainty exceeds a certain quantifiable threshold; we call this the uncertainty threshold principle. The philosophical and design implications of this result are discussed.
The entropy of the noncommutative acoustic black hole based on generalized uncertainty principle
M. A. Anacleto; F. A. Brito; E. Passos; W. P. Santos
2014-08-08
In this paper we investigate statistical entropy of a 3-dimensional rotating acoustic black hole based on generalized uncertainty principle. In our results we obtain an area entropy and a correction term associated with the noncommutative acoustic black hole when $\\lambda$ introduced in the generalized uncertainty principle takes a specific value. However, in this method, it is not needed to introduce the ultraviolet cut-off and divergences are eliminated. Moreover, the small mass approximation is not necessary in the original brick-wall model.
Allan Tameshtit
2012-04-09
High temperature and white noise approximations are frequently invoked when deriving the quantum Brownian equation for an oscillator. Even if this white noise approximation is avoided, it is shown that if the zero point energies of the environment are neglected, as they often are, the resultant equation will violate not only the basic tenet of quantum mechanics that requires the density operator to be positive, but also the uncertainty principle. When the zero-point energies are included, asymptotic results describing the evolution of the oscillator are obtained that preserve positivity and, therefore, the uncertainty principle.
Squeezed States, Uncertainty Relations and the Pauli Principle in Composite and Cosmological Models
NASA Technical Reports Server (NTRS)
Terazawa, Hidezumi
1996-01-01
The importance of not only uncertainty relations but also the Pauli exclusion principle is emphasized in discussing various 'squeezed states' existing in the universe. The contents of this paper include: (1) Introduction; (2) Nuclear Physics in the Quark-Shell Model; (3) Hadron Physics in the Standard Quark-Gluon Model; (4) Quark-Lepton-Gauge-Boson Physics in Composite Models; (5) Astrophysics and Space-Time Physics in Cosmological Models; and (6) Conclusion. Also, not only the possible breakdown of (or deviation from) uncertainty relations but also the superficial violation of the Pauli principle at short distances (or high energies) in composite (and string) models is discussed in some detail.
Satellite Test of the Equivalence Principle Uncertainty Analysis
NASA Astrophysics Data System (ADS)
Worden, Paul; Mester, John
2009-12-01
STEP, the Satellite Test of the Equivalence Principle, is intended to test the apparent equivalence of gravitational and inertial mass to 1 part in 1018 (Worden et al. in Adv. Space Res. 25(6):1205-1208, 2000). This will be an increase of more than five orders of magnitude over ground-based experiments and lunar laser ranging observations (Su et al. in Phys. Rev. D 50:3614-3636, 1994; Williams et al. in Phys. Rev. D 53:6730-6739, 1996; Schlamminger et al. in Phys. Rev. Lett. 100:041101, 2008). It is essential to have a comprehensive and consistent model of the possible error sources in an experiment of this nature to be able to understand and set requirements, and to evaluate design trade-offs. In the following pages we describe existing software for such an error model and the application of this software to the STEP experiment. In particular we address several issues, including charge and patch effect forces, where our understanding has improved since the launch of GP-B owing to the availability of GP-B data and preliminary analysis results (Everitt et al. in Space Sci. Rev., 2009, this issue; Silbergleit et al. in Space Sci. Rev., 2009, this issue; Keiser et al. in Space Sci. Rev., 2009, this issue; Heifetz et al. in Space Sci. Rev., 2009, this issue; Muhlfelder et al. in Space Sci. Rev., 2009, this issue).
Minimum physical length and the generalized uncertainty principle in string theory
Kenichi Konishi; Giampiero Paffuti; Paolo Provero
1990-01-01
A possible definition of path integrals for string theory is studied, based on a discretized version of Polyakov's generating functional. The finite resolution of string theory, as opposed to the infinite resolution in particle theory, clearly emerges from a renormalization group type analysis. We derive the existence of a minimum physical length (~10-33cm) and generalized form of the uncertainty principle,
New Uncertainty Principles for the Continuous Gabor Transform and the Continuous Wavelet Transform
Elke Wilczok
2000-01-01
Gabor and wavelet methods are preferred to classical Fourier methods, whenever the time dependence of the analyzed sig- nal is of the same importance as its frequency dependence. However, there exist strict limits to the maximal time-frequency resolution of these both transforms, similar to Heisenberg's uncertainty principle in Fourier analysis. Results of this type are the subject of the following
A generalized uncertainty principle and sparse representation in pairs of bases
Michael Elad; Alfred M. Bruckstein
2002-01-01
An elementary proof of a basic uncertainty principle concerning pairs of representations of vectors in different orthonormal bases is provided. The result, slightly stronger than stated before, has a direct impact on the uniqueness property of the sparse representation of such vectors using pairs of orthonormal bases as overcomplete dictionaries. The main contribution in this paper is the improvement of
Fast identification n-widths and uncertainty principles for LTI and slowly varying systems
George Zames; Lin Lin; Le Yi Wang
1994-01-01
The optimal worst-case uncertainty that can be achieved by identification depends on the observation time. In the first part of the paper, this dependence is evaluated for selected linear time invariant systems in the l1 and H? norms and shown to be derivable from a monotonicity principle. The minimal time required is shown to depend on the metric complexity of
Quantum-mechanical histories and the uncertainty principle: Information-theoretic inequalities
J. J. Halliwell
1993-01-01
This paper is generally concerned with understanding how the uncertainty principle arises in formulations of quantum mechanics, such as the decoherent histories approach, whose central goal is the assignment of probabilities to histories. We first consider histories characterized by position or momentum projections at two moments of time. Both exact and approximate (Gaussian) projections are studied. Shannon's information is used
The Generalized Uncertainty Principle and Harmonic Interaction in Three Spatial Dimensions
NASA Astrophysics Data System (ADS)
Hassanabadi, H.; Hooshmand, P.; Zarrinkamar, S.
2015-01-01
In three spatial dimensions, the generalized uncertainty principle is considered under an isotropic harmonic oscillator interaction in both non-relativistic and relativistic regions. By using novel transformations and separations of variables, the exact analytical solution of energy eigenvalues as well as the wave functions is obtained. Time evolution of the non-relativistic region is also reported.
Uncertainty Principle for Real Signals in the Linear Canonical Transform Domains
Kamalesh Kumar Sharma; Shiv Dutt Joshi
2008-01-01
The linear canonical transform (LCT) is a generalization of the fractional Fourier transform (FRFT) having applications in several areas of signal processing and optics. In this paper, we extend the uncertainty principle for real signals in the fractional Fourier domains to the linear canonical transform domains, giving us the tighter lower bound on the product of the spreads of the
ERIC Educational Resources Information Center
Ayene, Mengesha; Kriek, Jeanne; Damtie, Baylie
2011-01-01
Quantum mechanics is often thought to be a difficult subject to understand, not only in the complexity of its mathematics but also in its conceptual foundation. In this paper we emphasize students' depictions of the uncertainty principle and wave-particle duality of quantum events, phenomena that could serve as a foundation in building an…
Quantum States and Hardy's Formulation of the Uncertainty Principle : a Symplectic Approach
Maurice de Gosson; Franz Luef
2007-03-07
We express the condition for a phase space Gaussian to be the Wigner distribution of a mixed quantum state in terms of the symplectic capacity of the associated Wigner ellipsoid. Our results are motivated by Hardy's formulation of the uncertainty principle for a function and its Fourier transform. As a consequence we are able to state a more general form of Hardy's theorem.
Anne Ingeborg Myhr; Terje Traavik
2002-01-01
Commercialization of genetically modified organisms (GMOs) have sparked profound controversies concerning adequate approaches to risk regulation. Scientific uncertainty and ambiguity, omitted research areas, and lack of basic knowledge crucial to risk assessmentshave become apparent. The objective of this article is to discuss the policy and practical implementation of the Precautionary Principle. A major conclusion is that the void in scientific
The Uncertainty Principle derived by the finite transmission of light and information
Piero Chiarelli
2013-09-26
This work shows that in the frame of the stochastic generalization of the quantum hydrodynamic analogy (QHA) the uncertainty principle can be derived by the postulate of finite transmission speed of light and information . The theory shows that the measurement process performed in the large scale classical limit of stochastic QHA (SQHA), cannot have a duration smaller than the time need to the light to travel the distance up to which the quantum non-local interaction extend itself. The product of the minimum measuring time multiplied by the variance of energy fluctuation due to presence of stochastic noise shows to lead to the minimum uncertainty principle. The paper also shows that the uncertainty relations can be also derived if applied to the indetermination of position and momentum of a particle of mass m in a quantum fluctuating environment.
ERIC Educational Resources Information Center
Harbola, Varun
2011-01-01
In this paper, we accurately estimate the ground-state energy and the atomic radius of the helium atom and a helium-like Hookean atom by employing the uncertainty principle in conjunction with the variational approach. We show that with the use of the uncertainty principle, electrons are found to be spread over a radial region, giving an electron…
Tawfik, A., E-mail: a.tawfik@eng.mti.edu.eg [Egyptian Center for Theoretical Physics (ECTP), MTI University, 11571 Cairo (Egypt)
2013-07-01
We investigate the impacts of Generalized Uncertainty Principle (GUP) proposed by some approaches to quantum gravity such as String Theory and Doubly Special Relativity on black hole thermodynamics and Salecker-Wigner inequalities. Utilizing Heisenberg uncertainty principle, the Hawking temperature, Bekenstein entropy, specific heat, emission rate and decay time are calculated. As the evaporation entirely eats up the black hole mass, the specific heat vanishes and the temperature approaches infinity with an infinite radiation rate. It is found that the GUP approach prevents the black hole from the entire evaporation. It implies the existence of remnants at which the specific heat vanishes. The same role is played by the Heisenberg uncertainty principle in constructing the hydrogen atom. We discuss how the linear GUP approach solves the entire-evaporation-problem. Furthermore, the black hole lifetime can be estimated using another approach; the Salecker-Wigner inequalities. Assuming that the quantum position uncertainty is limited to the minimum wavelength of measuring signal, Wigner second inequality can be obtained. If the spread of quantum clock is limited to some minimum value, then the modified black hole lifetime can be deduced. Based on linear GUP approach, the resulting lifetime difference depends on black hole relative mass and the difference between black hole mass with and without GUP is not negligible.
Story, Lachel; Butts, Janie
2014-03-01
Nurses today are facing an ever changing health care system. Stimulated by health care reform and limited resources, nursing education is being challenged to prepare nurses for this uncertain environment. Looking to the past can offer possible solutions to the issues nursing education is confronting. Seven principles of da Vincian thinking have been identified (Gelb, 2004). As a follow-up to an exploration of the curiosità principle (Butts & Story, 2013), this article will explore the three principles of dimostrazione, sfumato, and corporalita. Nursing faculty can set the stage for a meaningful educational experience through these principles of demonstration (dimostrazione), uncertainty (sfumato), and cultivation (corporalita). Preparing nurses not only to manage but also to flourish in the current health care environment that will enhance the nurse's and patient's experience. PMID:23830068
Path Integral for non-relativistic Generalized Uncertainty Principle corrected Hamiltonian
Sudipta das; Souvik Pramanik
2012-09-12
Generalized Uncertainty Principle (GUP) has brought the idea of existence of minimum measurable length in Quantum physics. Depending on this GUP, non-relativistic Hamiltonian at the Planck scale is modified. In this article, we construct the kernel for this GUP corrected Hamiltonian for free particle by applying the Hamiltonian path integral approach and check the validity conditions for this kernel thoroughly. Interestingly, the probabilistic interpretation of this kernel induces a momentum upper bound in the theory which is comparable with GUP induced maximum momentum uncertainty.
Experimental investigation of the uncertainty principle in the presence of quantum memory
Robert Prevedel; Deny R. Hamel; Roger Colbeck; Kent Fisher; Kevin J. Resch
2010-12-01
Heisenberg's uncertainty principle provides a fundamental limitation on an observer's ability to simultaneously predict the outcome when one of two measurements is performed on a quantum system. However, if the observer has access to a particle (stored in a quantum memory) which is entangled with the system, his uncertainty is generally reduced. This effect has recently been quantified by Berta et al. [Nature Physics 6, 659 (2010)] in a new, more general uncertainty relation, formulated in terms of entropies. Using entangled photon pairs, an optical delay line serving as a quantum memory and fast, active feed-forward we experimentally probe the validity of this new relation. The behaviour we find agrees with the predictions of quantum theory and satisfies the new uncertainty relation. In particular, we find lower uncertainties about the measurement outcomes than would be possible without the entangled particle. This shows not only that the reduction in uncertainty enabled by entanglement can be significant in practice, but also demonstrates the use of the inequality to witness entanglement.
Quantum dynamics of the Taub universe in a generalized uncertainty principle framework
Battisti, Marco Valerio [ICRA-International Center for Relativistic Astrophysics, Rome (Italy); Dipartimento di Fisica (G9), Universita di Roma, 'La Sapienza' P.le A. Moro 5, 00185 Rome (Italy); Montani, Giovanni [ICRA-International Center for Relativistic Astrophysics, Rome (Italy); Dipartimento di Fisica (G9), Universita di Roma, 'La Sapienza' P.le A. Moro 5, 00185 Rome (Italy); ENEA C.R. Frascati (Dipartimento F.P.N.), Via Enrico Fermi 45, 00044 Frascati, Rome (Italy); ICRANET C.C. Pescara, P.le della Repubblica 10, 65100 Pescara (Italy)
2008-01-15
The implications of a generalized Uncertainty principle on the Taub cosmological model are investigated. The model is studied in the Arnowitt-Deser-Misner reduction of the dynamics and therefore a time variable is ruled out. Such a variable is quantized in a canonical way and the only physical degree of freedom of the system (related to the universe anisotropy) is quantized by means of a modified Heisenberg algebra. The analysis is performed at both the classical and quantum level. In particular, at quantum level, the motion of wave packets is investigated. The two main results obtained are as follows: (i) The classical singularity is probabilistically suppressed. The universe exhibits a stationary behavior and the probability amplitude is peaked in a determinate region. (ii) The generalized uncertainty principle wave packets provide the right behavior in the establishment of a quasi-isotropic configuration for the universe.
Influence of Generalized and Extended Uncertainty Principle on Thermodynamics of FRW universe
Tao Zhu; Ji-Rong Ren; Ming-Fan Li
2009-03-25
The influence of the generalized uncertainty principle (GUP) and extended uncertainty principle (EUP) on the thermodynamics of the Friedmann-Robertson-Walker (FRW) universe has been investigated. It is shown that the entropy of the apparent horizon of the FRW universe gets a correction if one considers the effect of the GUP or EUP. Moreover, starting with the modified entropy and applying the first law of thermodynamics, $dE=TdS$, to the apparent horizon of the FRW universe, we obtain the modified Friedmann equations. The influence of the GUP or EUP on the thermodynamics of the FRW universe provides a deep insight into the understanding of the quantum gravity or large length scale corrections to the dynamics of the FRW universe.
Doubly Special Relativity with a minimum speed and the Uncertainty Principle
Cláudio Nassif
2012-03-08
The present work aims to search for an implementation of a new symmetry in the space-time by introducing the idea of an invariant minimum speed scale ($V$). Such a lowest limit $V$, being unattainable by the particles, represents a fundamental and preferred reference frame connected to a universal background field (a vacuum energy) that breaks Lorentz symmetry. So there emerges a new principle of symmetry in the space-time at the subatomic level for very low energies close to the background frame ($v\\approx V$), providing a fundamental understanding for the uncertainty principle, i.e., the uncertainty relations should emerge from the space-time with an invariant minimum speed.
Space-time uncertainty principle and conformal symmetry in D-particle dynamics
Antal Jevicki; Tamiaki Yoneya
1998-01-01
Motivated by the space-time uncertainty principle, we establish a conformal symmetry in the dynamics of D-particles. The conformal symmetry, combined with the supersymmetric non-renormalization theorem, uniquely determines the classical form of the effective action for a probe D-particle in the background of a heavy D-particle source, previously constructed by Becker-Becker-Polchinski-Tseytlin. Our results strengthen the conjecture proposed by Maldacena on the
Schild Action and Space-Time Uncertainty Principle in String Theory
Tamiaki Yoneya
1997-01-01
We discuss the meaning of the Schild action from the viewpoint of a possible space-time uncertainty principle in string theory and present an interpretation of the Schild action which points toward a derivation of superstring theory as a theory of quantized space-time where the squared string scale, l(2}_{s) ~ alpha', plays the role of the minimum quantum for space-time areas.
Wontae Kim; Edwin J. Son; Myungseok Yoon
2008-01-09
We study thermodynamic quantities of an acoustic black hole and its thermodynamic stability in a cavity based on the generalized uncertainty principle. It can be shown that there is a minimal black hole which can be a stable remnant after black hole evaporation. Moreover, the behavior of the free energy shows that the large black hole is stable too. Therefore, the acoustic black hole can decay into the remnant or the large black hole.
Mu-in Park
2007-12-05
Recently, the Heisenberg's uncertainty principle has been extended to incorporate the existence of a large (cut-off) length scale in de Sitter or anti-de Sitter space, and the Hawking temperatures of the Schwarzshild-(anti) de Sitter black holes have been reproduced by using the extended uncertainty principle. I generalize the extended uncertainty to the case with an absolute minimum length and compute its modification to the Hawking temperature. I obtain a general trend that the generalized uncertainty principle due to the absolute minimum length ``always'' increases the Hawking temperature, implying ``faster'' decay, which is in conformity with the result in the asymptotically flat space. I also revisit the ``black hole-string'' phase transition, in the context of the generalized uncertainty principle.
Li Zhongheng [Department of Physics, Zhejiang University of Technology, Hangzhou 310032 (China)
2009-10-15
We derive new formulas for the spectral energy density and total energy density of massless particles in a general spherically symmetric static metric from a generalized uncertainty principle. Compared with blackbody radiation, the spectral energy density is strongly damped at high frequencies. For large values of r, the spectral energy density diminishes when r grows, but at the event horizon, the spectral energy density vanishes and therefore thermodynamic quantities near a black hole, calculated via the generalized uncertainty principle, do not require any cutoff parameter. We find that the total energy density can be expressed in terms of Hurwitz zeta functions. It should be noted that at large r (low local temperature), the difference between the total energy density and the Stefan-Boltzmann law is too small to be observed. However, as r approaches an event horizon, the effect of the generalized uncertainty principle becomes more and more important, which may be observable. As examples, the spectral energy densities in the background metric of a Schwarzschild black hole and of a Schwarzschild black hole plus quintessence are discussed. It is interesting to note that the maximum of the distribution shifts to higher frequencies when the quintessence equation of state parameter w decreases.
Generalized uncertainty principle and correction value to the black hole entropy
Zhao Hai-Xia; Li Huai-Fan; Hu Shuang-Qi; Zhao Ren
2006-08-04
Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein-Hawking entropy of the black hole. In particular, many researchers have expressed a vested interest in the coefficient of the logarithmic term of the black hole entropy correction term. In this paper, we calculate the correction value of the black hole entropy by utilizing the generalized uncertainty principle and obtain the correction term caused by the generalized uncertainty principle. Because in our calculation we think that the Bekenstein-Hawking area theorem is still valid after considering the generalized uncertainty principle, we derive that the coefficient of the logarithmic term of the black hole entropy correction term is negative. This result is different from the known result at present. Our method is valid not only for single horizon spacetime but also for double horizons spacetime. In the whole process, the physics idea is clear and calculation is simple. It offers a new way for studying the condition that Bekenstein-Hawking area theorem is valid.
Geodesics, Mass and the Uncertainty Principle in a Warped de Sitter Space-time
Jose A. Magpantay
2011-08-03
We present the explicit solution to the geodesic equations in a warped de Sitter space-time proposed by Randall-Sundrum. We find that a test particle moves in the bulk and is not restricted on a 3-brane (to be taken as our universe). On the 3-brane, the test particle moves with uniform velocity, giving the appearance that it is not subject to a force. But computing the particle's energy using the energy-momentum tensor yields a time-dependent energy that suggests a time-dependent mass. Thus, the extra force, which is the effect of the warped extra dimension on the particle's motion on the 3-brane, does not change the velocity but the mass of the particle. The particle's motion in the bulk also results in a time-dependent modification of the Heisenberg uncertainty principle as viewed on the 3-brane. These two results show that the classical physics along the extra dimension results in the time-dependence of particle masses and the uncertainty principle. If the particle masses are time-independent and the Heisenberg's uncertainty principle is to remain unchanged, then there must be a non-gravitational force that will restrict all particles on the 3-brane. Finally, we just note that although classically, these time-dependent corrections on the 3-brane can be removed, quantum mechanical corrections along the extra dimension will restore back the problem.
The uncertainty principle enables non-classical dynamics in an interferometer.
Dahlsten, Oscar C O; Garner, Andrew J P; Vedral, Vlatko
2014-01-01
The quantum uncertainty principle stipulates that when one observable is predictable there must be some other observables that are unpredictable. The principle is viewed as holding the key to many quantum phenomena and understanding it deeper is of great interest in the study of the foundations of quantum theory. Here we show that apart from being restrictive, the principle also plays a positive role as the enabler of non-classical dynamics in an interferometer. First we note that instantaneous action at a distance should not be possible. We show that for general probabilistic theories this heavily curtails the non-classical dynamics. We prove that there is a trade-off with the uncertainty principle that allows theories to evade this restriction. On one extreme, non-classical theories with maximal certainty have their non-classical dynamics absolutely restricted to only the identity operation. On the other extreme, quantum theory minimizes certainty in return for maximal non-classical dynamics. PMID:25105741
Zwolak, Michael
arXiv:1105.4865v1[quant-ph]24May2011 Relative entropy derivation of the uncertainty principle Laboratory, Los Alamos, NM 87545 We give a simple proof of the uncertainty principle with quantum side entropy. Our proof shows that the entropic uncertainty principle can be viewed as a data
Rioux, Frank
The Harmonic Oscillator and the Uncertainty Principle In atomic units the wave function of the Uncertainty Principle: the more sharply defined position is, the greater the uncertainty in momentum. Conversely, the greater the uncertainty in position, the more sharply the momentum is defined. Tunneling
The Heisenberg Uncertainty Principle and the Nyquist-Shannon Sampling Theorem
Pierre A. Millette
2011-08-16
The derivation of the Heisenberg Uncertainty Principle (HUP) from the Uncertainty Theorem of Fourier Transform theory demonstrates that the HUP arises from the dependency of momentum on wave number that exists at the quantum level. It also establishes that the HUP is purely a relationship between the effective widths of Fourier transform pairs of variables (i.e. conjugate variables). We note that the HUP is not a quantum mechanical measurement principle per se. We introduce the Quantum Mechanical equivalent of the Nyquist-Shannon Sampling Theorem of Fourier Transform theory, and show that it is a better principle to describe the measurement limitations of Quantum Mechanics. We show that Brillouin zones in Solid State physics are a manifestation of the Nyquist-Shannon Sampling Theorem at the quantum level. By comparison with other fields where Fourier Transform theory is used, we propose that we need to discern between measurement limitations and inherent limitations when interpreting the impact of the HUP on the nature of the quantum level. We further propose that while measurement limitations result in our perception of indeterminism at the quantum level, there is no evidence that there are any inherent limitations at the quantum level, based on the Nyquist-Shannon Sampling Theorem.
The Effect of Uncertainty Principle on the Thermodynamics of Early Universe
S. Rahvar; M. Sadegh Movahed; M Saadat
2005-08-15
We discuss the concept of measurement in cosmology from the relativistic and quantum mechanical points of view. The uncertainty principle within the particle horizon, excludes the momentum of particles to be less than $\\pi\\hbar H/c$. This effect modifies the standard thermodynamics of early universe for the ultra-relativistic particles such that the equation of state as well as dependence of energy density and pressure to the temperature. We show that this modification to the thermodynamics of early universe is important for energies $E>10^{17} GeV$. During the inflation, the particle horizon inflates to a huge size and makes the uncertainty in the momentum to be negligible.
David Batchelor
2010-07-30
The magnitude of the strong interaction is characterized by $\\alpha_s$, the coupling parameter in Quantum Chromodynamics (QCD), a parameter with an unexplained value in the Standard Model. In this paper, a candidate explanation for $\\alpha_s$ is derived from (1) the lifetime of quark-antiquark pairs in vacuum fluctuations given by the Uncertainty Principle, (2) the variation of $\\alpha_s$ as a function of energy in QCD, and (3) classical relativistic dynamics of the quarks and antiquarks. A semiclassical model for heavy quark-antiquark vacuum fluctuations is described herein, based on (2) and (3). The model in this paper predicts the measured value of $\\alpha_s(M_{Z^0})$ to be 0.121, which is in agreement with recent measurements within statistical uncertainties.
Using the uncertainty principle to design simple interactions for targeted self-assembly.
