The General Equation of Motion via the Special Theory of Relativity and Quantum Mechanics Part i: a New Approach to Newton Equation of Motion

NASA Astrophysics Data System (ADS)

Herein we present a whole new approach to the derivation of the Newton Equation of Motion; throughout Part II of the present work, this shall lead to the findings brought up within the frame of the general theory of relativity (such as the precession of the perihelion of the planets, and the deflection of light nearby a star). To the contrary of what had been generally achieved so far, our basis consists in supposing that the gravitational field, through the binding process, alters the "rest mass" of an object conveyed in it. In fact, the special theory of relativity already imposes such a change. Next to this theory, we use the classical Newtonian gravitational attraction, reigning between two static masses; we have previously shown however that the 1/r^2 dependency of the gravitational force is also imposed by the special theory of relativity [1]. Our metric, is (just like the one used by the general theory of relativity) altered by the gravitational field (in fact, by any field the "measurement unit" in hand interacts with); yet in our approach, this occurs via quantum mechanics. More specifically, the rest mass of an object in a gravitational field is decreased as much as its binding energy in the field. A mass deficiency conversely, via quantum mechanics, yields the stretching of the size of the object in hand, as well as the weakening of its internal energy. Henceforth we shall not need the "principle of equivalence" assumed by the general theory of relativity, in order to predict the occurrences dealt with this theory [2]. We start with the following interesting postulate, in fact nothing else but the conservation of energy, in the broader sense of the concept of "energy". Thus The rest mass of an object bound to a celestial body amounts less than its rest mass measured in empty space, and this as much as its binding energy vis-à-vis the gravitational field of concern. This yields (with the familiar notation), the interesting equation of motion ( e^-?_0(r_0)/(1-(v_0/c_0)^2)^1/2 )=Constant; ?_0(r_0)=GM_0/(r_0(c_0)^2); here M0 is the mass of the celestial body creating the gravitational field of concern; G is the universal gravitational constant; r0 points to a location picked up on the trajectory of the motion; v0 is the tangential velocity of the object at r_0, and c0 the speed of light in empty space. The above relationship tells us that the mass of the object in motion can be conceived as made of its mass brought from infinity, at the location defined by r0 on its trajectory, thus i) decreased as much as its binding energy, ii) but at the same time, increased by a Lorentz factor, due to its translational motion on the trajectory. The differentiation of this relationship leads to -(GM_0/(r_0)^2)(1-(v_0)^2/(c_0)^2)=v_0dv_0/dr0 This differential equation is the classical Newton Equation of Motion, were v0 , negligible as compared to c0 (the speed of light in empty space). [1] T. Yarman, Invariances Based on Mass And Charge Variation, Manufactured by Wave Mechanics, Making up The Rules of Universal Matter Architecture, Chimica Acta Turcica, Vol 27, 1999. [2] T. Yarman, A Novel Approach to The End Results of the General Theory of Relativity and to Bound Muon Decay Rate Retardation, DAMOP 2001 Meeting, APS, May 16 -19, 2001, London, Ontario, Canada.