A geometric relativistic dynamics under any conservative force

Author:

Friedman Yaakov1ORCID,Scarr Tzvi2,Steiner Joseph2

Affiliation:

1. Department of Mathematics and Physics, Jerusalem College of Technology, P. O. B. 16031, Jerusalem 91160, Israel

2. Department of Mathematics, Jerusalem College of Technology, P. O. B. 16031, Jerusalem 91160, Israel

Abstract

Riemann’s principle “force equals geometry” provided the basis for Einstein’s General Relativity — the geometric theory of gravitation. In this paper, we follow this principle to derive the dynamics for any static, conservative force. The geometry of spacetime of a moving object is described by a metric obtained from the potential of the force field acting on it. We introduce a generalization of Newton’s First Law — the Generalized Principle of Inertia stating that: An inanimate object moves inertially, that is, with constant velocity, in its own spacetime whose geometry is determined by the forces affecting it. Classical Newtonian dynamics is treated within this framework, using a properly defined Newtonian metric with respect to an inertial lab frame. We reveal a physical deficiency of this metric (responsible for the inability of Newtonian dynamics to account for relativistic behavior), and remove it. The dynamics defined by the corrected Newtonian metric leads to a new Relativistic Newtonian Dynamics for both massive objects and massless particles moving in any static, conservative force field, not necessarily gravitational. This dynamics reduces in the weak field, low velocity limit to classical Newtonian dynamics and also exactly reproduces the classical tests of General Relativity, as well as the post-Keplerian precession of binaries.

Publisher

World Scientific Pub Co Pte Lt

Subject

Physics and Astronomy (miscellaneous)

Reference29 articles.

1. Physics in Riemann’s Mathematical Papers

2. Translations and revisions by S. Bargmann;Einstein A.,1954

3. The classical geometrization of the electromagnetism

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