Edlund, E; Lindgren, O; Jacobi, M Nilsson
2013-07-14
We present a method that systematically simplifies isotropic interactions designed for targeted self-assembly. The uncertainty principle is used to show that an optimal simplification is achieved by a combination of heat kernel smoothing and Gaussian screening of the interaction potential in real and reciprocal space. We use this method to analytically design isotropic interactions for self-assembly of complex lattices and of materials with functional properties. The derived interactions are simple enough to narrow the gap between theory and experimental implementation of theory based designed self-assembling materials. PMID:23862929
On the stability of the dark energy based on generalized uncertainty principle
Antonio Pasqua; Surajit Chattopadhyay; Iuliia Khomenko
2012-11-29
The new agegraphic Dark Energy (NADE) model (based on generalized uncertainty principle) interacting with Dark Matter (DM) is considered in this study via power-law form of the scale factor $a(t)$. The equation of state (EoS) parameter $\\omega_{G}$ is observed to have a phantom-like behaviour. The stability of this model is investigated through the squared speed of sound $v_{s}^{2}$: it is found that $v_{s}^{2}$ always stays at negative level, which indicates instability of the considered model.
Generalized uncertainty principle in f(R) gravity for a charged black hole
Said, Jackson Levi [Physics Department, University of Malta, Msida (Malta); Adami, Kristian Zarb [Physics Department, University of Malta, Msida (Malta); Physics Department, University of Oxford, Oxford (United Kingdom)
2011-02-15
Using f(R) gravity in the Palatini formularism, the metric for a charged spherically symmetric black hole is derived, taking the Ricci scalar curvature to be constant. The generalized uncertainty principle is then used to calculate the temperature of the resulting black hole; through this the entropy is found correcting the Bekenstein-Hawking entropy in this case. Using the entropy the tunneling probability and heat capacity are calculated up to the order of the Planck length, which produces an extra factor that becomes important as black holes become small, such as in the case of mini-black holes.
Using the uncertainty principle to design simple interactions for targeted self-assembly
Erik Edlund; Oskar Lindgren; Martin Nilsson Jacobi
2012-11-23
We present a method that systematically simplifies isotropic interactions designed for targeted self-assembly. The uncertainty principle is used to show that an optimal simplification is achieved by a combination of heat kernel smoothing and Gaussian screening. We use this method to design isotropic interactions for self-assembly of complex lattices and of materials with functional properties. The interactions we derive are significantly simpler than those previously published, and it is realistic to discuss explicit experimental implementation of the designed self-assembling components.
Do the Modified Uncertainty Principle and Polymer Quantization predict same physics?
NASA Astrophysics Data System (ADS)
Majumder, Barun; Sen, Sourav
2012-10-01
In this Letter we study the effects of the Modified Uncertainty Principle as proposed in Ali et al. (2009) [5] in simple quantum mechanical systems and study its thermodynamic properties. We have assumed that the quantum particles follow Maxwell-Boltzmann statistics with no spin. We compare our results with the results found in the GUP and polymer quantum mechanical frameworks. Interestingly we find that the corrected thermodynamic entities are exactly the same compared to the polymer results but the length scale considered has a theoretically different origin. Hence we express the need of further study for an investigation whether these two approaches are conceptually connected in the fundamental level.
Generalized uncertainty principle, quantum gravity and Ho?ava-Lifshitz gravity
Yun Soo Myung
2009-09-29
We investigate a close connection between generalized uncertainty principle (GUP) and deformed Ho\\v{r}ava-Lifshitz (HL) gravity. The GUP commutation relations correspond to the UV-quantum theory, while the canonical commutation relations represent the IR-quantum theory. Inspired by this UV/IR quantum mechanics, we obtain the GUP-corrected graviton propagator by introducing UV-momentum $p_i=p_{0i}(1+\\beta p_{0}^2)$ and compare this with tensor propagators in the HL gravity. Two are the same up to $p_0^4$-order.
Wontae Kim; John J. Oh
2008-01-11
We derive the formula of the black hole entropy with a minimal length of the Planck size by counting quantum modes of scalar fields in the vicinity of the black hole horizon, taking into account the generalized uncertainty principle (GUP). This formula is applied to some intriguing examples of black holes - the Schwarzschild black hole, the Reissner-Nordstrom black hole, and the magnetically charged dilatonic black hole. As a result, it is shown that the GUP parameter can be determined by imposing the black hole entropy-area relationship, which has a Planck length scale and a universal form within the near-horizon expansion.
Yan-Gang Miao; Ying-Jie Zhao
2014-05-04
We propose an improved exponential Generalized Uncertainty Principle (GUP) by introducing a positive integer $n$ called the suppressing index. Due to the UV/IR mixing brought by the GUP, the states with momenta smaller than the critical momentum ($P P_{\\rm Crit}$) and thus have no contributions to the energy density of the vacuum. By considering the contributions just from the states with momenta larger than the critical momentum ($P > P_{\\rm Crit}$) and choosing a suitable suppressing index, $n \\sim 10^{123}$, we calculate the cosmological constant consistent with the experimentally observed value.
Uncertainty Principle for Control of Ensembles of Oscillators Driven by Common Noise
Denis S. Goldobin
2014-04-28
We discuss control techniques for noisy self-sustained oscillators with a focus on reliability, stability of the response to noisy driving, and oscillation coherence understood in the sense of constancy of oscillation frequency. For any kind of linear feedback control--single and multiple delay feedback, linear frequency filter, etc.--the phase diffusion constant, quantifying coherence, and the Lyapunov exponent, quantifying reliability, can be efficiently controlled but their ratio remains constant. Thus, an "uncertainty principle" can be formulated: the loss of reliability occurs when coherence is enhanced and, vice versa, coherence is weakened when reliability is enhanced. Treatment of this principle for ensembles of oscillators synchronized by common noise or global coupling reveals a substantial difference between the cases of slightly non-identical oscillators and identical ones with intrinsic noise.
Implication of the geodesic equation in the generalized uncertainty principle framework
NASA Astrophysics Data System (ADS)
Pramanik, Souvik
2014-07-01
The generalized uncertainty principle (GUP) corrected modified relativistic particle model has been derived in curved space-time. From this modified model, the equation of motion (EM) has been constructed relativistically in terms of the affine parameter (?) or proper time (?) and nonrelativistically in terms of coordinate time (t). In this context, the constraint analysis technique has been applied to get the EM. Interestingly, the EM obtained in both cases is the usual one. This result clearly indicates an important fact, that is, consistency of the equivalence principle in the GUP framework, and furthermore it can be concluded that with the GUP-corrected modified algebra it is impossible to get the GUP effect in point particle motion.
Covariant energy–momentum and an uncertainty principle for general relativity
Cooperstock, F.I., E-mail: cooperst@uvic.ca [Department of Physics and Astronomy, University of Victoria, P.O. Box 3055, Victoria, B.C. V8W 3P6 (Canada); Dupre, M.J., E-mail: mdupre@tulane.edu [Department of Mathematics, Tulane University, New Orleans, LA 70118 (United States)
2013-12-15
We introduce a naturally-defined totally invariant spacetime energy expression for general relativity incorporating the contribution from gravity. The extension links seamlessly to the action integral for the gravitational field. The demand that the general expression for arbitrary systems reduces to the Tolman integral in the case of stationary bounded distributions, leads to the matter-localized Ricci integral for energy–momentum in support of the energy localization hypothesis. The role of the observer is addressed and as an extension of the special relativistic case, the field of observers comoving with the matter is seen to compute the intrinsic global energy of a system. The new localized energy supports the Bonnor claim that the Szekeres collapsing dust solutions are energy-conserving. It is suggested that in the extreme of strong gravity, the Heisenberg Uncertainty Principle be generalized in terms of spacetime energy–momentum. -- Highlights: •We present a totally invariant spacetime energy expression for general relativity incorporating the contribution from gravity. •Demand for the general expression to reduce to the Tolman integral for stationary systems supports the Ricci integral as energy–momentum. •Localized energy via the Ricci integral is consistent with the energy localization hypothesis. •New localized energy supports the Bonnor claim that the Szekeres collapsing dust solutions are energy-conserving. •Suggest the Heisenberg Uncertainty Principle be generalized in terms of spacetime energy–momentum in strong gravity extreme.
Extended Generalized Uncertainty Principle and the Correction Value to the Black Hole Entropy
NASA Astrophysics Data System (ADS)
Bai, J. L.; Wen, T. D.
2015-01-01
Recently, great attention has been paid to the quantum correction value of black hole's Bekenstein-Hawking entropy, especially for the coefficient of the logarithmic correction term of the black hole entropy. On the basis of the GUP (Generalized Uncertainty Principle), we introduced the EGUP (Extended Generalized Uncertainty Principle), and calculated the correction value of three types of space-time by using the area theorem. The results showed that the coefficient of black hole entropy correction is positive. The calculation method is not only applied to the single horizon space-time, but also suitable for the double horizon space-time. The black hole entropy correction value was calculated based on the EGUP. Compared with the GUP, the EGUP can be applied in a large scale space-time, thus, its application scope is wider. The calculation method is concise, and the physical meaning is clear. It provides a reference for the determination of the coefficient of the logarithmic correction term to the black hole entropy.
Rioux, Frank
The Harmonic Oscillator and the Uncertainty Principle Schroedinger's equation in atomic units (h 4 e 1- 2 k 1 2 µ 1 2 p 2 k 1 8 µ 1 8 := #12;The uncertainty principle can now be illustrated of vibration (CTP =0.841)· and therefore the uncertainty in position. Consequently there is an increase
NASA Astrophysics Data System (ADS)
Tawfik, Abdel Nasser; El Dahab, Eiman Abou
2015-03-01
Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein-Hawking (black hole) entropy, which relates the entropy to the cross-sectional area of the black hole horizon. Using generalized uncertainty principle (GUP), corrections to the geometric entropy and thermodynamics of black hole will be introduced. The impact of GUP on the entropy near the horizon of three types of black holes: Schwarzschild, Garfinkle-Horowitz-Strominger and Reissner-Nordström is determined. It is found that the logarithmic divergence in the entropy-area relation turns to be positive. The entropy S, which is assumed to be related to horizon's two-dimensional area, gets an additional terms, for instance 2? {? }? ? {S}, where ? is the GUP parameter.
NASA Astrophysics Data System (ADS)
Ghosh, Sumit
2015-03-01
We have studied the energy band structure of a Dirac particle in presence of a generalised uncertainty principle (GUP). We start from defining a modified momentum operator and derive corresponding modified dispersion relation (MDR) and GUP. Apart from the forbidden band within the range ± m, m being the mass of the particle, we find the existence of additional forbidden bands at the both ends of the spectrum. Such band structure forbids a Dirac particle to penetrate a potential step of sufficient height (˜ E P , E P being Planck energy). This is also true for massless particle. Unlike the relativistic case, a massless particle also can reflect from a barrier of sufficient height. Finally we discuss about the Klein's paradox in presence of the GUP.
Tawfik, Abdel Nasser
2015-01-01
Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein-Hawking (black hole) entropy, which relates the entropy to the cross-sectional area of the black hole horizon. Using generalized uncertainty principle (GUP), corrections to the geometric entropy and thermodynamics of black hole will be introduced. The impact of GUP on the entropy near the horizon of three types of black holes; Schwarzschild, Garfinkle-Horowitz-Strominger and Reissner-Nordstr\\"om is determined. It is found that the logarithmic divergence in the entropy-area relation turns to be positive. The entropy $S$, which is assumed to be related to horizon's two-dimensional area, gets an additional terms, for instance $2\\, \\sqrt{\\pi}\\, \\alpha\\, \\sqrt{S}$, where $\\alpha$ is the GUP parameter.
An uncertainty principle underlying the pinwheel structure in the primary visual cortex
Davide Barbieri; Giovanna Citti; Gonzalo Sanguinetti; Alessandro Sarti
2010-07-08
The visual information in V1 is processed by an array of modules called orientation preference columns. In some species including humans, orientation columns are radially arranged around singular points like the spokes of a wheel, that are called pinwheels. The pinwheel structure has been observed first with optical imaging techniques and more recently by in vivo two-photon imaging proving their organization with single cell precision. In this research we provide evidence that pinwheels are de facto optimal distributions for coding at the best angular position and momentum. In the last years many authors have recognized that the functional architecture of V1 is locally invariant with respect to the symmetry group of rotations and translations SE(2). In the present study we show that the orientation cortical maps used to construct pinwheels can be modeled as coherent states, i.e. the configurations best localized both in angular position and angular momentum. The theory we adopt is based on the well known uncertainty principle, introduced by Heisenberg in quantum mechanics and later extended to many other groups of invariance. Here we state a corresponding principle in the cortical geometry with SE(2) symmetry, and by computing its minimizers we obtain a model of orientation activity maps in the cortex. As it is well known the pinwheels configuration is directly constructed from these activity maps, and we will be able to formally reproduce their structure starting from the group symmetries of the functional architecture of the visual cortex. The primary visual cortex is then modeled as an integrated system in which the set of simple cells implements the SE(2) group, the horizontal connectivity implements its Lie algebra and the pinwheels implement its minimal uncertainty states.
M R Setare
2005-04-21
In this letter, we investigate a possible modification to the temperature and entropy of $5-$dimensional Schwarzschild anti de Sitter black holes due to incorporating stringy corrections to the modified uncertainty principle. Then we subsequently argue for corrections to the Cardy-Verlinde formula in order to account for the corrected entropy. Then we show, one can taking into account the generalized uncertainty principle corrections of the Cardy-Verlinde entropy formula by just redefining the Virasoro operator $L_0$ and the central charge $c$.
Forough Nasseri
2005-10-25
We calculate the corrections to the Fine Structure Constant in the spacetime of a cosmic string. These corrections stem from the generalized uncertainty principle. In the absence of a cosmic string our result here is in agreement with our previous result.
G. Youinou; G. Palmiotti; M. Salvatorre; G. Imel; R. Pardo; F. Kondev; M. Paul
2010-01-01
An integral reactor physics experiment devoted to infer higher actinide (Am, Cm, Bk, Cf) neutron cross sections will take place in the US. This report presents the principle of the planned experiment as well as a first exercise aiming at quantifying the uncertainties related to the inferred quantities. It has been funded in part by the DOE Office of Science in the framework of the Recovery Act and has been given the name MANTRA for Measurement of Actinides Neutron TRAnsmutation. The principle is to irradiate different pure actinide samples in a test reactor like INL’s Advanced Test Reactor, and, after a given time, determine the amount of the different transmutation products. The precise characterization of the nuclide densities before and after neutron irradiation allows the energy integrated neutron cross-sections to be inferred since the relation between the two are the well-known neutron-induced transmutation equations. This approach has been used in the past and the principal novelty of this experiment is that the atom densities of the different transmutation products will be determined with the Accelerator Mass Spectroscopy (AMS) facility located at ANL. While AMS facilities traditionally have been limited to the assay of low-to-medium atomic mass materials, i.e., A < 100, there has been recent progress in extending AMS to heavier isotopes – even to A > 200. The detection limit of AMS being orders of magnitude lower than that of standard mass spectroscopy techniques, more transmutation products could be measured and, potentially, more cross-sections could be inferred from the irradiation of a single sample. Furthermore, measurements will be carried out at the INL using more standard methods in order to have another set of totally uncorrelated information.
Principles for Robust On-orbit Uncertainties Traceable to the SI (Invited)
NASA Astrophysics Data System (ADS)
Shirley, E. L.; Dykema, J. A.; Fraser, G. T.; Anderson, J.
2009-12-01
Climate-change research requires space-based measurements of the Earth’s spectral radiance, reflectance, and atmospheric properties with unprecedented accuracy. Increases in measurement accuracy would improve and accelerate the quantitative determination of decadal climate change. The increases would also permit attribution of climate change to anthropogenic causes and foster understanding of climate evolution on an accelerated time scale. Beyond merely answering key questions about global climate change, accurate measurements would also be of benefit by testing and refining climate models to enhance and quantify their predictive value. Accurate measurements imply traceability to the SI system of units. In this regard, traceability is a property of the result of a measurement, or the value of a standard, whereby it can be related to international standards through an unbroken chain of comparisons, all having stated (and realistic) uncertainties. SI-traceability allows one to compare measurements independent of locale, time, or sensor. In this way, SI-traceability alleviates the urgency to maintain a false assurance of measurement accuracy by having an unbroken time series of observations continually adjusted so that measurement results obtained with a given instrument match the measurement results of its recent predecessors. Moreover, to make quantitative inferences from measurement results obtained in various contexts, which might range, for instance, from radiometry to atmospheric chemistry, having SI-traceability throughout all work is essential. One can derive principles for robust claims of SI-traceability from lessons learned by the scientific community. In particular, National Measurement Institutes (NMIs), such as NIST, use several strategies in their realization of practical SI-traceable measurements of the highest accuracy: (1.) basing ultimate standards on fundamental physical phenomena, such as the Quantum Hall resistance, instead of measurement artifacts; (2.) developing a variety of approaches to measure a given physical quantity; (3.) conducting intercomparisons of measurements performed by different institutions; (4.) perpetually seeking complete understanding of all sources of measurement bias and uncertainty; (5.) rigorously analyzing measurement uncertainties; and (6.) maintaining a high level of transparency that permits peer review of measurement practices. It is imperative to establish SI-traceability at the beginning of an environmental satellite program. This includes planning for system-level pre-launch and, in particular, on-orbit instrument calibration. On-orbit calibration strategies should be insensitive to reasonably expected perturbations that arise during launch or on orbit, and one should employ strategies to validate on-orbit traceability. As a rule, optical systems with simple designs tend to be more amenable to robust calibration schemes.
Revisiting the Calculation of I/V Profiles in Molecular Junctions Using the Uncertainty Principle.
Ramos-Berdullas, Nicolás; Mandado, Marcos
2014-04-17
Ortiz and Seminario (J. Chem. Phys. 2007, 127, 111106/1-3) proposed some years ago a simple and direct approach to obtain I/V profiles from the combination of ab initio equilibrium electronic structure calculations and the uncertainty principle as an alternative or complementary tool to more sophisticated nonequilibrium Green's functions methods. In this work, we revisit the fundamentals of this approach and reformulate accordingly the expression of the electric current. By analogy to the spontaneous electron decay process in electron transitions, in our revision, the current is calculated upon the relaxing process from the "polarized" state induced by the external electric field to the electronic ground state. The electric current is obtained from the total charge transferred through the molecule and the corresponding electronic energy relaxation. The electric current expression proposed is more general compared with the previous expression employed by Ortiz and Seminario, where the charge variation must be tested among different slabs of atoms at the contact. This new approach has been tested on benzene-1,4-dithiolate attached to different gold clusters that represent the contact with the electrodes. Analysis of the total electron deformation density induced by the external electric voltage and properties associated with the electron deformation orbitals supports the conclusions obtained from the I/V profiles. PMID:24689867
Black-hole thermodynamics with modified dispersion relations and generalized uncertainty principles
Giovanni Amelino-Camelia; Michele Arzano; Yi Ling; Gianluca Mandanici
2005-06-22
In several approaches to the quantum-gravity problem evidence has emerged of the validity of a "GUP" (a Generalized position-momentum Uncertainty Principle) and/or a "MDR" (a modification of the energy-momentum dispersion relation), but very little is known about the implications of GUPs and MDRs for black-hole thermodynamics, another key topic for quantum-gravity research. We investigate an apparent link, already suggested in an earlier exploratory study involving two of us, between the possibility of a GUP and/or a MDR and the possibility of a log term in the area-entropy black-hole formula. We then obtain, from that same perspective, a modified relation between the mass of a black hole and its temperature, and we examine the validity of the "Generalized Second Law of black-hole thermodynamics" in theories with a GUP and/or a MDR. After an analysis of GUP- and MDR-modifications of the black-body radiation spectrum, we conclude the study with a description of the black-hole evaporation process.
A volume inequality for quantum Fisher information and the uncertainty principle
P. Gibilisco; D. Imparato; T. Isola
2007-06-06
Let $A_1,...,A_N$ be complex self-adjoint matrices and let $\\rho$ be a density matrix. The Robertson uncertainty principle $$ det(Cov_\\rho(A_h,A_j)) \\geq det(- \\frac{i}{2} Tr(\\rho [A_h,A_j])) $$ gives a bound for the quantum generalized covariance in terms of the commutators $[A_h,A_j]$. The right side matrix is antisymmetric and therefore the bound is trivial (equal to zero) in the odd case $N=2m+1$. Let $f$ be an arbitrary normalized symmetric operator monotone function and let $_{\\rho,f}$ be the associated quantum Fisher information. In this paper we conjecture the inequality $$ det (Cov_\\rho(A_h,A_j)) \\geq det (\\frac{f(0)}{2} _{\\rho,f}) $$ that gives a non-trivial bound for any natural number $N$ using the commutators $i[\\rho, A_h]$. The inequality has been proved in the cases $N=1,2$ by the joint efforts of many authors. In this paper we prove the case N=3 for real matrices.
Kees van den Bos; P. Marijn Poortvliet; Marjolein Maas; Joost Miedema; Ernst-Jan van den Ham
2005-01-01
This enquiry concerning the principles of cultural norms and values focuses on the impact of mortality and uncertainty salience on people’s reactions to events that violate or bolster their cultural norms and values. Five experiments show that both mortality and uncertainty salience influence people’s reactions to violations and bolstering of their cultural worldviews, yielding evidence for both terror and uncertainty
Liu Molin; Gui Yuanxing; Liu Hongya [School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian, 116024 (China)
2008-12-15
In this paper, we study the quantum statistical entropy in a 5D Ricci-flat black string solution, which contains a 4D Schwarzschild-de Sitter black hole on the brane, by using the improved thin-layer method with the generalized uncertainty principle. The entropy is the linear sum of the areas of the event horizon and the cosmological horizon without any cutoff and any constraint on the bulk's configuration rather than the usual uncertainty principle. The system's density of state and free energy are convergent in the neighborhood of horizon. The small-mass approximation is determined by the asymptotic behavior of metric function near horizons. Meanwhile, we obtain the minimal length of the position {delta}x, which is restrained by the surface gravities and the thickness of layer near horizons.
Molin Liu; Yuanxing Gui; Hongya Liu
2008-12-04
In this paper, we study the quantum statistical entropy in a 5D Ricci-flat black string solution, which contains a 4D Schwarzschild-de Sitter black hole on the brane, by using the improved thin-layer method with the generalized uncertainty principle. The entropy is the linear sum of the areas of the event horizon and the cosmological horizon without any cut-off and any constraint on the bulk's configuration rather than the usual uncertainty principle. The system's density of state and free energy are convergent in the neighborhood of horizon. The small-mass approximation is determined by the asymptotic behavior of metric function near horizons. Meanwhile, we obtain the minimal length of the position $\\Delta x$ which is restrained by the surface gravities and the thickness of layer near horizons.
Rahul Ghosh; Surajit Chattopadhyay; Ujjal Debnath
2011-10-22
This work is motivated by the work of Kim et al (2008), which considered the equation of state parameter for the new agegraphic dark energy based on generalized uncertainty principle coexisting with dark matter without interaction. In this work, we have considered the same dark energy inter- acting with dark matter in emergent, intermediate and logamediate scenarios of the universe. Also, we have investigated the statefinder, kerk and lerk parameters in all three scenarios under this inter- action. The energy density and pressure for the new agegraphic dark energy based on generalized uncertainty principle have been calculated and their behaviors have been investigated. The evolu- tion of the equation of state parameter has been analyzed in the interacting and non-interacting situations in all the three scenarios. The graphical analysis shows that the dark energy behaves like quintessence era for logamediate expansion and phantom era for emergent and intermediate expansions of the universe.
W. Freeden; V. Michel
1999-01-01
. Current activities and recent progress on constructive approximation and numerical analysis in physical geodesy are reported\\u000a upon. Two major topics of interest are focused upon, namely trial systems for purposes of global and local approximation and\\u000a methods for adequate geodetic application. A fundamental tool is an uncertainty principle, which gives appropriate bounds\\u000a for the quantification of space and momentum
Alexis Larranaga; Hector J. Hortua
2009-01-23
In this paper, we study the thermodynamical properties of the (2+1) dimensional black hole with a non-linear electrodynamics and with a negative cosmological constant, using the Generalized Uncertainty Principle (GUP). This approach shows that there is a minimum mass or remnant for the black hole, corresponding to the minimum radius of the event horizon that has a size of the order of the Planck scale. We also show that the heat capacity for this black hole is always positive.
A violation of the uncertainty principle implies a violation of the second law of thermodynamics
Esther Hänggi; Stephanie Wehner
2012-05-31
Uncertainty relations state that there exist certain incompatible measurements, to which the outcomes cannot be simultaneously predicted. While the exact incompatibility of quantum measurements dictated by such uncertainty relations can be inferred from the mathematical formalism of quantum theory, the question remains whether there is any more fundamental reason for the uncertainty relations to have this exact form. What, if any, would be the operational consequences if we were able to go beyond any of these uncertainty relations? We give a strong argument that justifies uncertainty relations in quantum theory by showing that violating them implies that it is also possible to violate the second law of thermodynamics. More precisely, we show that violating the uncertainty relations in quantum mechanics leads to a thermodynamic cycle with positive net work gain, which is very unlikely to exist in nature.
Maurice de Gosson; Franz Luef
2008-03-06
We extend Hardy's uncertainty principle for a square integrable function and its Fourier transform to the multidimensional case using a symplectic diagonalization. We use this extension to show that Hardy's uncertainty principle is equivalent to a statement on the Wigner distribution of the function. We give a geometric interpretation of our results in terms of the notion of symplectic capacity of an ellipsoid. Furthermore, we show that Hardy's uncertainty principle is valid for a general Lagrangian frame of the phase space. Finally, we discuss an extension of Hardy's theorem for the Wigner distribution for exponentials with convex exponents.
