Towards an extension of 1905 relativistic dynamics with a variable rest mass measuring potential energy

TL;DR

This paper extends Einstein's 1905 relativistic dynamics by proposing that rest mass varies with potential energy in a gravitational field, offering new insights into gravitational effects, atomic clocks, and planetary motion.

Contribution

It introduces a variable rest mass model based on potential energy, revises free fall and clock behavior, and applies the theory to Mercury's perihelion, suggesting potential paradigm shifts in physics.

Findings

Rest mass measures potential energy.

Gamma factor relates total and potential energy ratios.

Mercury's perihelion shift explained with the extended dynamics.

Abstract

From a rigorous historic analysis of 1686 I. Newton and 1905 A. Einstein works where the last derived the universal mass-energy relationship, it is concluded that rest mass measures potential energy. From the same formula used to obtain that relation, it is derived the ratio Total Energy/Potential Energy is equal to the gamma relativistic factor. It is derived a formula for the variation of a body rest mass with its position in a gravity field, explaining with it the behavior of an atomic clock. It is revised the bodies free fall in a gravitational field, finding that a constant total mass is equal to the gravitational mass, while the variable rest mass is equal to the inertial mass, maintaining all an identical behavior independent of their masses. A revision of the E\"otv\"os experiment concludes that it is unable to detect the found difference between inertial and gravitational mass. Applying the extended 1905 relativistic dynamics to Mercury, its perihelion shift is determined; it is concluded with the convenience to continue its development, what can imply a revision of Physics since 1905 with important results in the unification of natural forces and other open problems.