Entropic formulation of the uncertainty principle for the number and annihilation operators
Alexey E. Rastegin
2012-01-09
An entropic approach to formulating uncertainty relations for the number-annihilation pair is considered. We construct some normal operator that traces the annihilation operator as well as commuting quadratures with a complete system of common eigenfunctions. Expanding the measured wave function with respect to them, one obtains a relevant probability distribution. Another distribution is naturally generated by measuring the number operator. Due to the Riesz-Thorin theorem, there exists a nontrivial inequality between corresponding functionals of the above distributions. We find the bound in this inequality and further derive uncertainty relations in terms of both the Renyi and Tsallis entropies. Entropic uncertainty relations for continuous distribution as well as relations for discretized one are presented.
Jean-Pierre Dupuy; Alexei Grinbaum
2005-01-01
The analysis of our epistemic situation regarding singular events, such as abrupt climate change, shows essential limitations in the traditional modes of dealing with uncertainty. Typical cognitive barriers lead to the paralysis of action. What is needed is taking seriously the reality of the future. We argue for the application of the methodology of ongoing normative assessment. We show that
The effect of generalized uncertainty principle on square well, a case study
Ma, Meng-Sen, E-mail: mengsenma@gmail.com [Department of Physics, Shanxi Datong University, 037009 Datong (China); Institute of Theoretical Physics, Shanxi Datong University, 037009 Datong (China); Zhao, Ren [Institute of Theoretical Physics, Shanxi Datong University, 037009 Datong (China)
2014-08-15
According to a special case (? = 0) of the generalized uncertainty relation we derive the energy eigenvalues of the infinite potential well. It is shown that the obtained energy levels are different from the usual result with some correction terms. And the correction terms of the energy eigenvalues are independent of other parameters except ?. But the eigenstates will depend on another two parameters besides ?.
The Uncertainty Principle in Software Engineering Hadar Ziv Debra J. Richardson
Ziv, Hadar
to a simple network of softÂ ware artifacts based on an elevator control system. We discuss results, implications and potential benefits of the Bayesian approach. The elevator system therefore serves control system. We conclude with a discussion of issues and concerns in uncertainty modeling, both
Marchiolli, M.A., E-mail: marcelo_march@bol.com.br [Avenida General Osório 414, Centro, 14.870-100 Jaboticabal, SP (Brazil); Mendonça, P.E.M.F., E-mail: pmendonca@gmail.com [Academia da Força Aérea, C.P. 970, 13.643-970 Pirassununga, SP (Brazil)] [Academia da Força Aérea, C.P. 970, 13.643-970 Pirassununga, SP (Brazil)
2013-09-15
We introduce a self-consistent theoretical framework associated with the Schwinger unitary operators whose basic mathematical rules embrace a new uncertainty principle that generalizes and strengthens the Massar–Spindel inequality. Among other remarkable virtues, this quantum-algebraic approach exhibits a sound connection with the Wiener–Khinchin theorem for signal processing, which permits us to determine an effective tighter bound that not only imposes a new subtle set of restrictions upon the selective process of signals and wavelet bases, but also represents an important complement for property testing of unitary operators. Moreover, we establish a hierarchy of tighter bounds, which interpolates between the tightest bound and the Massar–Spindel inequality, as well as its respective link with the discrete Weyl function and tomographic reconstructions of finite quantum states. We also show how the Harper Hamiltonian and discrete Fourier operators can be combined to construct finite ground states which yield the tightest bound of a given finite-dimensional state vector space. Such results touch on some fundamental questions inherent to quantum mechanics and their implications in quantum information theory. -- Highlights: •Conception of a quantum-algebraic framework embracing a new uncertainty principle for unitary operators. •Determination of new restrictions upon the selective process of signals and wavelet bases. •Demonstration of looser bounds interpolating between the tightest bound and the Massar–Spindel inequality. •Construction of finite ground states properly describing the tightest bound. •Establishment of an important connection with the discrete Weyl function.
NASA Astrophysics Data System (ADS)
Furrer, Fabian
2014-10-01
A big challenge in continuous-variable quantum key distribution is to prove security against arbitrary coherent attacks including realistic assumptions such as finite-size effects. Recently, such a proof has been presented in [Phys. Rev. Lett. 109, 100502 (2012), 10.1103/PhysRevLett.109.100502] for a two-mode squeezed state protocol based on a novel uncertainty relation with quantum memories. But the transmission distances were fairly limited due to a direct reconciliation protocol. We prove here security against coherent attacks of a reverse-reconciliation protocol under similar assumptions but allowing distances of over 16 km for experimentally feasible parameters. We further clarify the limitations when using the uncertainty relation with quantum memories in security proofs of continuous-variable quantum key distribution.
Nori, Franco
2014-01-01
experimental data, and thus demonstrate that perfect distributional estimations can have nonzero error the spirit of Heisenberg's eponymous inequality, but do indicate a qualitatively different relationship of lectures [3]. The modern form of this principle extends the work of Heisenberg by directly relating
Uncertainty Principles and Identification n-Widths for LTI and Slowly Varying Systems
Lin; Le Yi Wang; George Zames
1992-01-01
In the identification of LTI systems, the optimal worst-case uncertainty depends on the observation time. This dependence is characterized via two notions of n-width, which are computed in the l1 and H¿ norms. The results are then applied to systems in which the law governing the evolution of the uncertain elements is not time invariant. Such systems can not be
An uncertainty principle for real signals in the fractional Fourier transform domain
Sudarshan Shinde; Vikram M. Gadre
2001-01-01
The fractional Fourier transform (FrFT) can be thought of as a generalization of the Fourier transform to rotate a signal representation by an arbitrary angle ? in the time-frequency plane. A lower bound on the uncertainty product of signal representations in two FrFT domains for real signals is obtained, and it is shown that a Gaussian signal achieves the lower
NASA Astrophysics Data System (ADS)
Mukhopadhyay, S.; Bhattacharyya, K.
2000-10-01
The kinship of a simple variational scheme involving the uncertainty product with a prevalent semiclassical nonlinear differential equation approach for finding energies of stationary states is established. This leads to a transparent physical interpretation of the embedded parameters in the latter approach, providing additionally a lower bound to the integration constant. The domain of applicability of this strategy is also extended to encompass neighbouring states. Other advantages of the simpler alternative route are stressed. Pilot calculations demonstrate nicely the efficacy of the endeavour.
David R Geelan
2013-06-14
Recent empirical work in the field of 'weak measurements' has yielded novel ways of more directly accessing and exploring the quantum wavefunction. Measuring either position or momentum for a photon in a 'weak' manner yields a wide range of possible values for the measurement, and can be done in such a way as to only minimally effect the wavefunction rather than to collapse it to a specific precise value. Measuring the other complementary variable (position or momentum) precisely at a later time ('post-selection') and averaging the weak measurements can yield information about the wavefunction that is not directly experimentally obtainable using other methods. This paper discusses two recent papers on weak measurement in the context of the uncertainty principle more broadly, and considers some possibilities for further research.
Yan-Gang Miao; Ying-Jie Zhao; Shao-Jun Zhang
2014-11-23
As a generalized uncertainty principle (GUP) leads to the effects of the minimal length of the order of the Planck scale and UV/IR mixing, some significant physical concepts and quantities are modified or corrected correspondingly. On the one hand, we derive the maximally localized states --- the physical states displaying the minimal length uncertainty associated with a new GUP proposed in our previous work. On the other hand, in the framework of this new GUP we calculate quantum corrections to the thermodynamic quantities of the Schwardzschild black hole, such as the Hawking temperature, the entropy, and the heat capacity, and give a remnant mass of the black hole at the end of the evaporation process. Moreover, we compare our results with that obtained in the frameworks of several other GUPs. In particular, we observe a significant difference between the situations with and without the consideration of the UV/IR mixing effect in the quantum corrections to the evaporation rate and the decay time. That is, the decay time can greatly be prolonged and even the Hawking radiation can stop in some sense in the former case, which implies that the quantum correction from the UV/IR mixing effect may give rise to a radical rather than a tiny influence to the Hawking radiation.
Andrei P. Kirilyuk
1999-03-25
The intrinsic multivaluedness of interaction process, revealed in Part I of this series of papers, is interpreted as the origin of the true dynamical (in particular, quantum) chaos. The latter is causally deduced as unceasing series of transitions, dynamically probabilistic by their origin, between the equally real, but incompatible 'realisations' (modes of interaction) of a system. The obtained set of realisations form the causally derived, intrinsically complete "space of events" providing the crucial extension of the notion of probability and the method of its first-principle calculation. The fundamental dynamic uncertainty thus revealed is specified for Hamiltonian quantum systems and applied to quantum chaos description in periodically perturbed systems. The ordinary semiclassical transition in our quantum-mechanical results leads to exact reproduction of the main features of chaotic behaviour of the system known from classical mechanics, which permits one to "re-establish" the correspondence principle for chaotic systems (inevitably lost in any their conventional, single-valued description). The causal dynamical randomness in the extended quantum mechanics is not restricted, however, to semiclassical conditions and generically occurs also in essentially quantum regimes, even though partial "quantum suppression of chaos" does exist and is specified in our description, as well as other particular types of the quantum (truly) chaotic behaviour.
NASA Astrophysics Data System (ADS)
McLeod, David; McLeod, Roger
2008-04-01
The electron model used in our other joint paper here requires revision of some foundational physics. That electron model followed from comparing the experimentally proved results of human vision models using spatial Fourier transformations, SFTs, of pincushion and Hermann grids. Visual systems detect ``negative'' electric field values for darker so-called ``illusory'' diagonals that are physical consequences of the lens SFT of the Hermann grid, distinguishing this from light ``illusory'' diagonals. This indicates that oppositely directed vectors of the separate illusions are discretely observable, constituting another foundational fault in quantum mechanics, QM. The SFT of human vision is merely the scaled SFT of QM. Reciprocal space results of wavelength and momentum mimic reciprocal relationships between space variable x and spatial frequency variable p, by the experiment mentioned. Nobel laureate physicist von B'ek'esey, physiology of hearing, 1961, performed pressure input Rect x inputs that the brain always reports as truncated Sinc p, showing again that the brain is an adjunct built by sight, preserves sign sense of EMF vectors, and is hard wired as an inverse SFT. These require vindication of Schr"odinger's actual, but incomplete, wave model of the electron as having physical extent over the wave, and question Heisenberg's uncertainty proposal.
NASA Astrophysics Data System (ADS)
Nasseri, Forough
2007-02-01
In this Reply, using G. de A. Marques' comment, we correct calculations and results presented in [F. Nasseri, Phys. Lett. B 632 (2006) 151] about corrections to the fine structure constant in the spacetime of a cosmic string from the generalized uncertainty principle.
Forough Nasseri
2006-12-14
In this Reply, using G.de.A.Marques' comment, we correct calculations and results presented in [Phys.Lett.B 632(2006) 151-154] about corrections to the fine structure constant in the spacetime of a cosmic string from the generalized uncertainty principle.
NASA Astrophysics Data System (ADS)
Marchiolli, M. A.; Mendonça, P. E. M. F.
2013-09-01
We introduce a self-consistent theoretical framework associated with the Schwinger unitary operators whose basic mathematical rules embrace a new uncertainty principle that generalizes and strengthens the Massar-Spindel inequality. Among other remarkable virtues, this quantum-algebraic approach exhibits a sound connection with the Wiener-Khinchin theorem for signal processing, which permits us to determine an effective tighter bound that not only imposes a new subtle set of restrictions upon the selective process of signals and wavelet bases, but also represents an important complement for property testing of unitary operators. Moreover, we establish a hierarchy of tighter bounds, which interpolates between the tightest bound and the Massar-Spindel inequality, as well as its respective link with the discrete Weyl function and tomographic reconstructions of finite quantum states. We also show how the Harper Hamiltonian and discrete Fourier operators can be combined to construct finite ground states which yield the tightest bound of a given finite-dimensional state vector space. Such results touch on some fundamental questions inherent to quantum mechanics and their implications in quantum information theory.
Femtoscopic scales in $p+p$ and $p+$Pb collisions in view of the uncertainty principle
V. M. Shapoval; P. Braun-Munzinger; Iu. A. Karpenko; Yu. M. Sinyukov
2013-07-26
A method for quantum corrections of Hanbury-Brown/Twiss (HBT) interferometric radii produced by semi-classical event generators is proposed. These corrections account for the basic indistinguishability and mutual coherence of closely located emitters caused by the uncertainty principle. A detailed analysis is presented for pion interferometry in $p+p$ collisions at LHC energy ($\\sqrt{s}=7$ TeV). A prediction is also presented of pion interferometric radii for $p+$Pb collisions at $\\sqrt{s}=5.02$ TeV. The hydrodynamic/hydrokinetic model with UrQMD cascade as 'afterburner' is utilized for this aim. It is found that quantum corrections to the interferometry radii improve significantly the event generator results which typically overestimate the experimental radii of small systems. A successful description of the interferometry structure of $p+p$ collisions within the corrected hydrodynamic model requires the study of the problem of thermalization mechanism, still a fundamental issue for ultrarelativistic $A+A$ collisions, also for high multiplicity $p+p$ and $p+$Pb events.
Fran De Aquino
2001-03-29
In a previous work it was shown that the gravitational and inertial masses are correlated by an adimensional factor, which depends on the incident radiation upon the particle. It was also shown that there is a direct correlation between the radiation absorbed by the particle and its gravitational mass, independently of the inertial mass. This finding has fundamental consequences to Unified Field Theory and Quantum Cosmology. Only in the absence of electromagnetic radiation the mentioned factor becomes equal to one. On the other hand, in specific electromagnetic conditions, it can be reduced, nullified or made negative. This means that there is the possibility of the gravitational masses can be reduced, nullified and made negative by means of electromagnetic radiation. This unexpected theoretical result was recently confirmed by an experiment (gr-qc/0005107). A fundamental consequence of the mentioned correlation is that , in specific ultra-high energy conditions, the gravitational and electromagnetic fields can be described by the same Hamiltonian , i.e., in these circumstances, they are unified. Such conditions can have occurred inclusive in the Initial Universe , before the first spontaneous breaking of symmetry. Taking as base this discovery, and starting from the gravitational mass of superparticles from the Initial Universe we show here that it is possible to deduce the reciprocal fine structure constant and the uncertainty principle directly from the Gravitation Theory(Unified Theory).
NASA Technical Reports Server (NTRS)
Chiao, Raymond Y.; Kwiat, Paul G.; Steinberg, Aephraim M.
1992-01-01
The energy-time uncertainty principle is on a different footing than the momentum position uncertainty principle: in contrast to position, time is a c-number parameter, and not an operator. As Aharonov and Bohm have pointed out, this leads to different interpretations of the two uncertainty principles. In particular, one must distinguish between an inner and an outer time in the definition of the spread in time, delta t. It is the inner time which enters the energy-time uncertainty principle. We have checked this by means of a correlated two-photon light source in which the individual energies of the two photons are broad in spectra, but in which their sum is sharp. In other words, the pair of photons is in an entangled state of energy. By passing one member of the photon pair through a filter with width delta E, it is observed that the other member's wave packet collapses upon coincidence detection to a duration delta t, such that delta E(delta t) is approximately equal to planks constant/2 pi, where this duration delta t is an inner time, in the sense of Aharonov and Bohm. We have measured delta t by means of a Michelson interferometer by monitoring the visibility of the fringes seen in coincidence detection. This is a nonlocal effect, in the sense that the two photons are far away from each other when the collapse occurs. We have excluded classical-wave explanations of this effect by means of triple coincidence measurements in conjunction with a beam splitter which follows the Michelson interferometer. Since Bell's inequalities are known to be violated, we believe that it is also incorrect to interpret this experimental outcome as if energy were a local hidden variable, i.e., as if each photon, viewed as a particle, possessed some definite but unknown energy before its detection.
NASA Astrophysics Data System (ADS)
Mazurova, Elena; Lapshin, Aleksey
2013-04-01
The method of discrete linear transformations that can be implemented through the algorithms of the Standard Fourier Transform (SFT), Short-Time Fourier Transform (STFT) or Wavelet transform (WT) is effective for calculating the components of the deflection of the vertical from discrete values of gravity anomaly. The SFT due to the action of Heisenberg's uncertainty principle indicates weak spatial localization that manifests in the following: firstly, it is necessary to know the initial digital signal on the complete number line (in case of one-dimensional transform) or in the whole two-dimensional space (if a two-dimensional transform is performed) in order to find the SFT. Secondly, the localization and values of the "peaks" of the initial function cannot be derived from its Fourier transform as the coefficients of the Fourier transform are formed by taking into account all the values of the initial function. Thus, the SFT gives the global information on all frequencies available in the digital signal throughout the whole time period. To overcome this peculiarity it is necessary to localize the signal in time and apply the Fourier transform only to a small portion of the signal; the STFT that differs from the SFT only by the presence of an additional factor (window) is used for this purpose. A narrow enough window is chosen to localize the signal in time and, according to Heisenberg's uncertainty principle, it results in have significant enough uncertainty in frequency. If one chooses a wide enough window it, according to the same principle, will increase time uncertainty. Thus, if the signal is narrowly localized in time its spectrum, on the contrary, is spread on the complete axis of frequencies, and vice versa. The STFT makes it possible to improve spatial localization, that is, it allows one to define the presence of any frequency in the signal and the interval of its presence. However, owing to Heisenberg's uncertainty principle, it is impossible to tell precisely, what frequency is present in the signal at the current moment of time: it is possible to speak only about the range of frequencies. Besides, it is impossible to specify precisely the time moment of the presence of this or that frequency: it is possible to speak only about the time frame. It is this feature that imposes major constrains on the applicability of the STFT. In spite of the fact that the problems of resolution in time and frequency result from a physical phenomenon (Heisenberg's uncertainty principle) and exist independent of the transform applied, there is a possibility to analyze any signal, using the alternative approach - the multiresolutional analysis (MRA). The wavelet-transform is one of the methods for making a MRA-type analysis. Thanks to it, low frequencies can be shown in a more detailed form with respect to time, and high ones - with respect to frequency. The paper presents the results of calculating of the components of the deflection of the vertical, done by the SFT, STFT and WT. The results are presented in the form of 3-d models that visually show the action of Heisenberg's uncertainty principle in the specified algorithms. The research conducted allows us to recommend the application of wavelet-transform to calculate of the components of the deflection of the vertical in the near-field zone. Keywords: Standard Fourier Transform, Short-Time Fourier Transform, Wavelet Transform, Heisenberg's uncertainty principle.
Grote, Gudela
2014-01-01
It is frequently lamented that human factors and ergonomics knowledge does not receive the attention and consideration that it deserves. In this paper I argue that in order to change this situation human factors/ergonomics based system design needs to be positioned as a strategic task within a conceptual framework that incorporates both business and design concerns. The management of uncertainty is presented as a viable candidate for such a framework. A case is described where human factors/ergonomics experts in a railway company have used the management of uncertainty perspective to address strategic concerns at firm level. Furthermore, system design is discussed in view of the relationship between organization and technology more broadly. System designers need to be supported in better understanding this relationship in order to cope with the uncertainties this relationship brings to the design process itself. Finally, the emphasis on uncertainty embedded in the recent surge of introducing risk management across all business sectors is suggested as another opportunity for bringing human factors and ergonomics expertise to the fore. PMID:23622735
Tetsuya Hara; Keita Sakai; Daigo Kajiura
2006-08-14
By a simple physical consideration and uncertain principle, we derive that temperature is proportional to the surface gravity and entropy is proportional to the surface area of the black hole. We apply the same consideration to de Sitter space and estimate the temperature and entropy of the space, then we deduce that the entropy is proportional to the boundary surface area. By the same consideration, we estimate the temperature and entropy in the uniformly accelerated system (Rindler coordinate). The cases in higher dimensions are considered.
Mezzasalma, Stefano A
2007-03-15
The theoretical basis of a recent theory of Brownian relativity for polymer solutions is deepened and reexamined. After the problem of relative diffusion in polymer solutions is addressed, its two postulates are formulated in all generality. The former builds a statistical equivalence between (uncorrelated) timelike and shapelike reference frames, that is, among dynamical trajectories of liquid molecules and static configurations of polymer chains. The latter defines the "diffusive horizon" as the invariant quantity to work with in the special version of the theory. Particularly, the concept of universality in polymer physics corresponds in Brownian relativity to that of covariance in the Einstein formulation. Here, a "universal" law consists of a privileged observation, performed from the laboratory rest frame and agreeing with any diffusive reference system. From the joint lack of covariance and simultaneity implied by the Brownian Lorentz-Poincaré transforms, a relative uncertainty arises, in a certain analogy with quantum mechanics. It is driven by the difference between local diffusion coefficients in the liquid solution. The same transformation class can be used to infer Fick's second law of diffusion, playing here the role of a gauge invariance preserving covariance of the spacetime increments. An overall, noteworthy conclusion emerging from this view concerns the statistics of (i) static macromolecular configurations and (ii) the motion of liquid molecules, which would be much more related than expected. PMID:17223124
Risk Management Principles for Nanotechnology
Gary E. Marchant; Douglas J. Sylvester; Kenneth W. Abbott
2008-01-01
Risk management of nanotechnology is challenged by the enormous uncertainties about the risks, benefits, properties, and future\\u000a direction of nanotechnology applications. Because of these uncertainties, traditional risk management principles such as acceptable\\u000a risk, cost–benefit analysis, and feasibility are unworkable, as is the newest risk management principle, the precautionary\\u000a principle. Yet, simply waiting for these uncertainties to be resolved before undertaking
Two new kinds of uncertainty relations
NASA Technical Reports Server (NTRS)
Uffink, Jos
1994-01-01
We review a statistical-geometrical and a generalized entropic approach to the uncertainty principle. Both approaches provide a strengthening and generalization of the standard Heisenberg uncertainty relations, but in different directions.
A Graphical Illustration of the Heisenberg Uncertainty Relationship Frank Rioux
Rioux, Frank
with high precision. The uncertainty principle requires that if the position of an object is precisely known below. x a( ) 2 a sin x a To illustrate the uncertainty principle and the reciprocal distribution, |(p,a)|2, is shown for three sizes, a = 1,2 and 3. The uncertainty principle is illustrated
Uncertainty in Computational Aerodynamics
NASA Technical Reports Server (NTRS)
Luckring, J. M.; Hemsch, M. J.; Morrison, J. H.
2003-01-01
An approach is presented to treat computational aerodynamics as a process, subject to the fundamental quality assurance principles of process control and process improvement. We consider several aspects affecting uncertainty for the computational aerodynamic process and present a set of stages to determine the level of management required to meet risk assumptions desired by the customer of the predictions.
Comparison of Classical and Quantum Mechanical Uncertainties.
ERIC Educational Resources Information Center
Peslak, John, Jr.
1979-01-01
Comparisons are made for the particle-in-a-box, the harmonic oscillator, and the one-electron atom. A classical uncertainty principle is derived and compared with its quantum-mechanical counterpart. The results are discussed in terms of the statistical interpretation of the uncertainty principle. (Author/BB)
Uncertainty and complementarity in axiomatic quantum mechanics
Pekka J. Lahti
1980-01-01
In this work an investigation of the uncertainty principle and the complementarity principle is carried through. A study of the physical content of these principles and their representation in the conventional Hilbert space formulation of quantum mechanics forms a natural starting point for this analysis. Thereafter is presented more general axiomatic framework for quantum mechanics, namely, a probability function formulation
Interpreting uncertainty terms.
Holtgraves, Thomas
2014-08-01
Uncertainty terms (e.g., some, possible, good, etc.) are words that do not have a fixed referent and hence are relatively ambiguous. A model is proposed that specifies how, from the hearer's perspective, recognition of facework as a potential motive for the use of an uncertainty term results in a calibration of the intended meaning of that term. Four experiments are reported that examine the impact of face threat, and the variables that affect it (e.g., power), on the manner in which a variety of uncertainty terms (probability terms, quantifiers, frequency terms, etc.) are interpreted. Overall, the results demonstrate that increased face threat in a situation will result in a more negative interpretation of an utterance containing an uncertainty term. That the interpretation of so many different types of uncertainty terms is affected in the same way suggests the operation of a fundamental principle of language use, one with important implications for the communication of risk, subjective experience, and so on. PMID:25090127
HARDY'S UNCERTAINTY PRINCIPLE ON SEMISIMPLE GROUPS
M. Cowling; A. Sitaram; M. Sundari
2000-01-01
2 for all in R, where >0, >0, and > 1=4, then f =0 . Sitaram and Sundari generalised this theorem to semisimple groups with one conjugacy class of Cartan subgroups and to the K-invariant case for general semisimple groups. We ex- tend the theorem to all semisimple groups.
An uncertainty principle in chromosome positioning
Luis A Parada; Jeffrey J Roix; Tom Misteli
2003-01-01
Chromosomes are non-randomly positioned in the mammalian interphase nucleus. It is not known how patterns of chromosome positions are established or to what degree spatial arrangements of chromosomes change during the cell cycle, especially during mitosis. Two reports have applied in vivo microscopy to track chromosomes in space and time. The results highlight the inherently imperfect and probabilistic nature of
Uncertainty Principle Estimates for Vector Fields
Carlos Pérez; Richard L. Wheeden
2001-01-01
We derive weighted norm estimates for integral operators of potential type and for their related maximal operators. These operators are generalizations of the classical fractional integrals and fractional maximal functions. The norm estimates are derived in the context of a space of homogeneous type. The conditions required of the weight functions involve generalizations of the Fefferman–Phong “r-bump” condition. The results
Nab: Measurement Principles, Apparatus and Uncertainties
D. Pocanic; R. Alarcon; L. P. Alonzi; S. Baessler; S. Balascuta; J. D. Bowman; M. A. Bychkov; J. Byrne; J. R. Calarco; V. Cianciolo; C. Crawford; E. Frlez; M. T. Gericke; G. L. Greene; R. K. Grzywacz; V. Gudkov; F. W. Hersman; A. Klein; J. Martin; S. A. Page; A. Palladino; S. I. Penttila; K. P. Rykaczewski; W. S. Wilburn; A. R. Young; G. R. Young
2008-10-01
The Nab collaboration will perform a precise measurement of 'a', the electron-neutrino correlation parameter, and 'b', the Fierz interference term in neutron beta decay, in the Fundamental Neutron Physics Beamline at the SNS, using a novel electric/magnetic field spectrometer and detector design. The experiment is aiming at the 10^{-3} accuracy level in (Delta a)/a, and will provide an independent measurement of lambda = G_A/G_V, the ratio of axial-vector to vector coupling constants of the nucleon. Nab also plans to perform the first ever measurement of 'b' in neutron decay, which will provide an independent limit on the tensor weak coupling.
Further results on the uncertainty threshold principle
R. Ku; M. Athans
1977-01-01
Additional quantitative results are presented for the existence of optimal decision rules and stochastic stability for linear systems with white random parameters with respect to quadratic performance criteria by examining a specific version of a multivariable optimization problem.
An Uncertainty Principle For Hankel Transforms
Margit R Osler; Michael Voit
. There exists a generalized Hankel transform of order ff \\\\Gamma1=2 onR, which is based on the eigenfunctions of the Dunkl operatorT ff f(x) = f0(x) +\\\\Gammaff +12\\\\Delta f(x) \\\\Gamma f(\\\\Gammax)x; f 2 C1(R):For ff = \\\\Gamma1=2 this transform coincides with the usual Fourier transform onR. In this paper the operator T ff replaces the usual first derivative in order
Uncertainty principle with quantum Fisher information
Attila Andai
2007-10-11
In this paper we prove a nontrivial lower bound for the determinant of the covariance matrix of quantum mechanical observables, which was conjectured by Gibilisco, Isola and Imparato. The lower bound is given in terms of the commutator of the state and the observables and their scalar product, which is generated by an arbitrary symmetric operator monotone function.
Uncertainty Principle and Quantum Fisher Information
P. Gibilisco; T. Isola
2006-02-10
We show that an inequality recently proved by Kosaki and Yanagi-Furuichi-Kuriyama [arXiv:quant-ph/0501152] has a natural geometric interpretation in terms of monotone metrics associated to Wigner-Yanase-Dyson information. Moreover we give a counterexample showing that the inequality does not hold for every monotone metric of this type.
Uncertainty principles and ideal atomic decomposition
David L. Donoho; Xiaoming Huo
2001-01-01
Suppose a discrete-time signal S(t), 0⩽t
Reformulating the Quantum Uncertainty Relation
Jun-Li Li; Cong-Feng Qiao
2015-02-23
Uncertainty principle is one of the cornerstones of quantum theory. In the literature, there are two types of uncertainty relations, the operator form concerning the variances of physical observables and the entropy form related to entropic quantities. Both these forms are inequalities involving pairwise observables, and are found to be nontrivial to incorporate multiple observables. In this work we introduce a new form of uncertainty relation which may give out complete trade-off relations for variances of observables in pure and mixed quantum systems. Unlike the prevailing uncertainty relations, which are either quantum state dependent or not directly measurable, our bounds for variances of observables are quantum state independent and immune from the "triviality" problem, the optimal ones. Furthermore, the new uncertainty relation may provide a geometric explanation for the reason why there are limitations on the simultaneous determination of different observables in $N$-dimensional Hilbert space.
Rényi entropy uncertainty relation for successive projective measurements
Jun Zhang; Yang Zhang; Chang-shui Yu
2014-11-27
We investigate the uncertainty principle for two successive projective measurements in terms of R\\'{e}nyi entropy based on a single quantum system. Our results cover a large family of the entropy (including the Shannon entropy) uncertainty relations with a lower optimal bound. We compare our relation with other formulations of the uncertainty principle in a two spin observables measured on a pure quantum state of qubit. It is shown that the low bound of our uncertainty relation has better tightness.
Rényi entropy uncertainty relation for successive projective measurements
NASA Astrophysics Data System (ADS)
Zhang, Jun; Zhang, Yang; Yu, Chang-shui
2015-02-01
We investigate the uncertainty principle for two successive projective measurements in terms of Rényi entropy based on a single quantum system. Our results cover a large family of the entropy (including the Shannon entropy) uncertainty relations with a lower optimal bound. We compare our relation with other formulations of the uncertainty principle in two-spin observables measured on a pure quantum state of qubit. It is shown that the low bound of our uncertainty relation has better tightness.
Improved entropic uncertainty relations and information exclusion relations
NASA Astrophysics Data System (ADS)
Coles, Patrick J.; Piani, Marco
2014-02-01
The uncertainty principle can be expressed in entropic terms, also taking into account the role of entanglement in reducing uncertainty. The information exclusion principle bounds instead the correlations that can exist between the outcomes of incompatible measurements on one physical system, and a second reference system. We provide a more stringent formulation of both the uncertainty principle and the information exclusion principle, with direct applications for, e.g., the security analysis of quantum key distribution, entanglement estimation, and quantum communication. We also highlight a fundamental distinction between the complementarity of observables in terms of uncertainty and in terms of information.
Seevinck, Michiel
to the uncertainty principle which have been developed recently, a statisticalgeometrical approach and a generalized. In other words, what is unsatisfactory with the traditional approach to the uncertainty principle? In the standard textbook approach the uncertainty principle for position and momentum is expressed
Majorization formulation of uncertainty in quantum mechanics
Partovi, M. Hossein [Department of Physics and Astronomy, California State University, Sacramento, California 95819-6041 (United States)
2011-11-15
Heisenberg's uncertainty principle is formulated for a set of generalized measurements within the framework of majorization theory, resulting in a partial uncertainty order on probability vectors that is stronger than those based on quasientropic measures. The theorem that emerges from this formulation guarantees that the uncertainty of the results of a set of generalized measurements without a common eigenstate has an inviolable lower bound which depends on the measurement set but not the state. A corollary to this theorem yields a parallel formulation of the uncertainty principle for generalized measurements corresponding to the entire class of quasientropic measures. Optimal majorization bounds for two and three mutually unbiased bases in two dimensions are calculated. Similarly, the leading term of the majorization bound for position and momentum measurements is calculated which provides a strong statement of Heisenberg's uncertainty principle in direct operational terms. Another theorem provides a majorization condition for the least-uncertain generalized measurement of a given state with interesting physical implications.
NSDL National Science Digital Library
Moore, P.G.
This article, authored by P.G. Moore for the Royal Statistical Society's website, provides well-defined exercises to assess the probabilities of decision-making and the degree of uncertainty. The author states the focus of the article as: "When analyzing situations which involve decisions to be made as between alternative courses of action under conditions of uncertainty, decision makers and their advisers are often called upon to assess judgmental probability distributions of quantities whose true values are unknown to them. How can this judgment be taught?" Moore provides five different exercises and even external reference for those interested in further study of the topic.
ERIC Educational Resources Information Center
Duerdoth, Ian
2009-01-01
The subject of uncertainties (sometimes called errors) is traditionally taught (to first-year science undergraduates) towards the end of a course on statistics that defines probability as the limit of many trials, and discusses probability distribution functions and the Gaussian distribution. We show how to introduce students to the concepts of…
Generalized Entropic Uncertainty Relations with Tsallis' Entropy
NASA Technical Reports Server (NTRS)
Portesi, M.; Plastino, A.
1996-01-01
A generalization of the entropic formulation of the Uncertainty Principle of Quantum Mechanics is considered with the introduction of the q-entropies recently proposed by Tsallis. The concomitant generalized measure is illustrated for the case of phase and number operators in quantum optics. Interesting results are obtained when making use of q-entropies as the basis for constructing generalized entropic uncertainty measures.
ERIC Educational Resources Information Center
Hewitt, Paul G.
2004-01-01
Some teachers have difficulty understanding Bernoulli's principle particularly when the principle is applied to the aerodynamic lift. Some teachers favor using Newton's laws instead of Bernoulli's principle to explain the physics behind lift. Some also consider Bernoulli's principle too difficult to explain to students and avoid teaching it…
Uncertainty Techniques Statistics, Least Squares, Regression,
Rostock, Universität
Uncertainty Techniques Statistics, Least Squares, Regression, ML-Estimation, Stochastic Processes Objectives 5 The Fourier series is an example for function approximation using the orthogonality principle. The least-squares principle does not require a statistical framework to make sense. Maximum likelihood
Holographic position uncertainty and the quantum-classical transition
C. L. Herzenberg
2010-04-16
Arguments based on general principles of quantum mechanics have suggested that a minimum length associated with Planck-scale unification may in the context of the holographic principle entail a new kind of observable uncertainty in the transverse position of macroscopically separated objects. Here, we address potential implications of such a position uncertainty for establishing an additional threshold between quantum and classical behavior.
Uncertainty in the Classroom--Teaching Quantum Physics
ERIC Educational Resources Information Center
Johansson, K. E.; Milstead, D.
2008-01-01
The teaching of the Heisenberg uncertainty principle provides one of those rare moments when science appears to contradict everyday life experiences, sparking the curiosity of the interested student. Written at a level appropriate for an able high school student, this article provides ideas for introducing the uncertainty principle and showing how…
Entropic uncertainty relation in de Sitter space
NASA Astrophysics Data System (ADS)
Jia, Lijuan; Tian, Zehua; Jing, Jiliang
2015-02-01
The uncertainty principle restricts our ability to simultaneously predict the measurement outcomes of two incompatible observables of a quantum particle. However, this uncertainty could be reduced and quantified by a new Entropic Uncertainty Relation (EUR). By the open quantum system approach, we explore how the nature of de Sitter space affects the EUR. When the quantum memory A freely falls in the de Sitter space, we demonstrate that the entropic uncertainty acquires an increase resulting from a thermal bath with the Gibbons-Hawking temperature. And for the static case, we find that the temperature coming from both the intrinsic thermal nature of the de Sitter space and the Unruh effect associated with the proper acceleration of A also brings effect on entropic uncertainty, and the higher the temperature, the greater the uncertainty and the quicker the uncertainty reaches the maximal value. And finally the possible mechanism behind this phenomenon is also explored.
The link between entropic uncertainty and nonlocality
NASA Astrophysics Data System (ADS)
Tomamichel, Marco; Hänggi, Esther
2013-02-01
Two of the most intriguing features of quantum physics are the uncertainty principle and the occurrence of nonlocal correlations. The uncertainty principle states that there exist pairs of incompatible measurements on quantum systems such that their outcomes cannot both be predicted. On the other hand, nonlocal correlations of measurement outcomes at different locations cannot be explained by classical physics, but appear in the presence of entanglement. Here, we show that these two fundamental quantum effects are quantitatively related. Namely, we provide an entropic uncertainty relation for the outcomes of two binary measurements, where the lower bound on the uncertainty is quantified in terms of the maximum Clauser-Horne-Shimony-Holt value that can be achieved with these measurements. We discuss applications of this uncertainty relation in quantum cryptography, in particular, to certify quantum sources using untrusted devices.
Reachability Under Uncertainty1 A.B. Kurzhanski
Varaiya, Pravin
under set-membership uncertainty. This principle allows one to describe the closed loop reach setReachability Under Uncertainty1 A.B. Kurzhanski , P. Varaiya Moscow State (Lomonosov) University setting. It defines possible notions of reach- ability under uncertainty emphasizing the differences
Entropic uncertainty relations in multidimensional position and momentum spaces
Huang Yichen [Department of Physics, University of California, Berkeley, Berkeley, California 94720 (United States)
2011-05-15
Commutator-based entropic uncertainty relations in multidimensional position and momentum spaces are derived, twofold generalizing previous entropic uncertainty relations for one-mode states. They provide optimal lower bounds and imply the multidimensional variance-based uncertainty principle. The article concludes with an open conjecture.
Minimum uncertainty states of angular momentum and angular position
Zambrini, Roberta
Minimum uncertainty states of angular momentum and angular position David T Pegg1 , Stephen M of linear momentum that satisfy the equality in the Heisenberg uncertainty principle for position for position and momentum. The corresponding uncertainty relation for angular momentum and angular position
Thomas, R.E.
1982-03-01
An evaluation is made of the suitability of analytical and statistical sampling methods for making uncertainty analyses. The adjoint method is found to be well-suited for obtaining sensitivity coefficients for computer programs involving large numbers of equations and input parameters. For this purpose the Latin Hypercube Sampling method is found to be inferior to conventional experimental designs. The Latin hypercube method can be used to estimate output probability density functions, but requires supplementary rank transformations followed by stepwise regression to obtain uncertainty information on individual input parameters. A simple Cork and Bottle problem is used to illustrate the efficiency of the adjoint method relative to certain statistical sampling methods. For linear models of the form Ax=b it is shown that a complete adjoint sensitivity analysis can be made without formulating and solving the adjoint problem. This can be done either by using a special type of statistical sampling or by reformulating the primal problem and using suitable linear programming software.
Principles of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Landé, Alfred
2013-10-01
Preface; Introduction: 1. Observation and interpretation; 2. Difficulties of the classical theories; 3. The purpose of quantum theory; Part I. Elementary Theory of Observation (Principle of Complementarity): 4. Refraction in inhomogeneous media (force fields); 5. Scattering of charged rays; 6. Refraction and reflection at a plane; 7. Absolute values of momentum and wave length; 8. Double ray of matter diffracting light waves; 9. Double ray of matter diffracting photons; 10. Microscopic observation of ? (x) and ? (p); 11. Complementarity; 12. Mathematical relation between ? (x) and ? (p) for free particles; 13. General relation between ? (q) and ? (p); 14. Crystals; 15. Transition density and transition probability; 16. Resultant values of physical functions; matrix elements; 17. Pulsating density; 18. General relation between ? (t) and ? (?); 19. Transition density; matrix elements; Part II. The Principle of Uncertainty: 20. Optical observation of density in matter packets; 21. Distribution of momenta in matter packets; 22. Mathematical relation between ? and ?; 23. Causality; 24. Uncertainty; 25. Uncertainty due to optical observation; 26. Dissipation of matter packets; rays in Wilson Chamber; 27. Density maximum in time; 28. Uncertainty of energy and time; 29. Compton effect; 30. Bothe-Geiger and Compton-Simon experiments; 31. Doppler effect; Raman effect; 32. Elementary bundles of rays; 33. Jeans' number of degrees of freedom; 34. Uncertainty of electromagnetic field components; Part III. The Principle of Interference and Schrödinger's equation: 35. Physical functions; 36. Interference of probabilities for p and q; 37. General interference of probabilities; 38. Differential equations for ?p (q) and Xq (p); 39. Differential equation for ?? (q); 40. The general probability amplitude ??' (Q); 41. Point transformations; 42. General theorem of interference; 43. Conjugate variables; 44. Schrödinger's equation for conservative systems; 45. Schrödinger's equation for non-conservative systems; 46. Pertubation theory; 47. Orthogonality, normalization and Hermitian conjugacy; 48. General matrix elements; Part IV. The Principle of Correspondence: 49. Contact transformations in classical mechanics; 50. Point transformations; 51. Contact transformations in quantum mechanics; 52. Constants of motion and angular co-ordinates; 53. Periodic orbits; 54. De Broglie and Schrödinger function; correspondence to classical mechanics; 55. Packets of probability; 56. Correspondence to hydrodynamics; 57. Motion and scattering of wave packets; 58. Formal correspondence between classical and quantum mechanics; Part V. Mathematical Appendix: Principle of Invariance: 59. The general theorem of transformation; 60. Operator calculus; 61. Exchange relations; three criteria for conjugacy; 62. First method of canonical transformation; 63. Second method of canonical transformation; 64. Proof of the transformation theorem; 65. Invariance of the matrix elements against unitary transformations; 66. Matrix mechanics; Index of literature; Index of names and subjects.
Assessor Training Measurement Uncertainty
NVLAP Assessor Training Measurement Uncertainty #12;Assessor Training 2009: Measurement Uncertainty Training 2009: Measurement Uncertainty 3 Measurement Uncertainty Â·Calibration and testing labs performing Training 2009: Measurement Uncertainty 4 Measurement Uncertainty Â·When the nature of the test precludes
Brigitte Falkenburg
The correspondence principle is due to Niels Bohr (1885–1962). According to Bohr, the principle justifies the use of formal\\u000a classical expressions in quantum theory and a physical interpretation of quantum theory in terms of classical concepts. The\\u000a principle emerged from his use of classical concepts and formal analogies in ? Bohr's atomic model of 1913. Before the rise of quantum
NSDL National Science Digital Library
Jacobs, Julie
Design Principles for Interactive Texts is a fun-to-use interactive text on the effective design of interactive texts for education. It summarizes basic principles of interface design from studies in psychology, skills-training, education, art & design, and other sources, illustrating the principles with many examples. The text should be of interest to anyone designing presentations, computer-based reading materials, student computer labs, or educational Web sites.
NASA Astrophysics Data System (ADS)
Lamport, Leslie
2012-08-01
Buridan's principle asserts that a discrete decision based upon input having a continuous range of values cannot be made within a bounded length of time. It appears to be a fundamental law of nature. Engineers aware of it can design devices so they have an infinitessimal probability of not making a decision quickly enough. Ignorance of the principle could have serious consequences.
NSDL National Science Digital Library
Nave, Carl R.
This site from HyperPhysics provides a description of Pascal's Principle, which explains how pressure is transmitted in an enclosed fluid. Drawings and sample calculations are provided. Examples illustrating the principle include a hydraulic press and an automobile hydraulic lift.
ERIC Educational Resources Information Center
MacBeath, John; Swaffield, Sue; Frost, David
2009-01-01
This article provides an overview of the "Carpe Vitam: Leadership for Learning" project, accounting for its provenance and purposes, before focusing on the principles for practice that constitute an important part of the project's legacy. These principles framed the dialogic process that was a dominant feature of the project and are presented,…
Angular performance measure for tighter uncertainty relations
Hradil, Z.; Rehacek, J. [Department of Optics, Palacky University, 17. listopadu 50, 772 00 Olomouc (Czech Republic); Klimov, A. B. [Departamento de Fisica, Universidad de Guadalajara, 44420 Guadalajara, Jalisco (Mexico); Rigas, I.; Sanchez-Soto, L. L. [Departamento de Optica, Facultad de Fisica, Universidad Complutense, E-28040 Madrid (Spain)
2010-01-15
The uncertainty principle places a fundamental limit on the accuracy with which we can measure conjugate quantities. However, the fluctuations of these variables can be assessed in terms of different estimators. We propose an angular performance that allows for tighter uncertainty relations for angle and angular momentum. The differences with previous bounds can be significant for particular states and indeed may be amenable to experimental measurement with the present technology.
Messaging climate change uncertainty
NASA Astrophysics Data System (ADS)
Cooke, Roger M.
2015-01-01
Climate change is full of uncertainty and the messengers of climate science are not getting the uncertainty narrative right. To communicate uncertainty one must first understand it, and then avoid repeating the mistakes of the past.
NASA Astrophysics Data System (ADS)
Li, Qian; Cao, Huai-Xin; Du, Hong-Ke
2015-02-01
The uncertainty principle in quantum mechanics is a fundamental relation with different forms, including Heisenberg's uncertainty relation and Schrodinger's uncertainty relation. We discuss the generalized Wigner-Yanase correlation and the generalized covariance of operators and establish a generalization of Schrodinger's uncertainty relation expressed in terms of Wigner-Yanase information.
The physical origins of the uncertainty theorem
NASA Astrophysics Data System (ADS)
Giese, Albrecht
2013-10-01
The uncertainty principle is an important element of quantum mechanics. It deals with certain pairs of physical parameters which cannot be determined to an arbitrary level of precision at the same time. According to the so-called Copenhagen interpretation of quantum mechanics, this uncertainty is an intrinsic property of the physical world. - This paper intends to show that there are good reasons for adopting a different view. According to the author, the uncertainty is not a property of the physical world but rather a limitation of our knowledge about the actual state of a physical process. This view conforms to the quantum theory of Louis de Broglie and to Albert Einstein's interpretation.
Predicting radio occultation uncertainties
Withers, Paul
s Ignore variations in amplitude A Phase noise characterizes variations in f (Allan deviation) Thermal of one cycle For small /A, uncertainty in phase is therefore /A Hence uncertainty in phase is Uncertainty and f for the experimenter to influence #12;Venus (VEX) Ne uncertainty is predicted well, but neutral
Uncertainty Relation for Mutual Information
James Schneeloch; Curtis J. Broadbent; John C. Howell
2014-12-17
We postulate the existence of a universal uncertainty relation between the quantum and classical mutual informations between pairs of quantum systems. Specifically, we propose that the sum of the classical mutual information, determined by two mutually unbiased pairs of observables, never exceeds the quantum mutual information. We call this the complementary-quantum correlation (CQC) relation and prove its validity for pure states, for states with one maximally mixed subsystem, and for all states when one measurement is minimally disturbing. We provide results of a Monte Carlo simulation suggesting the CQC relation is generally valid. Importantly, we also show that the CQC relation represents an improvement to an entropic uncertainty principle in the presence of a quantum memory, and that it can be used to verify an achievable secret key rate in the quantum one-time pad cryptographic protocol.
Time Crystals from Minimum Time Uncertainty
Mir Faizal; Mohammed M. Khalil; Saurya Das
2014-12-29
Motivated by the Generalized Uncertainty Principle, covariance, and a minimum measurable time, we propose a deformation of the Heisenberg algebra, and show that this leads to corrections to all quantum mechanical systems. We also demonstrate that such a deformation implies a discrete spectrum for time. In other words, time behaves like a crystal.
Extended Uncertainty Relation and Rough Estimate of Cosmological Constant
Choong Sun Kim
2014-04-25
One brief idea on the extended uncertainty relation and the dynamical quantization of space-time at the Planck scale is presented. The extended uncertainty relation could be a guiding principle toward the renormalizable quantum gravity. Cosmological constant in the Universe as a quantum effect is also roughly estimated.
NSDL National Science Digital Library
Michael Horton
2009-05-30
In this lab, students will use a little background information about Bernoulli's principle to figure out how the spinning of a moving ball affects its trajectory. The activity is inquiry in that students will be discovering this relationship on their own.
NSDL National Science Digital Library
Integrated Teaching and Learning Program and Laboratory,
Bernoulli's principle relates the pressure of a fluid to its elevation and its speed. Bernoulli's equation can be used to approximate these parameters in water, air or any fluid that has very low viscosity. Students learn about the relationships between the components of the Bernoulli equation through real-life engineering examples and practice problems.
Cleghorn, R. A.
1965-01-01
There are four lines of development that might be called psychosomatic principles. The first represents the work initiated by Claude Bernard, Cannon, and others, in neurophysiology and endocrinology in relationship to stress. The second is the application of psychoanalytic formulations to the understanding of illness. The third is in the development of the social sciences, particularly anthropology, social psychology and sociology with respect to the emotional life of man, and, fourth, there is an increased application of epidemiological techniques to the understanding and incidence of disease and its causes. These principles can be applied to the concepts of comprehensive medicine and they bid fair to be unifying and helpful in its study. This means that future practitioners, as well as those working in the field of psychosomatic medicine, are going to have to have a much more precise knowledge of the influence of emotions on bodily processes. PMID:14259334
NASA Technical Reports Server (NTRS)
Sato, Toru
1989-01-01
Discussed here is a kind of radar called atmospheric radar, which has as its target clear air echoes from the earth's atmosphere produced by fluctuations of the atmospheric index of refraction. Topics reviewed include the vertical structure of the atmosphere, the radio refractive index and its fluctuations, the radar equation (a relation between transmitted and received power), radar equations for distributed targets and spectral echoes, near field correction, pulsed waveforms, the Doppler principle, and velocity field measurements.
Uncertainties in scientific measurements
Holden, N.E.
1986-11-16
Some examples of nuclear data in which the uncertainty has been underestimated, or at least appears to be underestimated, are reviewed. The subjective aspect of the problem of systematic uncertainties is discussed. Historical aspects of the data uncertainty problem are noted. 64 refs., 6 tabs.
Direct Aerosol Forcing Uncertainty
Mccomiskey, Allison
Understanding sources of uncertainty in aerosol direct radiative forcing (DRF), the difference in a given radiative flux component with and without aerosol, is essential to quantifying changes in Earth's radiation budget. We examine the uncertainty in DRF due to measurement uncertainty in the quantities on which it depends: aerosol optical depth, single scattering albedo, asymmetry parameter, solar geometry, and surface albedo. Direct radiative forcing at the top of the atmosphere and at the surface as well as sensitivities, the changes in DRF in response to unit changes in individual aerosol or surface properties, are calculated at three locations representing distinct aerosol types and radiative environments. The uncertainty in DRF associated with a given property is computed as the product of the sensitivity and typical measurement uncertainty in the respective aerosol or surface property. Sensitivity and uncertainty values permit estimation of total uncertainty in calculated DRF and identification of properties that most limit accuracy in estimating forcing. Total uncertainties in modeled local diurnally averaged forcing range from 0.2 to 1.3 W m-2 (42 to 20%) depending on location (from tropical to polar sites), solar zenith angle, surface reflectance, aerosol type, and aerosol optical depth. The largest contributor to total uncertainty in DRF is usually single scattering albedo; however decreasing measurement uncertainties for any property would increase accuracy in DRF. Comparison of two radiative transfer models suggests the contribution of modeling error is small compared to the total uncertainty although comparable to uncertainty arising from some individual properties.
Assessing Uncertainty in Intelligence
Jeffrey A. Friedman; Richard Zeckhauser
2012-01-01
This article addresses the challenge of managing uncertainty when producing estimative intelligence. Much of the theory and practice of estimative intelligence aims to eliminate or reduce uncertainty, but this is often impossible or infeasible. This article instead argues that the goal of estimative intelligence should be to assess uncertainty. By drawing on a body of nearly 400 declassified National Intelligence
Direct Aerosol Forcing Uncertainty
Mccomiskey, Allison
2008-01-15
Understanding sources of uncertainty in aerosol direct radiative forcing (DRF), the difference in a given radiative flux component with and without aerosol, is essential to quantifying changes in Earth's radiation budget. We examine the uncertainty in DRF due to measurement uncertainty in the quantities on which it depends: aerosol optical depth, single scattering albedo, asymmetry parameter, solar geometry, and surface albedo. Direct radiative forcing at the top of the atmosphere and at the surface as well as sensitivities, the changes in DRF in response to unit changes in individual aerosol or surface properties, are calculated at three locations representing distinct aerosol types and radiative environments. The uncertainty in DRF associated with a given property is computed as the product of the sensitivity and typical measurement uncertainty in the respective aerosol or surface property. Sensitivity and uncertainty values permit estimation of total uncertainty in calculated DRF and identification of properties that most limit accuracy in estimating forcing. Total uncertainties in modeled local diurnally averaged forcing range from 0.2 to 1.3 W m-2 (42 to 20%) depending on location (from tropical to polar sites), solar zenith angle, surface reflectance, aerosol type, and aerosol optical depth. The largest contributor to total uncertainty in DRF is usually single scattering albedo; however decreasing measurement uncertainties for any property would increase accuracy in DRF. Comparison of two radiative transfer models suggests the contribution of modeling error is small compared to the total uncertainty although comparable to uncertainty arising from some individual properties.
Position Uncertainty in the Heisenberg Uncertainty Relation
Seiji Kosugi
2010-02-26
Position measurements are examined under the assumption that object position x_t and probe position X_t just after the measurement are expressed by a linear combination of positions x_0 and X_0 just before the measurement. The Heisenberg uncertainty relation between the position uncertainty and momentum disturbance holds when the measurement error \\epsilon(x_t) for the object position x_t is adopted as the position uncertainty. However, the uncertainty in the measurement result obtained for x_0 is the standard deviation of the measurement result, and not the measurement error \\epsilon(x_0). This difference is due to the reduction of a wave packet. The validity of the linearity assumption is examined in detail.
Universal Uncertainty Relations
NASA Astrophysics Data System (ADS)
Friedland, Shmuel; Gheorghiu, Vlad; Gour, Gilad
2013-12-01
Uncertainty relations are a distinctive characteristic of quantum theory that impose intrinsic limitations on the precision with which physical properties can be simultaneously determined. The modern work on uncertainty relations employs entropic measures to quantify the lack of knowledge associated with measuring noncommuting observables. However, there is no fundamental reason for using entropies as quantifiers; any functional relation that characterizes the uncertainty of the measurement outcomes defines an uncertainty relation. Starting from a very reasonable assumption of invariance under mere relabeling of the measurement outcomes, we show that Schur-concave functions are the most general uncertainty quantifiers. We then discover a fine-grained uncertainty relation that is given in terms of the majorization order between two probability vectors, significantly extending a majorization-based uncertainty relation first introduced in M. H. Partovi, Phys. Rev. A 84, 052117 (2011). Such a vector-type uncertainty relation generates an infinite family of distinct scalar uncertainty relations via the application of arbitrary uncertainty quantifiers. Our relation is therefore universal and captures the essence of uncertainty in quantum theory.
Uncertainty in audiometer calibration
NASA Astrophysics Data System (ADS)
Aurélio Pedroso, Marcos; Gerges, Samir N. Y.; Gonçalves, Armando A., Jr.
2004-02-01
The objective of this work is to present a metrology study necessary for the accreditation of audiometer calibration procedures at the National Brazilian Institute of Metrology Standardization and Industrial Quality—INMETRO. A model for the calculation of measurement uncertainty was developed. Metrological aspects relating to audiometer calibration, traceability and measurement uncertainty were quantified through comparison between results obtained at the Industrial Noise Laboratory—LARI of the Federal University of Santa Catarina—UFSC and the Laboratory of Electric/acoustics—LAETA of INMETRO. Similar metrological performance of the measurement system used in both laboratories was obtained, indicating that the interlaboratory results are compatible with the expected values. The uncertainty calculation was based on the documents: EA-4/02 Expression of the Uncertainty of Measurement in Calibration (European Co-operation for Accreditation 1999 EA-4/02 p 79) and Guide to the Expression of Uncertainty in Measurement (International Organization for Standardization 1993 1st edn, corrected and reprinted in 1995, Geneva, Switzerland). Some sources of uncertainty were calculated theoretically (uncertainty type B) and other sources were measured experimentally (uncertainty type A). The global value of uncertainty calculated for the sound pressure levels (SPLs) is similar to that given by other calibration institutions. The results of uncertainty related to measurements of SPL were compared with the maximum uncertainties Umax given in the standard IEC 60645-1: 2001 (International Electrotechnical Commission 2001 IEC 60645-1 Electroacoustics—Audiological Equipment—Part 1:—Pure-Tone Audiometers).
Uncertainty and Cognitive Control
Mushtaq, Faisal; Bland, Amy R.; Schaefer, Alexandre
2011-01-01
A growing trend of neuroimaging, behavioral, and computational research has investigated the topic of outcome uncertainty in decision-making. Although evidence to date indicates that humans are very effective in learning to adapt to uncertain situations, the nature of the specific cognitive processes involved in the adaptation to uncertainty are still a matter of debate. In this article, we reviewed evidence suggesting that cognitive control processes are at the heart of uncertainty in decision-making contexts. Available evidence suggests that: (1) There is a strong conceptual overlap between the constructs of uncertainty and cognitive control; (2) There is a remarkable overlap between the neural networks associated with uncertainty and the brain networks subserving cognitive control; (3) The perception and estimation of uncertainty might play a key role in monitoring processes and the evaluation of the “need for control”; (4) Potential interactions between uncertainty and cognitive control might play a significant role in several affective disorders. PMID:22007181
Uncertainties in Gapped Graphene
Eylee Jung; Kwang S. Kim; DaeKil Park
2012-03-20
Motivated by graphene-based quantum computer we examine the time-dependence of the position-momentum and position-velocity uncertainties in the monolayer gapped graphene. The effect of the energy gap to the uncertainties is shown to appear via the Compton-like wavelength $\\lambda_c$. The uncertainties in the graphene are mainly contributed by two phenomena, spreading and zitterbewegung. While the former determines the uncertainties in the long-range of time, the latter gives the highly oscillation to the uncertainties in the short-range of time. The uncertainties in the graphene are compared with the corresponding values for the usual free Hamiltonian $\\hat{H}_{free} = (p_1^2 + p_2^2) / 2 M$. It is shown that the uncertainties can be under control within the quantum mechanical law if one can choose the gap parameter $\\lambda_c$ freely.
Physics and Operational Research: measure of uncertainty via Nonlinear Programming
NASA Astrophysics Data System (ADS)
Davizon-Castillo, Yasser A.
2008-03-01
Physics and Operational Research presents an interdisciplinary interaction in problems such as Quantum Mechanics, Classical Mechanics and Statistical Mechanics. The nonlinear nature of the physical phenomena in a single well and double well quantum systems is resolved via Nonlinear Programming (NLP) techniques (Kuhn-Tucker conditions, Dynamic Programming) subject to Heisenberg Uncertainty Principle and an extended equality uncertainty relation to exploit the NLP Lagrangian method. This review addresses problems in Kinematics and Thermal Physics developing uncertainty relations for each case of study, under a novel way to quantify uncertainty.
The Precautionary Principle in Environmental Science
David Kriebel; Joel Tickner; Paul Epstein; John Lemons; Richard Levins; Edward L. Loechler; Margaret Quinn; Ruthann Rudel; Ted Schettler; Michael Stoto
Environmental scientists play a key role in society's responses to environmental problems, and many of the studies they perform are intended ultimately to affect policy. The precautionary principle, pro- posed as a new guideline in environmental decision making, has four central components: taking pre- ventive action in the face of uncertainty; shifting the burden of proof to the proponents of
Adaptive framework for uncertainty analysis in electromagnetic field measurements.
Prieto, Javier; Alonso, Alonso A; de la Rosa, Ramón; Carrera, Albano
2015-04-01
Misinterpretation of uncertainty in the measurement of the electromagnetic field (EMF) strength may lead to an underestimation of exposure risk or an overestimation of required measurements. The Guide to the Expression of Uncertainty in Measurement (GUM) has internationally been adopted as a de facto standard for uncertainty assessment. However, analyses under such an approach commonly assume unrealistic static models or neglect relevant prior information, resulting in non-robust uncertainties. This study proposes a principled and systematic framework for uncertainty analysis that fuses information from current measurements and prior knowledge. Such a framework dynamically adapts to data by exploiting a likelihood function based on kernel mixtures and incorporates flexible choices of prior information by applying importance sampling. The validity of the proposed techniques is assessed from measurements performed with a broadband radiation meter and an isotropic field probe. The developed framework significantly outperforms GUM approach, achieving a reduction of 28 % in measurement uncertainty. PMID:25143178
MOUSE UNCERTAINTY ANALYSIS SYSTEM
The original MOUSE (Modular Oriented Uncertainty System) system was designed to deal with the problem of uncertainties in Environmental engineering calculations, such as a set of engineering cost or risk analysis equations. t was especially intended for use by individuals with li...
Electoral Knowledge and Uncertainty.
ERIC Educational Resources Information Center
Blood, R. Warwick; And Others
Research indicates that the media play a role in shaping the information that voters have about election options. Knowledge of those options has been related to actual vote, but has not been shown to be strongly related to uncertainty. Uncertainty, however, does seem to motivate voters to engage in communication activities, some of which may…
The Generalized Uncertainty Principle and Black Hole Remnants
Ronald J. Adler; Pisin Chen; David I. Santiago
2001-01-01
In the current standard viewpoint small black holes are believed to emit radiation as black bodies at the Hawking temperature, at least until they reach Planck size, after which their fate is open to conjecture. A cogent argument against the existence of remnants is that, since no evident quantum number prevents it, black holes should radiate completely away to photons
Uncertainty principle and minimal energy dissipation in the computer
Rolf Landauer
1982-01-01
Reversible computation is briefly reviewed, utilizing a refined version of the Bennett-Fredkin-Turing machine, invoked in an earlier paper. A dissipationless classical version of this machine, which has no internal frietion, and where the computational velocity is determined by the initial kinetic energy, is also described. Such a machine requires perfect parts and also requires the unrealisstic assumption that the many
The Heisenberg Uncertainty Principle Demonstrated with An Electron Diffraction Experiment
ERIC Educational Resources Information Center
Matteucci, Giorgio; Ferrari, Loris; Migliori, Andrea
2010-01-01
An experiment analogous to the classical diffraction of light from a circular aperture has been realized with electrons. The results are used to introduce undergraduate students to the wave behaviour of electrons. The diffraction fringes produced by the circular aperture are compared to those predicted by quantum mechanics and are exploited to…
An uncertainty principle for fermions with generalized kinetic energy
Ingrid Daubechies
1983-01-01
We derive semiclassical upper bounds for the number of bound states and the sum of negative eigenvalues of the one-particle Hamiltoniansh=f(?i?)+V(x) acting onL2(?n). These bounds are then used to derive a lower bound on the kinetic energy\\u000a
THE UNCERTAINTY PRINCIPLE ASSOCIATED WITH THE CONTINUOUS SHEARLET TRANSFORM
STEPHAN DAHLKE; GITTA KUTYNIOK; PETER MAASS; CHEN SAGIV; HANS-GEORG STARK; GERD TESCHKE
2008-01-01
Finding optimal representations of signals in higher dimensions, in particular directional representations, is currently the subject of intensive research. Since the classical wavelet transform does not provide precise directional information in the sense of resolving the wavefront set, several new representation systems were proposed in the past, including ridgelets, curvelets and, more recently, shearlets. In this paper we study and
Heisenberg uncertainty principle and economic analogues of basic physical quantities
Vladimir Soloviev; Vladimir Saptsin
2011-11-10
From positions, attained by modern theoretical physics in understanding of the universe bases, the methodological and philosophical analysis of fundamental physical concepts and their formal and informal connections with the real economic measurings is carried out. Procedures for heterogeneous economic time determination, normalized economic coordinates and economic mass are offered, based on the analysis of time series, the concept of economic Plank's constant has been proposed. The theory has been approved on the real economic dynamic's time series, including stock indices, Forex and spot prices, the achieved results are open for discussion.
A no-pure-boost uncertainty principle from spacetime noncommutativity
Giovanni Amelino-Camelia; Giulia Gubitosi; Antonino Marcianó; Pierre Martinetti; Flavio Mercati
2007-07-12
We study boost and space-rotation transformations in kappa-Minkowski noncommutative spacetime, using the techniques that some of us had previously developed (hep-th/0607221) for a description of translations in kappa-Minkowski, which in particular led to the introduction of translation transformation parameters that do not commute with the spacetime coordinates. We find a similar description of boosts and space rotations, which allows us to identify some associated conserved charges, but the form of the commutators between transformation parameters and spacetime coordinates is incompatible with the possibility of a pure boost.
Role of the precautionary principle in water recycling
A. I. Schäfera; S. Beder
2006-01-01
In an engineering context the precautionary principle is often perceived as an excuse to do nothing or a substantial barrier to technical progress. The precautionary principle requires that remedial measures be taken in situations of scientific uncertainty where evidence of harm cannot be proven but potential damage to human or environmental health is significant. In this paper the scope of
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.
Archimedes' Principle, Pascal's Law and Bernoulli's Principle
NSDL National Science Digital Library
2014-09-18
Students are introduced to Pascal's law, Archimedes' principle and Bernoulli's principle. Fundamental definitions, equations, practice problems and engineering applications are supplied. A PowerPoint® presentation, practice problems and grading rubric are provided.
ESTIMATING UNCERTAINTIES FOR GEOPHYSICAL
Kreinovich, Vladik
1 ESTIMATING UNCERTAINTIES FOR GEOPHYSICAL TOMOGRAPHY Diane I. Doser*, Kevin D. Crain*, Mark R. The inversion method uses the conjugate gradient technique, incorporating expert knowl- edge of data and model
ESTIMATING UNCERTAINTIES FOR GEOPHYSICAL
Kreinovich, Vladik
1 ESTIMATING UNCERTAINTIES FOR GEOPHYSICAL TOMOGRAPHY Diane I. Doser*, Kevin D. Crain*, Mark R. The inversion method uses the conjugate gradient technique, incorporating expert knowlÂ edge of data and model
Communicating scientific uncertainty
Fischhoff, Baruch; Davis, Alex L.
2014-01-01
All science has uncertainty. Unless that uncertainty is communicated effectively, decision makers may put too much or too little faith in it. The information that needs to be communicated depends on the decisions that people face. Are they (i) looking for a signal (e.g., whether to evacuate before a hurricane), (ii) choosing among fixed options (e.g., which medical treatment is best), or (iii) learning to create options (e.g., how to regulate nanotechnology)? We examine these three classes of decisions in terms of how to characterize, assess, and convey the uncertainties relevant to each. We then offer a protocol for summarizing the many possible sources of uncertainty in standard terms, designed to impose a minimal burden on scientists, while gradually educating those whose decisions depend on their work. Its goals are better decisions, better science, and better support for science. PMID:25225390
Communicating scientific uncertainty.
Fischhoff, Baruch; Davis, Alex L
2014-09-16
All science has uncertainty. Unless that uncertainty is communicated effectively, decision makers may put too much or too little faith in it. The information that needs to be communicated depends on the decisions that people face. Are they (i) looking for a signal (e.g., whether to evacuate before a hurricane), (ii) choosing among fixed options (e.g., which medical treatment is best), or (iii) learning to create options (e.g., how to regulate nanotechnology)? We examine these three classes of decisions in terms of how to characterize, assess, and convey the uncertainties relevant to each. We then offer a protocol for summarizing the many possible sources of uncertainty in standard terms, designed to impose a minimal burden on scientists, while gradually educating those whose decisions depend on their work. Its goals are better decisions, better science, and better support for science. PMID:25225390
Uncertainty: Medicine's Frequent Companion
... no means rare. Back to top The Elusive Gold Standard The "gold standard" is a concept commonly embraced by doctors — ... one or the other. The biopsy is the gold standard, and there is generally little uncertainty about ...
Evaluating prediction uncertainty
McKay, M.D. [Los Alamos National Lab., NM (United States)
1995-03-01
The probability distribution of a model prediction is presented as a proper basis for evaluating the uncertainty in a model prediction that arises from uncertainty in input values. Determination of important model inputs and subsets of inputs is made through comparison of the prediction distribution with conditional prediction probability distributions. Replicated Latin hypercube sampling and variance ratios are used in estimation of the distributions and in construction of importance indicators. The assumption of a linear relation between model output and inputs is not necessary for the indicators to be effective. A sequential methodology which includes an independent validation step is applied in two analysis applications to select subsets of input variables which are the dominant causes of uncertainty in the model predictions. Comparison with results from methods which assume linearity shows how those methods may fail. Finally, suggestions for treating structural uncertainty for submodels are presented.
Dasymetric Modeling and Uncertainty
Nagle, Nicholas N.; Buttenfield, Barbara P.; Leyk, Stefan; Speilman, Seth
2014-01-01
Dasymetric models increase the spatial resolution of population data by incorporating related ancillary data layers. The role of uncertainty in dasymetric modeling has not been fully addressed as of yet. Uncertainty is usually present because most population data are themselves uncertain, and/or the geographic processes that connect population and the ancillary data layers are not precisely known. A new dasymetric methodology - the Penalized Maximum Entropy Dasymetric Model (P-MEDM) - is presented that enables these sources of uncertainty to be represented and modeled. The P-MEDM propagates uncertainty through the model and yields fine-resolution population estimates with associated measures of uncertainty. This methodology contains a number of other benefits of theoretical and practical interest. In dasymetric modeling, researchers often struggle with identifying a relationship between population and ancillary data layers. The PEDM model simplifies this step by unifying how ancillary data are included. The P-MEDM also allows a rich array of data to be included, with disparate spatial resolutions, attribute resolutions, and uncertainties. While the P-MEDM does not necessarily produce more precise estimates than do existing approaches, it does help to unify how data enter the dasymetric model, it increases the types of data that may be used, and it allows geographers to characterize the quality of their dasymetric estimates. We present an application of the P-MEDM that includes household-level survey data combined with higher spatial resolution data such as from census tracts, block groups, and land cover classifications. PMID:25067846
Quantum Uncertainty Considerations for Gravitational Lens Interferometry
Laurance R. Doyle; David P. Carico
2008-12-19
The measurement of the gravitational lens delay time between light paths has relied, to date, on the source having sufficient variability to allow photometric variations from each path to be compared. However, the delay times of many gravitational lenses cannot be measured because the intrinsic source amplitude variations are too small to be detectable. At the fundamental quantum mechanical level, such photometric time stamps allow which-path knowledge, removing the ability to obtain an interference pattern. However, if the two paths can be made equal (zero time delay) then interference can occur. We describe an interferometric approach to measuring gravitational lens delay times using a quantum-eraser/restorer approach, whereby the time travel along the two paths may be rendered measurably equal. Energy and time being non-commuting observables, constraints on the photon energy in the energy-time uncertainty principle, via adjustments of the width of the radio bandpass, dictate the uncertainty of the time delay and therefore whether the path taken along one or the other gravitational lens geodesic is knowable. If one starts with interference, for example, which-path information returns when the bandpass is broadened (constraints on the energy are relaxed) to the point where the uncertainty principle allows a knowledge of the arrival time to better than the gravitational lens delay time itself, at which point the interference will disappear. We discuss the near-term feasibility of such measurements in light of current narrow-band radio detectors and known short time-delay gravitational lenses.
Network planning under uncertainties
NASA Astrophysics Data System (ADS)
Ho, Kwok Shing; Cheung, Kwok Wai
2008-11-01
One of the main focuses for network planning is on the optimization of network resources required to build a network under certain traffic demand projection. Traditionally, the inputs to this type of network planning problems are treated as deterministic. In reality, the varying traffic requirements and fluctuations in network resources can cause uncertainties in the decision models. The failure to include the uncertainties in the network design process can severely affect the feasibility and economics of the network. Therefore, it is essential to find a solution that can be insensitive to the uncertain conditions during the network planning process. As early as in the 1960's, a network planning problem with varying traffic requirements over time had been studied. Up to now, this kind of network planning problems is still being active researched, especially for the VPN network design. Another kind of network planning problems under uncertainties that has been studied actively in the past decade addresses the fluctuations in network resources. One such hotly pursued research topic is survivable network planning. It considers the design of a network under uncertainties brought by the fluctuations in topology to meet the requirement that the network remains intact up to a certain number of faults occurring anywhere in the network. Recently, the authors proposed a new planning methodology called Generalized Survivable Network that tackles the network design problem under both varying traffic requirements and fluctuations of topology. Although all the above network planning problems handle various kinds of uncertainties, it is hard to find a generic framework under more general uncertainty conditions that allows a more systematic way to solve the problems. With a unified framework, the seemingly diverse models and algorithms can be intimately related and possibly more insights and improvements can be brought out for solving the problem. This motivates us to seek a generic framework for solving the network planning problem under uncertainties. In addition to reviewing the various network planning problems involving uncertainties, we also propose that a unified framework based on robust optimization can be used to solve a rather large segment of network planning problem under uncertainties. Robust optimization is first introduced in the operations research literature and is a framework that incorporates information about the uncertainty sets for the parameters in the optimization model. Even though robust optimization is originated from tackling the uncertainty in the optimization process, it can serve as a comprehensive and suitable framework for tackling generic network planning problems under uncertainties. In this paper, we begin by explaining the main ideas behind the robust optimization approach. Then we demonstrate the capabilities of the proposed framework by giving out some examples of how the robust optimization framework can be applied to the current common network planning problems under uncertain environments. Next, we list some practical considerations for solving the network planning problem under uncertainties with the proposed framework. Finally, we conclude this article with some thoughts on the future directions for applying this framework to solve other network planning problems.
NASA Astrophysics Data System (ADS)
Jones, P. W.; Strelitz, R. A.
2012-12-01
The output of a simulation is best comprehended through the agency and methods of visualization, but a vital component of good science is knowledge of uncertainty. While great strides have been made in the quantification of uncertainty, especially in simulation, there is still a notable gap: there is no widely accepted means of simultaneously viewing the data and the associated uncertainty in one pane. Visualization saturates the screen, using the full range of color, shadow, opacity and tricks of perspective to display even a single variable. There is no room in the visualization expert's repertoire left for uncertainty. We present a method of visualizing uncertainty without sacrificing the clarity and power of the underlying visualization that works as well in 3-D and time-varying visualizations as it does in 2-D. At its heart, it relies on a principal tenet of continuum mechanics, replacing the notion of value at a point with a more diffuse notion of density as a measure of content in a region. First, the uncertainties calculated or tabulated at each point are transformed into a piecewise continuous field of uncertainty density . We next compute a weighted Voronoi tessellation of a user specified N convex polygonal/polyhedral cells such that each cell contains the same amount of uncertainty as defined by . The problem thus devolves into minimizing . Computation of such a spatial decomposition is O(N*N ), and can be computed iteratively making it possible to update easily over time as well as faster. The polygonal mesh does not interfere with the visualization of the data and can be easily toggled on or off. In this representation, a small cell implies a great concentration of uncertainty, and conversely. The content weighted polygons are identical to the cartogram familiar to the information visualization community in the depiction of things voting results per stat. Furthermore, one can dispense with the mesh or edges entirely to be replaced by symbols or glyphs at the generating points (effectively the center of the polygon). This methodology readily admits to rigorous statistical analysis using standard components found in R and thus entirely compatible with the visualization package we use (Visit and/or ParaView), the language we use (Python) and the UVCDAT environment that provides the programmer and analyst workbench. We will demonstrate the power and effectiveness of this methodology in climate studies. We will further argue that our method of defining (or predicting) values in a region has many advantages over the traditional visualization notion of value at a point.
Ragnar E. Löfstedt; Baruch Fischhoff; Ilya R. Fischhoff
2002-01-01
Precautionary principles have been proposed as a fundamental element of sound risk management. Their advocates see them as guiding action in the face of uncertainty, encouraging the adoption of measures that reduce serious risks to health, safety, and the environment. Their opponents may reject the very idea of precautionary principles, find specific principles unacceptably vague or see them as clearly
Uncertainty Analysis in Space Radiation Protection
NASA Technical Reports Server (NTRS)
Cucinotta, Francis A.
2011-01-01
Space radiation is comprised of high energy and charge (HZE) nuclei, protons, and secondary radiation including neutrons. The uncertainties in estimating the health risks from galactic cosmic rays (GCR) are a major limitation to the length of space missions, the evaluation of potential risk mitigation approaches, and application of the As Low As Reasonably Achievable (ALARA) principle. For long duration space missio ns, risks may approach radiation exposure limits, therefore the uncertainties in risk projections become a major safety concern and methodologies used for ground-based works are not deemed to be sufficient. NASA limits astronaut exposures to a 3% risk of exposure induced death (REID) and protects against uncertainties in risks projections using an assessment of 95% confidence intervals in the projection model. We discuss NASA s approach to space radiation uncertainty assessments and applications for the International Space Station (ISS) program and design studies of future missions to Mars and other destinations. Several features of NASA s approach will be discussed. Radiation quality descriptions are based on the properties of radiation tracks rather than LET with probability distribution functions (PDF) for uncertainties derived from radiobiology experiments at particle accelerators. The application of age and gender specific models for individual astronauts is described. Because more than 90% of astronauts are never-smokers, an alternative risk calculation for never-smokers is used and will be compared to estimates for an average U.S. population. Because of the high energies of the GCR limits the benefits of shielding and the limited role expected for pharmaceutical countermeasures, uncertainty reduction continues to be the optimal approach to improve radiation safety for space missions.
Principles and Methods Chromatography
Lebendiker, Mario
Edition AC 18-1022-29 Principles and Methods Affinity Chromatography #12;Antibody Purification-1142-75 Protein Purification Handbook 18-1132-29 Ion Exchange Chromatography Principles and Methods 18-1114-21 Affinity Chromatography Principles and Methods 18-1022-29 Hydrophobic Interaction Chromatography Principles
Measurement uncertainty relations
Busch, Paul, E-mail: paul.busch@york.ac.uk [Department of Mathematics, University of York, York (United Kingdom)] [Department of Mathematics, University of York, York (United Kingdom); Lahti, Pekka, E-mail: pekka.lahti@utu.fi [Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turku (Finland)] [Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turku (Finland); Werner, Reinhard F., E-mail: reinhard.werner@itp.uni-hannover.de [Institut für Theoretische Physik, Leibniz Universität, Hannover (Germany)
2014-04-15
Measurement uncertainty relations are quantitative bounds on the errors in an approximate joint measurement of two observables. They can be seen as a generalization of the error/disturbance tradeoff first discussed heuristically by Heisenberg. Here we prove such relations for the case of two canonically conjugate observables like position and momentum, and establish a close connection with the more familiar preparation uncertainty relations constraining the sharpness of the distributions of the two observables in the same state. Both sets of relations are generalized to means of order ? rather than the usual quadratic means, and we show that the optimal constants are the same for preparation and for measurement uncertainty. The constants are determined numerically and compared with some bounds in the literature. In both cases, the near-saturation of the inequalities entails that the state (resp. observable) is uniformly close to a minimizing one.
Asymmetric Uncertainty Expression for High Gradient Aerodynamics
NASA Technical Reports Server (NTRS)
Pinier, Jeremy T
2012-01-01
When the physics of the flow around an aircraft changes very abruptly either in time or space (e.g., flow separation/reattachment, boundary layer transition, unsteadiness, shocks, etc), the measurements that are performed in a simulated environment like a wind tunnel test or a computational simulation will most likely incorrectly predict the exact location of where (or when) the change in physics happens. There are many reasons for this, includ- ing the error introduced by simulating a real system at a smaller scale and at non-ideal conditions, or the error due to turbulence models in a computational simulation. The un- certainty analysis principles that have been developed and are being implemented today do not fully account for uncertainty in the knowledge of the location of abrupt physics changes or sharp gradients, leading to a potentially underestimated uncertainty in those areas. To address this problem, a new asymmetric aerodynamic uncertainty expression containing an extra term to account for a phase-uncertainty, the magnitude of which is emphasized in the high-gradient aerodynamic regions is proposed in this paper. Additionally, based on previous work, a method for dispersing aerodynamic data within asymmetric uncer- tainty bounds in a more realistic way has been developed for use within Monte Carlo-type analyses.
The propagation of uncertainty for humidity calculations
NASA Astrophysics Data System (ADS)
Lovell-Smith, J.
2009-12-01
This paper addresses the international humidity community's need for standardization of methods for propagation of uncertainty associated with humidity generators and for handling uncertainty associated with the reference water vapour-pressure and enhancement-factor equations. The paper outlines uncertainty calculations for the mixing ratio, dew-point temperature and relative humidity output from humidity generators, and in particular considers controlling equations for a theoretical hybrid humidity generator combining single-pressure (1-P), two-pressure (2-P) and two-flow (2-F) principles. Also considered is the case where the humidity generator is used as a stable source with traceability derived from a reference hygrometer, i.e. a dew-point meter, a relative humidity meter or a wet-bulb psychrometer. Most humidity generators in use at national metrology institutes can be considered to be special cases of those considered here and sensitivity coefficients for particular types may be extracted. The ability to account for correlations between input variables and between different instances of the evaluation of the reference equations is discussed. The uncertainty calculation examples presented here are representative of most humidity calculations.
Serenity in political uncertainty.
Doumit, Rita; Afifi, Rema A; Devon, Holli A
2015-01-01
College students are often faced with academic and personal stressors that threaten their well-being. Added to that may be political and environmental stressors such as acts of violence on the streets, interruptions in schooling, car bombings, targeted religious intimidations, financial hardship, and uncertainty of obtaining a job after graduation. Research on how college students adapt to the latter stressors is limited. The aims of this study were (1) to investigate the associations between stress, uncertainty, resilience, social support, withdrawal coping, and well-being for Lebanese youth during their first year of college and (2) to determine whether these variables predicted well-being. A sample of 293 first-year students enrolled in a private university in Lebanon completed a self-reported questionnaire in the classroom setting. The mean age of sample participants was 18.1 years, with nearly an equal percentage of males and females (53.2% vs 46.8%), who lived with their family (92.5%), and whose family reported high income levels (68.4%). Multiple regression analyses revealed that best determinants of well-being are resilience, uncertainty, social support, and gender that accounted for 54.1% of the variance. Despite living in an environment of frequent violence and political uncertainty, Lebanese youth in this study have a strong sense of well-being and are able to go on with their lives. This research adds to our understanding on how adolescents can adapt to stressors of frequent violence and political uncertainty. Further research is recommended to understand the mechanisms through which young people cope with political uncertainty and violence. PMID:25658930
Simple Resonance Hierarchy for Surmounting Quantum Uncertainty
Amoroso, Richard L. [Noetic Advanced Studies Institute, Oakland, CA 94610-1422 (United States)
2010-12-22
For a hundred years violation or surmounting the Quantum Uncertainty Principle has remained a Holy Grail of both theoretical and empirical physics. Utilizing an operationally completed form of Quantum Theory cast in a string theoretic Higher Dimensional (HD) form of Dirac covariant polarized vacuum with a complex Einstein energy dependent spacetime metric, M{sub 4{+-}}C{sub 4} with sufficient degrees of freedom to be causally free of the local quantum state, we present a simple empirical model for ontologically surmounting the phenomenology of uncertainty through a Sagnac Effect RF pulsed Laser Oscillated Vacuum Energy Resonance hierarchy cast within an extended form of a Wheeler-Feynman-Cramer Transactional Calabi-Yau mirror symmetric spacetime bachcloth.
Uncertainty quantification for Markov chain models.
Meidani, Hadi; Ghanem, Roger
2012-12-01
Transition probabilities serve to parameterize Markov chains and control their evolution and associated decisions and controls. Uncertainties in these parameters can be associated with inherent fluctuations in the medium through which a chain evolves, or with insufficient data such that the inferential value of the chain is jeopardized. The behavior of Markov chains associated with such uncertainties is described using a probabilistic model for the transition matrices. The principle of maximum entropy is used to characterize the probability measure of the transition rates. The formalism is demonstrated on a Markov chain describing the spread of disease, and a number of quantities of interest, pertaining to different aspects of decision-making, are investigated. PMID:23278037
[Stereotactic body radiation therapy: uncertainties and margins].
Lacornerie, T; Marchesi, V; Reynaert, N
2014-01-01
The principles governing stereotactic body radiation therapy are tight margins and large dose gradients around targets. Every step of treatment preparation and delivery must be evaluated before applying this technique in the clinic. Uncertainties remain in each of these steps: delineation, prescription with the biological equivalent dose, treatment planning, patient set-up taking into account movements, the machine accuracy. The calculation of margins to take into account uncertainties differs from conventional radiotherapy because of the delivery of few fractions and large dose gradients around the target. The quest of high accuracy is complicated by the difficulty to reach it and the lack of consensus regarding the prescription. Many schemes dose/number of fractions are described in clinical studies and there are differences in the way describing the delivered doses. While waiting for the ICRU report dedicated to this technique, it seems desirable to use the quantities proposed in ICRU Report 83 (IMRT) to report the dose distribution. PMID:25023588
Treatment of Data Uncertainties
Larson, N.M. [Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831-6171 (United States)
2005-05-24
The generation and use of data covariance matrices are discussed within the context of the analysis of neutron-induced cross-section data via the R-matrix code SAMMY. Two complementary approaches are described, the first involving mathematical manipulation of Bayes' equations and the second utilizing computer simulations. A new procedure for propagating uncertainties on unvaried parameters will allow the effect of all relevant experimental uncertainties to be reflected in the analysis results, without placing excessive additional burden on the analyst. Implementation of this procedure within SAMMY is described and illustrated through the simulations.
Orbital State Uncertainty Realism
NASA Astrophysics Data System (ADS)
Horwood, J.; Poore, A. B.
2012-09-01
Fundamental to the success of the space situational awareness (SSA) mission is the rigorous inclusion of uncertainty in the space surveillance network. The *proper characterization of uncertainty* in the orbital state of a space object is a common requirement to many SSA functions including tracking and data association, resolution of uncorrelated tracks (UCTs), conjunction analysis and probability of collision, sensor resource management, and anomaly detection. While tracking environments, such as air and missile defense, make extensive use of Gaussian and local linearity assumptions within algorithms for uncertainty management, space surveillance is inherently different due to long time gaps between updates, high misdetection rates, nonlinear and non-conservative dynamics, and non-Gaussian phenomena. The latter implies that "covariance realism" is not always sufficient. SSA also requires "uncertainty realism"; the proper characterization of both the state and covariance and all non-zero higher-order cumulants. In other words, a proper characterization of a space object's full state *probability density function (PDF)* is required. In order to provide a more statistically rigorous treatment of uncertainty in the space surveillance tracking environment and to better support the aforementioned SSA functions, a new class of multivariate PDFs are formulated which more accurately characterize the uncertainty of a space object's state or orbit. The new distribution contains a parameter set controlling the higher-order cumulants which gives the level sets a distinctive "banana" or "boomerang" shape and degenerates to a Gaussian in a suitable limit. Using the new class of PDFs within the general Bayesian nonlinear filter, the resulting filter prediction step (i.e., uncertainty propagation) is shown to have the *same computational cost as the traditional unscented Kalman filter* with the former able to maintain a proper characterization of the uncertainty for up to *ten times as long* as the latter. The filter correction step also furnishes a statistically rigorous *prediction error* which appears in the likelihood ratios for scoring the association of one report or observation to another. Thus, the new filter can be used to support multi-target tracking within a general multiple hypothesis tracking framework. Additionally, the new distribution admits a distance metric which extends the classical Mahalanobis distance (chi^2 statistic). This metric provides a test for statistical significance and facilitates single-frame data association methods with the potential to easily extend the covariance-based track association algorithm of Hill, Sabol, and Alfriend. The filtering, data fusion, and association methods using the new class of orbital state PDFs are shown to be mathematically tractable and operationally viable.
NASA Astrophysics Data System (ADS)
Silverman, Mark P.
2014-07-01
1. Tools of the trade; 2. The 'fundamental problem' of a practical physicist; 3. Mother of all randomness I: the random disintegration of matter; 4. Mother of all randomness II: the random creation of light; 5. A certain uncertainty; 6. Doing the numbers: nuclear physics and the stock market; 7. On target: uncertainties of projectile flight; 8. The guesses of groups; 9. The random flow of energy I: power to the people; 10. The random flow of energy II: warning from the weather underground; Index.
NASA Technical Reports Server (NTRS)
Brown, Laurie M.
1993-01-01
An historical account is given of the circumstances whereby the uncertainty relations were introduced into physics by Heisenberg. The criticisms of QED on measurement-theoretical grounds by Landau and Peierls are then discussed, as well as the response to them by Bohr and Rosenfeld. Finally, some examples are given of how the new freedom to advance radical proposals, in part the result of the revolution brought about by 'uncertainty,' was implemented in dealing with the new phenomena encountered in elementary particle physics in the 1930's.
Equivalence of wave-particle duality to entropic uncertainty
Patrick J. Coles; J?drzej Kaniewski; Stephanie Wehner
2014-09-16
Interferometers capture a basic mystery of quantum mechanics: a single particle can exhibit wave behavior, yet that wave behavior disappears when one tries to determine the particle's path inside the interferometer. This idea has been formulated quantitively as an inequality, e.g., by Englert and Jaeger, Shimony, and Vaidman, which upper bounds the sum of the interference visibility and the path distinguishability. Such wave-particle duality relations (WPDRs) are often thought to be conceptually inequivalent to Heisenberg's uncertainty principle, although this has been debated. Here we show that WPDRs correspond precisely to a modern formulation of the uncertainty principle in terms of entropies, namely the min- and max-entropies. This observation unifies two fundamental concepts in quantum mechanics. Furthermore, it leads to a robust framework for deriving novel WPDRs by applying entropic uncertainty relations to interferometric models. As an illustration, we derive a novel relation that captures the coherence in a quantum beam splitter.
Equivalence of wave-particle duality to entropic uncertainty.
Coles, Patrick J; Kaniewski, Jedrzej; Wehner, Stephanie
2014-01-01
Interferometers capture a basic mystery of quantum mechanics: a single particle can exhibit wave behaviour, yet that wave behaviour disappears when one tries to determine the particle's path inside the interferometer. This idea has been formulated quantitatively as an inequality, for example, by Englert and Jaeger, Shimony and Vaidman, which upper bounds the sum of the interference visibility and the path distinguishability. Such wave-particle duality relations (WPDRs) are often thought to be conceptually inequivalent to Heisenberg's uncertainty principle, although this has been debated. Here we show that WPDRs correspond precisely to a modern formulation of the uncertainty principle in terms of entropies, namely, the min- and max-entropies. This observation unifies two fundamental concepts in quantum mechanics. Furthermore, it leads to a robust framework for deriving novel WPDRs by applying entropic uncertainty relations to interferometric models. As an illustration, we derive a novel relation that captures the coherence in a quantum beam splitter. PMID:25524138
Equivalence of wave–particle duality to entropic uncertainty
NASA Astrophysics Data System (ADS)
Coles, Patrick J.; Kaniewski, Jedrzej; Wehner, Stephanie
2014-12-01
Interferometers capture a basic mystery of quantum mechanics: a single particle can exhibit wave behaviour, yet that wave behaviour disappears when one tries to determine the particle’s path inside the interferometer. This idea has been formulated quantitatively as an inequality, for example, by Englert and Jaeger, Shimony and Vaidman, which upper bounds the sum of the interference visibility and the path distinguishability. Such wave–particle duality relations (WPDRs) are often thought to be conceptually inequivalent to Heisenberg’s uncertainty principle, although this has been debated. Here we show that WPDRs correspond precisely to a modern formulation of the uncertainty principle in terms of entropies, namely, the min- and max-entropies. This observation unifies two fundamental concepts in quantum mechanics. Furthermore, it leads to a robust framework for deriving novel WPDRs by applying entropic uncertainty relations to interferometric models. As an illustration, we derive a novel relation that captures the coherence in a quantum beam splitter.
Mass Uncertainty and Application For Space Systems
NASA Technical Reports Server (NTRS)
Beech, Geoffrey
2013-01-01
Expected development maturity under contract (spec) should correlate with Project/Program Approved MGA Depletion Schedule in Mass Properties Control Plan. If specification NTE, MGA is inclusive of Actual MGA (A5 & A6). If specification is not an NTE Actual MGA (e.g. nominal), then MGA values are reduced by A5 values and A5 is representative of remaining uncertainty. Basic Mass = Engineering Estimate based on design and construction principles with NO embedded margin MGA Mass = Basic Mass * assessed % from approved MGA schedule. Predicted Mass = Basic + MGA. Aggregate MGA % = (Aggregate Predicted - Aggregate Basic) /Aggregate Basic.
Multiresolutional models of uncertainty generation and reduction
NASA Technical Reports Server (NTRS)
Meystel, A.
1989-01-01
Kolmogorov's axiomatic principles of the probability theory, are reconsidered in the scope of their applicability to the processes of knowledge acquisition and interpretation. The model of uncertainty generation is modified in order to reflect the reality of engineering problems, particularly in the area of intelligent control. This model implies algorithms of learning which are organized in three groups which reflect the degree of conceptualization of the knowledge the system is dealing with. It is essential that these algorithms are motivated by and consistent with the multiresolutional model of knowledge representation which is reflected in the structure of models and the algorithms of learning.
Risk, uncertainty and knowledge
Andy Alaszewski; Patrick Brown
2007-01-01
While the development of modern medicine is associated with both increases in scientific knowledge and improved outcomes in health care it is also associated with increased uncertainty as expert and lay knowledge bases have diverged and separated. The development of a principal-agent relationship in the late nineteenth and early twentieth century in which medical practitioners used their specialist knowledge to
Uncertainty Analysis Economic Evaluations
Bhulai, Sandjai
is the calculated profitability? What if the costs overrun during implementation of the project? What the influence of these uncertainties on the economic indicators. Economic evaluations in the oil industry (most likely) set of parameters. Usually some parameters, such as project costs or reserves, are varied
Identity Uncertainty Stuart Russell
Russell, Stuart
Identity Uncertainty Stuart Russell Computer Science Division University of California, Berkeley, CA 94720, USA russell@cs.berkeley.edu Abstract We are often uncertain about the identity of objects probabilis- tic approach to reasoning about identity under uncer- tainty in the framework of first
Uncertainties in repository modeling
Wilson, J.R.
1996-12-31
The distant future is ver difficult to predict. Unfortunately, our regulators are being enchouraged to extend ther regulatory period form the standard 10,000 years to 1 million years. Such overconfidence is not justified due to uncertainties in dating, calibration, and modeling.
MRST partons and uncertainties
A. D. Martin; R. G. Roberts; W. J. Stirling; R. S. Thorne
2003-01-01
We discuss uncertainties in the extraction of parton distributions from global analyses of DIS and related data. We present conservative sets of partons, at both NLO and NNLO, which are stable to x,Q^2,W^2 cuts on the data. We give the corresponding values of alpha(M_Z^2) and the cross sections for W production at the Tevatron.
Project management under uncertainty
R. M. Skitmore; S. G. Stradling; A. P. Tuohy
1989-01-01
Morris' (1986) analysis of the factors affecting project success and failure is considered in relation to the psychology of judgement under uncertainty. A model is proposed whereby project managers may identify the specific circumstances in which human decision-making is prone to systematic error, and hence may apply a number of de-biasing techniques.
Position-momentum uncertainty relations based on moments of arbitrary order
Zozor, Steeve [Laboratoire Grenoblois d'Image, Parole, Signal et Automatique (GIPSA-Lab, CNRS), 961 rue de la Houille Blanche, F-38402 Saint Martin d'Heres (France); Portesi, Mariela [Instituto de Fisica La Plata (CONICET), and Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, 1900 La Plata (Argentina); Sanchez-Moreno, Pablo [Instituto Carlos I de Fisica Teorica y Computacional, Universidad de Granada, E-18071 Granada (Spain); Departamento de Matematica Aplicada, Universidad de Granada, E-18071 Granada (Spain); Dehesa, Jesus S. [Instituto Carlos I de Fisica Teorica y Computacional, Universidad de Granada, E-18071 Granada (Spain); Departamento de Fisica Atomica, Molecular y Nuclear, Universidad de Granada, E-18071 Granada (Spain)
2011-05-15
The position-momentum uncertainty-like inequality based on moments of arbitrary order for d-dimensional quantum systems, which is a generalization of the celebrated Heisenberg formulation of the uncertainty principle, is improved here by use of the Renyi-entropy-based uncertainty relation. The accuracy of the resulting lower bound is physico-computationally analyzed for the two main prototypes in d-dimensional physics: the hydrogenic and oscillator-like systems.
Chemical Principls Exemplified
ERIC Educational Resources Information Center
Plumb, Robert C.
1973-01-01
Two topics are discussed: (1) Stomach Upset Caused by Aspirin, illustrating principles of acid-base equilibrium and solubility; (2) Physical Chemistry of the Drinking Duck, illustrating principles of phase equilibria and thermodynamics. (DF)
NASA Astrophysics Data System (ADS)
Massimi, Michela
2012-10-01
1. The exclusion principle: a philosophical overview; 2. The origins of the exclusion principle: an extremely natural prescriptive rule; 3. From the old quantum theory to the new quantum theory: reconsidering Kuhn's incommensurability; 4. How Pauli's rule became the exclusion principle: from the Fermi-Dirac statistics to the spin-statistics theorem; 5. The exclusion principle opens up new avenues: from the eightfold way to quantum chromodynamics.
Anthropic principle in cosmology
Brandon Carter
2006-06-27
A brief explanation of the meaning of the anthropic principle - as a prescription for the attribution of a priori probability weighting - is illustrated by various cosmological and local applications, in which the relevant conclusions are contrasted with those that could be obtained from (less plausible) alternative prescriptions such as the vaguer and less restrictive ubiquity principle, or the more sterile and restrictive autocentric principle.
ERIC Educational Resources Information Center
Beim, George
This book is written to give a better understanding of the principles of modern soccer to coaches and players. In nine chapters the following elements of the game are covered: (1) the development of systems; (2) the principles of attack; (3) the principles of defense; (4) training games; (5) strategies employed in restarts; (6) physical fitness…
Reconsidering Archimedes' Principle
Jeffrey Bierman; Eric Kincanon
2003-01-01
Archimedes' principle as stated originally by Archimedes and in modern texts can lead to an incorrect prediction if the submerged object is in contact with a solid surface. In this paper we look experimentally at a submerged object and show that though the theoretical explanations of the principle are valid, the statement of the principle needs clarification.
Chemical Principles Exemplified
ERIC Educational Resources Information Center
Plumb, Robert C.
1970-01-01
This is the first of a new series of brief ancedotes about materials and phenomena which exemplify chemical principles. Examples include (1) the sea-lab experiment illustrating principles of the kinetic theory of gases, (2) snow-making machines illustrating principles of thermodynamics in gas expansions and phase changes, and (3) sunglasses that…
MRST partons and uncertainties
A. D. Martin; R. G. Roberts; W. J. Stirling; R. S. Thorne
2003-01-01
We discuss uncertainties in the extraction of parton distributions from\\u000aglobal analyses of DIS and related data. We present conservative sets of\\u000apartons, at both NLO and NNLO, which are stable to x,Q^2,W^2 cuts on the data.\\u000aWe give the corresponding values of alpha(M_Z^2) and the cross sections for W\\u000aproduction at the Tevatron.
Predicting System Performance with Uncertainty
Yan, B.; Malkawi, A.
2012-01-01
The main purpose of this research is to include uncertainty that lies in modeling process and that arises from input values when predicting system performance, and to incorporate uncertainty related to system controls in a computationally...
Essays on uncertainty in economics
Simsek, Alp
2010-01-01
This thesis consists of four essays about "uncertainty" and how markets deal with it. Uncertainty is about subjective beliefs, and thus it often comes with heterogeneous beliefs that may be present temporarily or even ...
Uncertainties in parton distribution functions
A. D. Martin; R. G. Roberts; W. J. Stirling; R. S. Thorne
2000-01-01
We discuss the uncertainty in the predictions for hard scattering cross sections at hadron colliders due to uncertainties in the input parton distributions, using W production at the LHC as an example.
Calibration Under Uncertainty.
Swiler, Laura Painton; Trucano, Timothy Guy
2005-03-01
This report is a white paper summarizing the literature and different approaches to the problem of calibrating computer model parameters in the face of model uncertainty. Model calibration is often formulated as finding the parameters that minimize the squared difference between the model-computed data (the predicted data) and the actual experimental data. This approach does not allow for explicit treatment of uncertainty or error in the model itself: the model is considered the %22true%22 deterministic representation of reality. While this approach does have utility, it is far from an accurate mathematical treatment of the true model calibration problem in which both the computed data and experimental data have error bars. This year, we examined methods to perform calibration accounting for the error in both the computer model and the data, as well as improving our understanding of its meaning for model predictability. We call this approach Calibration under Uncertainty (CUU). This talk presents our current thinking on CUU. We outline some current approaches in the literature, and discuss the Bayesian approach to CUU in detail.
Deterministic uncertainty analysis
Worley, B.A.
1987-12-01
This paper presents a deterministic uncertainty analysis (DUA) method for calculating uncertainties that has the potential to significantly reduce the number of computer runs compared to conventional statistical analysis. The method is based upon the availability of derivative and sensitivity data such as that calculated using the well known direct or adjoint sensitivity analysis techniques. Formation of response surfaces using derivative data and the propagation of input probability distributions are discussed relative to their role in the DUA method. A sample problem that models the flow of water through a borehole is used as a basis to compare the cumulative distribution function of the flow rate as calculated by the standard statistical methods and the DUA method. Propogation of uncertainties by the DUA method is compared for ten cases in which the number of reference model runs was varied from one to ten. The DUA method gives a more accurate representation of the true cumulative distribution of the flow rate based upon as few as two model executions compared to fifty model executions using a statistical approach. 16 refs., 4 figs., 5 tabs.
FLIR ATR using location uncertainty
Gang Liu; Robert M. Haralick
2000-01-01
A model-based FLIR ATR algorithm is described. It utilizes boundary contrast for target detection and recognition. Boundary contrast is related to the location uncertainty at target boundary points. A polygon model is used for deriving target centroid location uncertainty caused by the boundary point location uncertainty. The significance of the work lies in the sound mathematical models used in deriving
Calculating efficiencies and their uncertainties
Paterno, Marc; /Fermilab
2004-12-01
The commonly used methods for the calculation of the statistical uncertainties in cut efficiencies (''Poisson'' and ''binomial'' errors) are both defective, as is seen in extreme cases. A method for the calculation of uncertainties based upon Bayes' Theorem is presented; this method has no problem with extreme cases. A program for the calculation of such uncertainties is also available.
Using Models that Incorporate Uncertainty
ERIC Educational Resources Information Center
Caulkins, Jonathan P.
2002-01-01
In this article, the author discusses the use in policy analysis of models that incorporate uncertainty. He believes that all models should consider incorporating uncertainty, but that at the same time it is important to understand that sampling variability is not usually the dominant driver of uncertainty in policy analyses. He also argues that…
Uncertainty relations as Hilbert space geometry
NASA Technical Reports Server (NTRS)
Braunstein, Samuel L.
1994-01-01
Precision measurements involve the accurate determination of parameters through repeated measurements of identically prepared experimental setups. For many parameters there is a 'natural' choice for the quantum observable which is expected to give optimal information; and from this observable one can construct an Heinsenberg uncertainty principle (HUP) bound on the precision attainable for the parameter. However, the classical statistics of multiple sampling directly gives us tools to construct bounds for the precision available for the parameters of interest (even when no obvious natural quantum observable exists, such as for phase, or time); it is found that these direct bounds are more restrictive than those of the HUP. The implication is that the natural quantum observables typically do not encode the optimal information (even for observables such as position, and momentum); we show how this can be understood simply in terms of the Hilbert space geometry. Another striking feature of these bounds to parameter uncertainty is that for a large enough number of repetitions of the measurements all V quantum states are 'minimum uncertainty' states - not just Gaussian wave-packets. Thus, these bounds tell us what precision is achievable as well as merely what is allowed.
Uncertainties in risk assessment at USDOE facilities
Hamilton, L.D.; Holtzman, S.; Meinhold, A.F.; Morris, S.C.; Rowe, M.D.
1994-01-01
The United States Department of Energy (USDOE) has embarked on an ambitious program to remediate environmental contamination at its facilities. Decisions concerning cleanup goals, choices among cleanup technologies, and funding prioritization should be largely risk-based. Risk assessments will be used more extensively by the USDOE in the future. USDOE needs to develop and refine risk assessment methods and fund research to reduce major sources of uncertainty in risk assessments at USDOE facilities. The terms{open_quote} risk assessment{close_quote} and{open_quote} risk management{close_quote} are frequently confused. The National Research Council (1983) and the United States Environmental Protection Agency (USEPA, 1991a) described risk assessment as a scientific process that contributes to risk management. Risk assessment is the process of collecting, analyzing and integrating data and information to identify hazards, assess exposures and dose responses, and characterize risks. Risk characterization must include a clear presentation of {open_quotes}... the most significant data and uncertainties...{close_quotes} in an assessment. Significant data and uncertainties are {open_quotes}...those that define and explain the main risk conclusions{close_quotes}. Risk management integrates risk assessment information with other considerations, such as risk perceptions, socioeconomic and political factors, and statutes, to make and justify decisions. Risk assessments, as scientific processes, should be made independently of the other aspects of risk management (USEPA, 1991a), but current methods for assessing health risks are based on conservative regulatory principles, causing unnecessary public concern and misallocation of funds for remediation.
Improvement of Statistical Decisions under Parametric Uncertainty
NASA Astrophysics Data System (ADS)
Nechval, Nicholas A.; Nechval, Konstantin N.; Purgailis, Maris; Berzins, Gundars; Rozevskis, Uldis
2011-10-01
A large number of problems in production planning and scheduling, location, transportation, finance, and engineering design require that decisions be made in the presence of uncertainty. Decision-making under uncertainty is a central problem in statistical inference, and has been formally studied in virtually all approaches to inference. The aim of the present paper is to show how the invariant embedding technique, the idea of which belongs to the authors, may be employed in the particular case of finding the improved statistical decisions under parametric uncertainty. This technique represents a simple and computationally attractive statistical method based on the constructive use of the invariance principle in mathematical statistics. Unlike the Bayesian approach, an invariant embedding technique is independent of the choice of priors. It allows one to eliminate unknown parameters from the problem and to find the best invariant decision rule, which has smaller risk than any of the well-known decision rules. To illustrate the proposed technique, application examples are given.
Direct Tests of Measurement Uncertainty Relations: What It Takes
NASA Astrophysics Data System (ADS)
Busch, Paul; Stevens, Neil
2015-02-01
The uncertainty principle being a cornerstone of quantum mechanics, it is surprising that, in nearly 90 years, there have been no direct tests of measurement uncertainty relations. This lacuna was due to the absence of two essential ingredients: appropriate measures of measurement error (and disturbance) and precise formulations of such relations that are universally valid and directly testable. We formulate two distinct forms of direct tests, based on different measures of error. We present a prototype protocol for a direct test of measurement uncertainty relations in terms of value deviation errors (hitherto considered nonfeasible), highlighting the lack of universality of these relations. This shows that the formulation of universal, directly testable measurement uncertainty relations for state-dependent error measures remains an important open problem. Recent experiments that were claimed to constitute invalidations of Heisenberg's error-disturbance relation, are shown to conform with the spirit of Heisenberg's principle if interpreted as direct tests of measurement uncertainty relations for error measures that quantify distances between observables.
Direct tests of measurement uncertainty relations: what it takes.
Busch, Paul; Stevens, Neil
2015-02-20
The uncertainty principle being a cornerstone of quantum mechanics, it is surprising that, in nearly 90 years, there have been no direct tests of measurement uncertainty relations. This lacuna was due to the absence of two essential ingredients: appropriate measures of measurement error (and disturbance) and precise formulations of such relations that are universally valid and directly testable. We formulate two distinct forms of direct tests, based on different measures of error. We present a prototype protocol for a direct test of measurement uncertainty relations in terms of value deviation errors (hitherto considered nonfeasible), highlighting the lack of universality of these relations. This shows that the formulation of universal, directly testable measurement uncertainty relations for state-dependent error measures remains an important open problem. Recent experiments that were claimed to constitute invalidations of Heisenberg's error-disturbance relation, are shown to conform with the spirit of Heisenberg's principle if interpreted as direct tests of measurement uncertainty relations for error measures that quantify distances between observables. PMID:25763941
Ashford, Nicholas
2005-01-01
The precautionary principle is in sharp political focus today because (1) the nature of scientific uncertainty is changing and (2) there is increasing pressure to base governmental action on allegedly more "rational" ...
Picturing Data With Uncertainty
NASA Technical Reports Server (NTRS)
Kao, David; Love, Alison; Dungan, Jennifer L.; Pang, Alex
2004-01-01
NASA is in the business of creating maps for scientific purposes to represent important biophysical or geophysical quantities over space and time. For example, maps of surface temperature over the globe tell scientists where and when the Earth is heating up; regional maps of the greenness of vegetation tell scientists where and when plants are photosynthesizing. There is always uncertainty associated with each value in any such map due to various factors. When uncertainty is fully modeled, instead of a single value at each map location, there is a distribution expressing a set of possible outcomes at each location. We consider such distribution data as multi-valued data since it consists of a collection of values about a single variable. Thus, a multi-valued data represents both the map and its uncertainty. We have been working on ways to visualize spatial multi-valued data sets effectively for fields with regularly spaced units or grid cells such as those in NASA's Earth science applications. A new way to display distributions at multiple grid locations is to project the distributions from an individual row, column or other user-selectable straight transect from the 2D domain. First at each grid cell in a given slice (row, column or transect), we compute a smooth density estimate from the underlying data. Such a density estimate for the probability density function (PDF) is generally more useful than a histogram, which is a classic density estimate. Then, the collection of PDFs along a given slice are presented vertically above the slice and form a wall. To minimize occlusion of intersecting slices, the corresponding walls are positioned at the far edges of the boundary. The PDF wall depicts the shapes of the distributions very dearly since peaks represent the modes (or bumps) in the PDFs. We've defined roughness as the number of peaks in the distribution. Roughness is another useful summary information for multimodal distributions. The uncertainty of the multi-valued data can also be interpreted by the number of peaks and the widths of the peaks as shown by the PDF walls.
Uncertainty quantification in lattice QCD calculations for nuclear physics
NASA Astrophysics Data System (ADS)
Beane, Silas R.; Detmold, William; Orginos, Kostas; Savage, Martin J.
2015-03-01
The numerical technique of lattice quantum chromodynamics (LQCD) holds the promise of connecting the nuclear forces, nuclei, the spectrum and structure of hadrons, and the properties of matter under extreme conditions with the underlying theory of the strong interactions, quantum chromodynamics. A distinguishing, and thus far unique, feature of this formulation is that all of the associated uncertainties, both statistical and systematic can, in principle, be systematically reduced to any desired precision with sufficient computational and human resources. We review the sources of uncertainty inherent in LQCD calculations for nuclear physics, and discuss how each is quantified in current efforts.
Uncertainty Quantification in Lattice QCD Calculations for Nuclear Physics
Silas R. Beane; William Detmold; Kostas Orginos; Martin J. Savage
2014-10-11
The numerical technique of Lattice QCD holds the promise of connecting the nuclear forces, nuclei, the spectrum and structure of hadrons, and the properties of matter under extreme conditions with the underlying theory of the strong interactions, quantum chromodynamics. A distinguishing, and thus far unique, feature of this formulation is that all of the associated uncertainties, both statistical and systematic can, in principle, be systematically reduced to any desired precision with sufficient computational and human resources. We review the sources of uncertainty inherent in Lattice QCD calculations for nuclear physics, and discuss how each is quantified in current efforts.
Uncertainty in adaptive capacity
NASA Astrophysics Data System (ADS)
Adger, W. Neil; Vincent, Katharine
2005-03-01
The capacity to adapt is a critical element of the process of adaptation: it is the vector of resources that represent the asset base from which adaptation actions can be made. Adaptive capacity can in theory be identified and measured at various scales, from the individual to the nation. The assessment of uncertainty within such measures comes from the contested knowledge domain and theories surrounding the nature of the determinants of adaptive capacity and the human action of adaptation. While generic adaptive capacity at the national level, for example, is often postulated as being dependent on health, governance and political rights, and literacy, and economic well-being, the determinants of these variables at national levels are not widely understood. We outline the nature of this uncertainty for the major elements of adaptive capacity and illustrate these issues with the example of a social vulnerability index for countries in Africa. To cite this article: W.N. Adger, K. Vincent, C. R. Geoscience 337 (2005).
Antarctic Photochemistry: Uncertainty Analysis
NASA Technical Reports Server (NTRS)
Stewart, Richard W.; McConnell, Joseph R.
1999-01-01
Understanding the photochemistry of the Antarctic region is important for several reasons. Analysis of ice cores provides historical information on several species such as hydrogen peroxide and sulfur-bearing compounds. The former can potentially provide information on the history of oxidants in the troposphere and the latter may shed light on DMS-climate relationships. Extracting such information requires that we be able to model the photochemistry of the Antarctic troposphere and relate atmospheric concentrations to deposition rates and sequestration in the polar ice. This paper deals with one aspect of the uncertainty inherent in photochemical models of the high latitude troposphere: that arising from imprecision in the kinetic data used in the calculations. Such uncertainties in Antarctic models tend to be larger than those in models of mid to low latitude clean air. One reason is the lower temperatures which result in increased imprecision in kinetic data, assumed to be best characterized at 298K. Another is the inclusion of a DMS oxidation scheme in the present model. Many of the rates in this scheme are less precisely known than are rates in the standard chemistry used in many stratospheric and tropospheric models.
Probabilistic Mass Growth Uncertainties
NASA Technical Reports Server (NTRS)
Plumer, Eric; Elliott, Darren
2013-01-01
Mass has been widely used as a variable input parameter for Cost Estimating Relationships (CER) for space systems. As these space systems progress from early concept studies and drawing boards to the launch pad, their masses tend to grow substantially, hence adversely affecting a primary input to most modeling CERs. Modeling and predicting mass uncertainty, based on historical and analogous data, is therefore critical and is an integral part of modeling cost risk. This paper presents the results of a NASA on-going effort to publish mass growth datasheet for adjusting single-point Technical Baseline Estimates (TBE) of masses of space instruments as well as spacecraft, for both earth orbiting and deep space missions at various stages of a project's lifecycle. This paper will also discusses the long term strategy of NASA Headquarters in publishing similar results, using a variety of cost driving metrics, on an annual basis. This paper provides quantitative results that show decreasing mass growth uncertainties as mass estimate maturity increases. This paper's analysis is based on historical data obtained from the NASA Cost Analysis Data Requirements (CADRe) database.
Managing Uncertainty in Data and Models: UncertWeb
NASA Astrophysics Data System (ADS)
Nativi, S.; Cornford, D.; Pebesma, E. J.
2010-12-01
There is an increasing recognition that issues of quality, error and uncertainty are central concepts to both scientific progress and practical decision making. Recent moves towards evidence driven policy and complex, uncertain scientific investigations into climate change and its likely impacts have heightened the awareness that uncertainty is critical in linking our observations and models to reality. The most natural, principled framework is provided by Bayesian approaches, which recognise a variety of sources of uncertainty such as aleatory (variability), epistemic (lack of knowledge) and possibly ontological (lack of agreed definitions). Most current information models used in the geosciences do not fully support the communication of uncertain results, although some do provide limited support for quality information in metadata. With the UncertWeb project (http://www.uncertweb.org), involving statisticians, geospatial and application scientists and informaticians we are developing a framework for representing and communicating uncertainty in observational data and models which builds on existing standards such as the Observations and Measurements conceptual model, and related Open Geospatial Consortium and ISO standards to allow the communication and propagation of uncertainty in chains of model services. A key component is the description of uncertainties in observational data, based on a revised version of UncertML, a conceptual model and encoding for representing uncertain quantities. In this talk we will describe how we envisage using UncertML with existing standards to describe the uncertainty in observational data and how this uncertainty information can then be propagated through subsequent analysis. We will highlight some of the tools which we are developing within UncertWeb to support the management of uncertainty in web based geoscientific applications.
Group environmental preference aggregation: the principle of environmental justice
Davos, C.A.
1986-01-01
The aggregation of group environmental preference presents a challenge of principle that has not, as yet, been satisfactorily met. One such principle, referred to as an environmental justice, is established based on a concept of social justice and axioms for rational choice under uncertainty. It requires that individual environmental choices be so decided that their supporters will least mind being anyone at random in the new environment. The application of the principle is also discussed. Its only information requirement is a ranking of alternative choices by each interested party. 25 references.
Uncertainty relation in Schwarzschild spacetime
NASA Astrophysics Data System (ADS)
Feng, Jun; Zhang, Yao-Zhong; Gould, Mark D.; Fan, Heng
2015-04-01
We explore the entropic uncertainty relation in the curved background outside a Schwarzschild black hole, and find that Hawking radiation introduces a nontrivial modification on the uncertainty bound for particular observer, therefore it could be witnessed by proper uncertainty game experimentally. We first investigate an uncertainty game between a free falling observer and his static partner holding a quantum memory initially entangled with the quantum system to be measured. Due to the information loss from Hawking decoherence, we find an inevitable increase of the uncertainty on the outcome of measurements in the view of static observer, which is dependent on the mass of the black hole, the distance of observer from event horizon, and the mode frequency of quantum memory. To illustrate the generality of this paradigm, we relate the entropic uncertainty bound with other uncertainty probe, e.g., time-energy uncertainty. In an alternative game between two static players, we show that quantum information of qubit can be transferred to quantum memory through a bath of fluctuating quantum fields outside the black hole. For a particular choice of initial state, we show that the Hawking decoherence cannot counteract entanglement generation after the dynamical evolution of system, which triggers an effectively reduced uncertainty bound that violates the intrinsic limit -log2 ? c. Numerically estimation for a proper choice of initial state shows that our result is comparable with possible real experiments. Finally, a discussion on the black hole firewall paradox in the context of entropic uncertainty relation is given.
THE PRECAUTIONARY PRINCIPLE AND CHEMICAL RISKS Olivier GODARD
Boyer, Edmond
uncertainty. Against this background, the links between the PP and the REACH regulation for chemical products: Precautionary principle, Europe, risk management, chemicals, REACH JEL CLASSIFICATION: D81; K32; L65 1 Senior. It developed as a policy and law concept over the last twenty-five years, mainly in Europe. A key date
Design Principles for Robust Grasping in Unstructured Environments
with grasping under uncertainty can be addressed by careful mechanical design of robot hands. In particular, I hand control, can grasp a wide range of target objects in the presence of large positioning errors. ivDesign Principles for Robust Grasping in Unstructured Environments A thesis presented by Aaron
Earthquake Loss Estimation Uncertainties
NASA Astrophysics Data System (ADS)
Frolova, Nina; Bonnin, Jean; Larionov, Valery; Ugarov, Aleksander
2013-04-01
The paper addresses the reliability issues of strong earthquakes loss assessment following strong earthquakes with worldwide Systems' application in emergency mode. Timely and correct action just after an event can result in significant benefits in saving lives. In this case the information about possible damage and expected number of casualties is very critical for taking decision about search, rescue operations and offering humanitarian assistance. Such rough information may be provided by, first of all, global systems, in emergency mode. The experience of earthquakes disasters in different earthquake-prone countries shows that the officials who are in charge of emergency response at national and international levels are often lacking prompt and reliable information on the disaster scope. Uncertainties on the parameters used in the estimation process are numerous and large: knowledge about physical phenomena and uncertainties on the parameters used to describe them; global adequacy of modeling techniques to the actual physical phenomena; actual distribution of population at risk at the very time of the shaking (with respect to immediate threat: buildings or the like); knowledge about the source of shaking, etc. Needless to be a sharp specialist to understand, for example, that the way a given building responds to a given shaking obeys mechanical laws which are poorly known (if not out of the reach of engineers for a large portion of the building stock); if a carefully engineered modern building is approximately predictable, this is far not the case for older buildings which make up the bulk of inhabited buildings. The way population, inside the buildings at the time of shaking, is affected by the physical damage caused to the buildings is not precisely known, by far. The paper analyzes the influence of uncertainties in strong event parameters determination by Alert Seismological Surveys, of simulation models used at all stages from, estimating shaking intensity to assessing the damage to different elements at risk, of the databases on different elements at risk, such as population and building stock distribution, as well critical facilities characteristics, on the reliability of expected loss estimations at regional and global scale.
Uncertainty in Seismic Hazard Assessment
NASA Astrophysics Data System (ADS)
Wang, Z.
2006-12-01
Uncertainty is a part of our life, and society has to deal with it, even though it is sometimes difficult to estimate. This is particularly true in seismic hazard assessment for large events, such as the mega-tsunami in Southeast Asia and the great New Madrid earthquakes in the central United States. There are two types of uncertainty in seismic hazard assessment: temporal and spatial. Temporal uncertainty describes distribution of the events in time and is estimated from the historical records, while spatial uncertainty describes distribution of physical measurements generated at a specific point by the events and is estimated from the measurements at the point. These uncertainties are of different characteristics and generally considered separately in hazard assessment. For example, temporal uncertainty (i.e., the probability of exceedance in a period) is considered separately from spatial uncertainty (a confidence level of physical measurement) in flood hazard assessment. Although estimating spatial uncertainty in seismic hazard assessment is difficult because there are not enough physical measurements (i.e., ground motions), it can be supplemented by numerical modeling. For example, the ground motion uncertainty or tsunami uncertainty at a point of interest has been estimated from numerical modeling. Estimating temporal uncertainty is particularly difficult, especially for large earthquakes, because there are not enough instrumental, historical, and geological records. Therefore, the temporal and spatial uncertainties in seismic hazard assessment are of different characteristics and should be determined separately. Probabilistic seismic hazard analysis (PSHA), the most widely used method to assess seismic hazard for various aspects of public and financial policy, uses spatial uncertainty (ground motion uncertainty) to extrapolate temporal uncertainty (ground motion occurrence), however. This extrapolation, or so-called ergodic assumption, is caused by a mathematical error in hazard calculation of PSHA: incorrectly equating the conditional exceedance probability of the ground-motion attenuation relationship (a function) to the exceedance probability of the ground-motion uncertainty (a variable). An alternative approach has been developed to correct the error and to determine temporal and spatial uncertainties separately.
NASA Astrophysics Data System (ADS)
Petzinger, Tom
I am trying to make money in the biotech industry from complexity science. And I am doing it with inspiration that I picked up on the edge of Appalachia spending time with June Holley and ACEnet when I was a Wall Street Journal reporter. I took some of those ideas to Pittsburgh, in biotechnology, in a completely private setting with an economic development focus, but also with a mission t o return profit to private capital. And we are doing that. I submit as a hypothesis, something we are figuring out in the post- industrial era, that business evolves. It is not the definition of business, but business critically involves the design of systems in which uncertainty is treated as a certainty. That is what I have seen and what I have tried to put into practice.
MRST partons and uncertainties.
Martin, A D; Roberts, R G; Stirling, W James; Thorne, Robert S
ar X iv :h ep -p h/ 03 07 26 2v 1 2 1 Ju l 2 00 3 IPPP/03/43 DCPT/03/86 Cavendish-HEP-2003/13 21 July 2003 MRST partons and uncertainties A.D. Martin1, R.G. Roberts1, W.J. Stirling1 and R.S. Thorne2 1IPPP, Durham, DH1 3LE, UK 2Cavendish... : D. Stump et al., Phys. Rev. D65 (2002) 014012; CTEQ Collaboration: J. Pumplin et al., Phys. Rev. D65 (2002) 014013. [2] A.D. Martin, R.G. Roberts, W.J. Stirling and R.S. Thorne, Eur. Phys. J. C28 (2003) 455. [3] A.D. Martin, R.G. Roberts, W...
Uncertainty quantification in molecular dynamics
NASA Astrophysics Data System (ADS)
Rizzi, Francesco
This dissertation focuses on uncertainty quantification (UQ) in molecular dynamics (MD) simulations. The application of UQ to molecular dynamics is motivated by the broad uncertainty characterizing MD potential functions and by the complexity of the MD setting, where even small uncertainties can be amplified to yield large uncertainties in the model predictions. Two fundamental, distinct sources of uncertainty are investigated in this work, namely parametric uncertainty and intrinsic noise. Intrinsic noise is inherently present in the MD setting, due to fluctuations originating from thermal effects. Averaging methods can be exploited to reduce the fluctuations, but due to finite sampling, this effect cannot be completely filtered, thus yielding a residual uncertainty in the MD predictions. Parametric uncertainty, on the contrary, is introduced in the form of uncertain potential parameters, geometry, and/or boundary conditions. We address the UQ problem in both its main components, namely the forward propagation, which aims at characterizing how uncertainty in model parameters affects selected observables, and the inverse problem, which involves the estimation of target model parameters based on a set of observations. The dissertation highlights the challenges arising when parametric uncertainty and intrinsic noise combine to yield non-deterministic, noisy MD predictions of target macroscale observables. Two key probabilistic UQ methods, namely Polynomial Chaos (PC) expansions and Bayesian inference, are exploited to develop a framework that enables one to isolate the impact of parametric uncertainty on the MD predictions and, at the same time, properly quantify the effect of the intrinsic noise. Systematic applications to a suite of problems of increasing complexity lead to the observation that an uncertain PC representation built via Bayesian regression is the most suitable model for the representation of uncertain MD predictions of target observables in the presence of intrinsic noise and parametric uncertainty. The dissertation is organized in successive, self-contained problems of increasing complexity aimed at investigating the target UQ challenge in a progressive fashion.
Assessment Principles and Tools
Golnik, Karl C.
2014-01-01
The goal of ophthalmology residency training is to produce competent ophthalmologists. Competence can only be determined by appropriately assessing resident performance. There are accepted guiding principles that should be applied to competence assessment methods. These principles are enumerated herein and ophthalmology-specific assessment tools that are available are described. PMID:24791100
Bailey Willis
1910-01-01
The broad general principles of paleogeography, which I would cite as most fundamental, are as follows: 1. Ocean basins are permanent hollows of the earth's surface and have occupied their present sites since an early date in the development of geographic features. This principle does not exclude notable changes in the positions of their margins, which on the whole have
Basic principle of superconductivity
Tian De Cao
2009-11-10
The basic principle of superconductivity is suggested in this paper. There have been two vital wrong suggestions on the basic principle, one is the relation between superconductivity and the Bose-Einstein condensation (BEC), and another is the relation between superconductivity and pseudogap.
NSDL National Science Digital Library
Dr. Rod Nave
This tutorial provides instruction on Pauli's exclusion principle, formulated by physicist Wolfgang Pauli in 1925, which states that no two electrons in an atom can have identical quantum numbers. Topics include a mathematical statement of the principle, descriptions of some of its applications, and its role in ionic and covalent bonding, nuclear shell structure, and nuclear binding energy.
Buoyancy: Archimedes Principle
NSDL National Science Digital Library
2010-07-30
This applied mathematics lesson describes the mathematic principles behind buoyancy in aerostatic machines. In it, students are given an introduction to the forces at work in buoyancy, including Archimedes Principle, and are asked to solve problems relating to volume, density, weight, and buoyancy of objects in particular environments.
How Uncertainty Bounds the Shape Index of Simple Cells
2014-01-01
We propose a theoretical motivation to quantify actual physiological features, such as the shape index distributions measured by Jones and Palmer in cats and by Ringach in macaque monkeys. We will adopt the uncertainty principle associated to the task of detection of position and orientation as the main tool to provide quantitative bounds on the family of simple cells concretely implemented in primary visual cortex. Mathematics Subject Classification (2000)2010: 62P10, 43A32, 81R15. PMID:24742044
How uncertainty bounds the shape index of simple cells.
Barbieri, D; Citti, G; Sarti, A
2014-01-01
We propose a theoretical motivation to quantify actual physiological features, such as the shape index distributions measured by Jones and Palmer in cats and by Ringach in macaque monkeys. We will adopt the uncertainty principle associated to the task of detection of position and orientation as the main tool to provide quantitative bounds on the family of simple cells concretely implemented in primary visual cortex.Mathematics Subject Classification (2000)2010: 62P10, 43A32, 81R15. PMID:24742044
Inflation Uncertainty, Output Growth Uncertainty and Macroeconomic Performance
Stilianos Fountas; Menelaos Karanasos; Jinki Kim
2006-01-01
We use a bivariate generalized autoregressive conditionally heteroskedastic (GARCH) model of inflation and output growth to examine the causality relationship among nominal uncertainty, real uncertainty and macroeconomic performance measured by the inflation and output growth rates. The application of the constant conditional correlation GARCH(1,1) model leads to a number of interesting conclusions. First, inflation does cause negative welfare effects, both
ERIC Educational Resources Information Center
Lofstedt, Ragnar E.; Fischhoff, Baruch; Fischhoff, Ilya R.
2002-01-01
Precautionary principles have been proposed as a fundamental element of sound risk management. Their advocates see them as guiding action in the face of uncertainty, encouraging the adoption of measures that reduce serious risks to health, safety, and the environment. Their opponents may reject the very idea of precautionary principles, find…
Uncertainty of testing methods--what do we (want to) know?
Paparella, Martin; Daneshian, Mardas; Hornek-Gausterer, Romana; Kinzl, Maximilian; Mauritz, Ilse; Mühlegger, Simone
2013-01-01
It is important to stimulate innovation for regulatory testing methods. Scrutinizing the knowledge of (un)certainty of data from actual standard in vivo methods could foster the interest in new testing approaches. Since standard in vivo data often are used as reference data for model development, improved uncertainty accountability also would support the validation of new in vitro and in silico methods, as well as the definition of acceptance criteria for the new methods. Hazard and risk estimates, transparent for their uncertainty, could further support the 3Rs, since they may help focus additional information requirements on aspects of highest uncertainty. Here we provide an overview on the various types of uncertainties in quantitative and qualitative terms and suggest improving this knowledge base. We also reference principle concepts on how to use uncertainty information for improved hazard characterization and development of new testing methods. PMID:23665803
Gorassini, Monica
In spite of many years of research there is still much uncertainty regarding the nature of proprioceptive signals and the role of these signals in kinaesthesia and movement control. The uncertainty mainly with the inverse of the above models, indicating that the nervous system could in principle process spindle firing
Maximum predictive power and the superposition principle
NASA Technical Reports Server (NTRS)
Summhammer, Johann
1994-01-01
In quantum physics the direct observables are probabilities of events. We ask how observed probabilities must be combined to achieve what we call maximum predictive power. According to this concept the accuracy of a prediction must only depend on the number of runs whose data serve as input for the prediction. We transform each probability to an associated variable whose uncertainty interval depends only on the amount of data and strictly decreases with it. We find that for a probability which is a function of two other probabilities maximum predictive power is achieved when linearly summing their associated variables and transforming back to a probability. This recovers the quantum mechanical superposition principle.
Uncertainty analysis in RECCAP
NASA Astrophysics Data System (ADS)
Enting, I. G.
2010-12-01
The Global Carbon Project RECCAP exercise aims to produce regional analyses of net carbon fluxes between the atmosphere and the land and ocean carbon systems. The project aims to synthesise multiple source of information from modelling, inversions and inventory studies. A careful analysis of uncertainty is essential, both for the final synthesis and for assuring consistency in the process of combining disparate inputs. A unifying approach is to treat the overall analysis as a process of statistical estimation. The broadest-scale grouping of approaches is `top-down' vs. `bottom-up' techniques, but each of these needs to be further partitioned. Top-down approaches generally take the form of inversions, using measurements of carbon dioxide concentrations to either deduce surface concentrations or deduce parameters in spatially-explicit process-based models. These two types of inversion will have somewhat different statistical characteristics, but each will achieve only limited spatial resolution due to the ill-conditioned nature of the inversion. Bottom-up techniques aim to resolve great spatial detail. They comprise both census-type studies (mainly for anthropogenic emissions) and modelling studies with remotely-sensed data to provide spatially and temporally explicit forcing or constraints. Again, these two types of approach are likely to have quite different statistical characteristics. An important issue in combining information is consistency between definitions used for the disparate components. Cases where there is significant potential for ambiguity include wildfire and delayed responses to land-use change. A particular concern is the potential for `double counting' when combining bottom-up estimates with the results of inversion techniques that have incorporated Bayesian constraints using the same data as is used in the bottom-up estimates. The communication of distribution of uncertainty in one time and two space dimensions poses particular challenges. Temporal variability can be usefully characterised in terms of long-term trends, seasonal cycles and irregular variability. Additional choices need to be made concerning the frequency ranges that define each of these components. Spatial resolution remains problematic with the diffuse boundaries of top-down approaches failing to match the sharp boundaries from bottom-up techniques.
Jennifer L. Gibbs; Nicole B. Ellison; Chih-Hui Lai
2011-01-01
This study investigates relationships between privacy concerns, uncertainty reduction behaviors, and self-disclosure among online dating participants, drawing on uncertainty reduction theory and the warranting principle. The authors propose a conceptual model integrating privacy concerns, self-efficacy, and Internet experience with uncertainty reduction strategies and amount of self-disclosure and then test this model on a nationwide sample of online dating participants (
Environmental assessments: Uncertainties in implementation
Hunsaker; D. B. Jr
1987-01-01
A review of the regulations, guidance, statutes, and case law affecting Environmental Assessment (EA) preparation has identified a number of uncertainties that, if clarified, would facilitate EA preparation and National Environmental Policy ACT (NEPA) implementation. Recommendations are made for clarifying the uncertainties regarding EA preparation to help EAs fulfill their intended role in the NEPA process and to thereby facilitate
Housing Uncertainty and Childhood Impatience
ERIC Educational Resources Information Center
Anil, Bulent; Jordan, Jeffrey L.; Zahirovic-Herbert, Velma
2011-01-01
The study demonstrates a direct link between housing uncertainty and children's time preferences, or patience. We show that students who face housing uncertainties through mortgage foreclosures and eviction learn impatient behavior and are therefore at greater risk of making poor intertemporal choices such as dropping out of school. We find that…
Hydrology, society, change and uncertainty
NASA Astrophysics Data System (ADS)
Koutsoyiannis, Demetris
2014-05-01
Heraclitus, who predicated that "panta rhei", also proclaimed that "time is a child playing, throwing dice". Indeed, change and uncertainty are tightly connected. The type of change that can be predicted with accuracy is usually trivial. Also, decision making under certainty is mostly trivial. The current acceleration of change, due to unprecedented human achievements in technology, inevitably results in increased uncertainty. In turn, the increased uncertainty makes the society apprehensive about the future, insecure and credulous to a developing future-telling industry. Several scientific disciplines, including hydrology, tend to become part of this industry. The social demand for certainties, no matter if these are delusional, is combined by a misconception in the scientific community confusing science with uncertainty elimination. However, recognizing that uncertainty is inevitable and tightly connected with change will help to appreciate the positive sides of both. Hence, uncertainty becomes an important object to study, understand and model. Decision making under uncertainty, developing adaptability and resilience for an uncertain future, and using technology and engineering means for planned change to control the environment are important and feasible tasks, all of which will benefit from advancements in the Hydrology of Uncertainty.
Pandemic influenza: certain uncertainties
Morens, David M.; Taubenberger, Jeffery K.
2011-01-01
SUMMARY For at least five centuries, major epidemics and pandemics of influenza have occurred unexpectedly and at irregular intervals. Despite the modern notion that pandemic influenza is a distinct phenomenon obeying such constant (if incompletely understood) rules such as dramatic genetic change, cyclicity, “wave” patterning, virus replacement, and predictable epidemic behavior, much evidence suggests the opposite. Although there is much that we know about pandemic influenza, there appears to be much more that we do not know. Pandemics arise as a result of various genetic mechanisms, have no predictable patterns of mortality among different age groups, and vary greatly in how and when they arise and recur. Some are followed by new pandemics, whereas others fade gradually or abruptly into long-term endemicity. Human influenza pandemics have been caused by viruses that evolved singly or in co-circulation with other pandemic virus descendants and often have involved significant transmission between, or establishment of, viral reservoirs within other animal hosts. In recent decades, pandemic influenza has continued to produce numerous unanticipated events that expose fundamental gaps in scientific knowledge. Influenza pandemics appear to be not a single phenomenon but a heterogeneous collection of viral evolutionary events whose similarities are overshadowed by important differences, the determinants of which remain poorly understood. These uncertainties make it difficult to predict influenza pandemics and, therefore, to adequately plan to prevent them. PMID:21706672
The Bayesian brain: phantom percepts resolve sensory uncertainty.
De Ridder, Dirk; Vanneste, Sven; Freeman, Walter
2014-07-01
Phantom perceptions arise almost universally in people who sustain sensory deafferentation, and in multiple sensory domains. The question arises 'why' the brain creates these false percepts in the absence of an external stimulus? The model proposed answers this question by stating that our brain works in a Bayesian way, and that its main function is to reduce environmental uncertainty, based on the free-energy principle, which has been proposed as a universal principle governing adaptive brain function and structure. The Bayesian brain can be conceptualized as a probability machine that constantly makes predictions about the world and then updates them based on what it receives from the senses. The free-energy principle states that the brain must minimize its Shannonian free-energy, i.e. must reduce by the process of perception its uncertainty (its prediction errors) about its environment. As completely predictable stimuli do not reduce uncertainty, they are not worthwhile of conscious processing. Unpredictable things on the other hand are not to be ignored, because it is crucial to experience them to update our understanding of the environment. Deafferentation leads to topographically restricted prediction errors based on temporal or spatial incongruity. This leads to an increase in topographically restricted uncertainty, which should be adaptively addressed by plastic repair mechanisms in the respective sensory cortex or via (para)hippocampal involvement. Neuroanatomically, filling in as a compensation for missing information also activates the anterior cingulate and insula, areas also involved in salience, stress and essential for stimulus detection. Associated with sensory cortex hyperactivity and decreased inhibition or map plasticity this will result in the perception of the false information created by the deafferented sensory areas, as a way to reduce increased topographically restricted uncertainty associated with the deafferentation. In conclusion, the Bayesian updating of knowledge via active sensory exploration of the environment, driven by the Shannonian free-energy principle, provides an explanation for the generation of phantom percepts, as a way to reduce uncertainty, to make sense of the world. PMID:22516669
Chemical Principles Exemplified
ERIC Educational Resources Information Center
Plumb, Robert C.
1972-01-01
Collection of two short descriptions of chemical principles seen in life situations: the autocatalytic reaction seen in the bombardier beetle, and molecular potential energy used for quick roasting of beef. Brief reference is also made to methanol lighters. (PS)
Buoyancy and Archimedes Principle
NSDL National Science Digital Library
Summary Buoyancy is based on Archimedes' Principle which states that the buoyant force acting upward on an object completely or partially immersed in a fluid equals the weight of the fluid displaced by the ...
Archimedes' Principle in Action
ERIC Educational Resources Information Center
Kires, Marian
2007-01-01
The conceptual understanding of Archimedes' principle can be verified in experimental procedures which determine mass and density using a floating object. This is demonstrated by simple experiments using graduated beakers. (Contains 5 figures.)
Principles of Information Assurance
NSDL National Science Digital Library
This course on the Principles of Information Assurance is provided by the Cyber Security Education Consortium (CSEC). The course includes introductory security principles and gives students "an understanding of the current threats and vulnerabilities of the cyber landscape, plus other topics relating to the information assurance field." Links are provided to learn more about the Major Topics Covered, Course Learning Objectives, and Course Outline. The Course Outline includes a list of careers that require the knowledge from this course and related textbooks.
Archimedes' Principle and Applications Objectives
Yu, Jaehoon
Lab 9 Archimedes' Principle and Applications Objectives: Upon successful completion of this exercise you will have ... 1. ... utilized Archimedes' principle to determine the density and specific gravity of a variety of substances. 2. ... utilized Archimedes' principle to determine the density
PIV uncertainty quantification by image matching
NASA Astrophysics Data System (ADS)
Sciacchitano, Andrea; Wieneke, Bernhard; Scarano, Fulvio
2013-04-01
A novel method is presented to quantify the uncertainty of PIV data. The approach is a posteriori, i.e. the unknown actual error of the measured velocity field is estimated using the velocity field itself as input along with the original images. The principle of the method relies on the concept of super-resolution: the image pair is matched according to the cross-correlation analysis and the residual distance between matched particle image pairs (particle disparity vector) due to incomplete match between the two exposures is measured. The ensemble of disparity vectors within the interrogation window is analyzed statistically. The dispersion of the disparity vector returns the estimate of the random error, whereas the mean value of the disparity indicates the occurrence of a systematic error. The validity of the working principle is first demonstrated via Monte Carlo simulations. Two different interrogation algorithms are considered, namely the cross-correlation with discrete window offset and the multi-pass with window deformation. In the simulated recordings, the effects of particle image displacement, its gradient, out-of-plane motion, seeding density and particle image diameter are considered. In all cases good agreement is retrieved, indicating that the error estimator is able to follow the trend of the actual error with satisfactory precision. Experiments where time-resolved PIV data are available are used to prove the concept under realistic measurement conditions. In this case the ‘exact’ velocity field is unknown; however a high accuracy estimate is obtained with an advanced interrogation algorithm that exploits the redundant information of highly temporally oversampled data (pyramid correlation, Sciacchitano et al (2012 Exp. Fluids 53 1087-105)). The image-matching estimator returns the instantaneous distribution of the estimated velocity measurement error. The spatial distribution compares very well with that of the actual error with maxima in the highly sheared regions and in the 3D turbulent regions. The high level of correlation between the estimated error and the actual error indicates that this new approach can be utilized to directly infer the measurement uncertainty from PIV data. A procedure is shown where the results of the error estimation are employed to minimize the measurement uncertainty by selecting the optimal interrogation window size.
A variational principle in optics.
Rubinstein, Jacob; Wolansky, Gershon
2004-11-01
We derive a new variational principle in optics. We first formulate the principle for paraxial waves and then generalize it to arbitrary waves. The new principle, unlike the Fermat principle, concerns both the phase and the intensity of the wave. In particular, the principle provides a method for finding the ray mapping between two surfaces in space from information on the wave's intensity there. We show how to apply the new principle to the problem of phase reconstruction from intensity measurements. PMID:15535374
Experimental Nuclear Reaction Data Uncertainties: Basic Concepts and Documentation
Smith, D.L. [Argonne National Laboratory, 1710 Avenida Del Mundo 1506, Coronado, CA 92118 (United States)] [Argonne National Laboratory, 1710 Avenida Del Mundo 1506, Coronado, CA 92118 (United States); Otuka, N. [Nuclear Data Section, International Atomic Energy Agency, Wagramerstrasse 5, A-1400 Wien (Austria)] [Nuclear Data Section, International Atomic Energy Agency, Wagramerstrasse 5, A-1400 Wien (Austria)
2012-12-15
This paper has been written to provide experimental nuclear data researchers and data compilers with practical guidance on dealing with experimental nuclear reaction data uncertainties. It outlines some of the properties of random variables as well as principles of data uncertainty estimation, and illustrates them by means of simple examples which are relevant to the field of nuclear data. Emphasis is placed on the importance of generating mathematical models (or algorithms) that can adequately represent individual experiments for the purpose of estimating uncertainties in their results. Several types of uncertainties typically encountered in nuclear data experiments are discussed. The requirements and procedures for reporting information on measurement uncertainties for neutron reaction data, so that they will be useful in practical applications, are addressed. Consideration is given to the challenges and opportunities offered by reports, conference proceedings, journal articles, and computer libraries as vehicles for reporting and documenting numerical experimental data. Finally, contemporary formats used to compile reported experimental covariance data in the widely used library EXFOR are discussed, and several samples of EXFOR files are presented to demonstrate their use.
Experimental Nuclear Reaction Data Uncertainties: Basic Concepts and Documentation
NASA Astrophysics Data System (ADS)
Smith, D. L.; Otuka, N.
2012-12-01
This paper has been written to provide experimental nuclear data researchers and data compilers with practical guidance on dealing with experimental nuclear reaction data uncertainties. It outlines some of the properties of random variables as well as principles of data uncertainty estimation, and illustrates them by means of simple examples which are relevant to the field of nuclear data. Emphasis is placed on the importance of generating mathematical models (or algorithms) that can adequately represent individual experiments for the purpose of estimating uncertainties in their results. Several types of uncertainties typically encountered in nuclear data experiments are discussed. The requirements and procedures for reporting information on measurement uncertainties for neutron reaction data, so that they will be useful in practical applications, are addressed. Consideration is given to the challenges and opportunities offered by reports, conference proceedings, journal articles, and computer libraries as vehicles for reporting and documenting numerical experimental data. Finally, contemporary formats used to compile reported experimental covariance data in the widely used library EXFOR are discussed, and several samples of EXFOR files are presented to demonstrate their use.
M. U. Karelin; A. M. Lazaruk
2000-06-12
For configurational space of arbitrary dimension a strict form of the uncertainty principle has been obtained, which takes into account the dependence of inequality limit on the effective number of pure states present in given statistical mixture. It is shown that in a state with minimal uncertainty the density operators eigenfunctions coincide with the stationary wavefunctions of a multidimensional harmonic oscillator. The mixed state obtained has a permutational symmetry which is typical for a system of identical bosons.
One-dimensional hydrogen atom with minimal length uncertainty and maximal momentum
Pouria Pedram
2013-02-16
We present exact energy eigenvalues and eigenfunctions of the one-dimensional hydrogen atom in the framework of the Generalized (Gravitational) Uncertainty Principle (GUP). This form of GUP is consistent with various theories of quantum gravity such as string theory, loop quantum gravity, black-hole physics, and doubly special relativity and implies a minimal length uncertainty and a maximal momentum. We show that the quantized energy spectrum exactly agrees with the semiclassical results.
Uncertainty in perception and the Hierarchical Gaussian Filter
Mathys, Christoph D.; Lomakina, Ekaterina I.; Daunizeau, Jean; Iglesias, Sandra; Brodersen, Kay H.; Friston, Karl J.; Stephan, Klaas E.
2014-01-01
In its full sense, perception rests on an agent's model of how its sensory input comes about and the inferences it draws based on this model. These inferences are necessarily uncertain. Here, we illustrate how the Hierarchical Gaussian Filter (HGF) offers a principled and generic way to deal with the several forms that uncertainty in perception takes. The HGF is a recent derivation of one-step update equations from Bayesian principles that rests on a hierarchical generative model of the environment and its (in)stability. It is computationally highly efficient, allows for online estimates of hidden states, and has found numerous applications to experimental data from human subjects. In this paper, we generalize previous descriptions of the HGF and its account of perceptual uncertainty. First, we explicitly formulate the extension of the HGF's hierarchy to any number of levels; second, we discuss how various forms of uncertainty are accommodated by the minimization of variational free energy as encoded in the update equations; third, we combine the HGF with decision models and demonstrate the inversion of this combination; finally, we report a simulation study that compared four optimization methods for inverting the HGF/decision model combination at different noise levels. These four methods (Nelder–Mead simplex algorithm, Gaussian process-based global optimization, variational Bayes and Markov chain Monte Carlo sampling) all performed well even under considerable noise, with variational Bayes offering the best combination of efficiency and informativeness of inference. Our results demonstrate that the HGF provides a principled, flexible, and efficient—but at the same time intuitive—framework for the resolution of perceptual uncertainty in behaving agents. PMID:25477800
Uncertainty in perception and the Hierarchical Gaussian Filter.
Mathys, Christoph D; Lomakina, Ekaterina I; Daunizeau, Jean; Iglesias, Sandra; Brodersen, Kay H; Friston, Karl J; Stephan, Klaas E
2014-01-01
In its full sense, perception rests on an agent's model of how its sensory input comes about and the inferences it draws based on this model. These inferences are necessarily uncertain. Here, we illustrate how the Hierarchical Gaussian Filter (HGF) offers a principled and generic way to deal with the several forms that uncertainty in perception takes. The HGF is a recent derivation of one-step update equations from Bayesian principles that rests on a hierarchical generative model of the environment and its (in)stability. It is computationally highly efficient, allows for online estimates of hidden states, and has found numerous applications to experimental data from human subjects. In this paper, we generalize previous descriptions of the HGF and its account of perceptual uncertainty. First, we explicitly formulate the extension of the HGF's hierarchy to any number of levels; second, we discuss how various forms of uncertainty are accommodated by the minimization of variational free energy as encoded in the update equations; third, we combine the HGF with decision models and demonstrate the inversion of this combination; finally, we report a simulation study that compared four optimization methods for inverting the HGF/decision model combination at different noise levels. These four methods (Nelder-Mead simplex algorithm, Gaussian process-based global optimization, variational Bayes and Markov chain Monte Carlo sampling) all performed well even under considerable noise, with variational Bayes offering the best combination of efficiency and informativeness of inference. Our results demonstrate that the HGF provides a principled, flexible, and efficient-but at the same time intuitive-framework for the resolution of perceptual uncertainty in behaving agents. PMID:25477800
Uncertainty in emissions projections for climate models
Webster, Mort David.; Babiker, Mustafa H.M.; Mayer, Monika.; Reilly, John M.; Harnisch, Jochen.; Hyman, Robert C.; Sarofim, Marcus C.; Wang, Chien.
Future global climate projections are subject to large uncertainties. Major sources of this uncertainty are projections of anthropogenic emissions. We evaluate the uncertainty in future anthropogenic emissions using a ...
Photometric Uncertainties within Hinode XRT
NASA Astrophysics Data System (ADS)
Kobelski, Adam; Saar, S. H.; Weber, M. A.; McKenzie, D. E.; Reeves, K. K.
2012-05-01
We have developed estimates of the systematic uncertainties for the X-Ray Telescope (XRT) on Hinode. These estimates are included as optional returns from the standard XRT data reduction software, xrt_prep.pro. Included in these software estimates are uncertainties from instrument vignetting, dark current subtraction, split bias leveling, Fourier filtering and JPEG compression. Sources of uncertainty that rely heavily on models of plasma radiation or assumptions of elemental abundances, such as photon noise, are discussed, but not included in the software. It will be shown that the photon noise is much larger than the systematic uncertainty. This work is supported by NASA under contract NNM07AB07C with the Harvard-Smithsonian Astrophysical Observatory
Extended Equivalence Principle: Implications for Gravity, Geometry and Thermodynamics
C. Sivaram; Kenath Arun
2012-05-17
The equivalence principle was formulated by Einstein in an attempt to extend the concept of inertial frames to accelerated frames, thereby bringing in gravity. In recent decades, it has been realised that gravity is linked not only with geometry of space-time but also with thermodynamics especially in connection with black hole horizons, vacuum fluctuations, dark energy, etc. In this work we look at how the equivalence principle manifests itself in these different situations where we have strong gravitational fields. In recent years the generalised uncertainty principle has been invoked to connect gravity and curvature with quantum physics and now we may also need an extended equivalence principle to connect quantum theory with gravity.
Flood risk curves and uncertainty bounds
Bruno Merz; Annegret H. Thieken
2009-01-01
Although flood risk assessments are frequently associated with significant uncertainty, formal uncertainty analyses are the\\u000a exception rather than the rule. We propose to separate two fundamentally different types of uncertainty in flood risk analyses:\\u000a aleatory and epistemic uncertainty. Aleatory uncertainty refers to quantities that are inherently variable in time, space\\u000a or populations of individuals or objects. Epistemic uncertainty results from