Explaining atomic clock behavior in a gravitational field with only 1905 Relativity

TL;DR

This paper revisits Einstein's 1905 relativity to explain atomic clock behavior in gravity, proposing a potential energy-based interpretation of rest mass and deriving a gravity model without singularities.

Contribution

It introduces a 1905-based relativistic gravity model where rest mass measures potential energy, providing an alternative explanation for gravitational effects on atomic clocks.

Findings

Derived a formula for rest mass as a function of distance in a gravitational field.

Achieved clock rate change predictions close to General Relativity without singularities.

Highlighted differences between 1905 Relativity and modern theories.

Abstract

Supported only in the two 1905 Einstein's papers on Relativity and a very rigid respect for the historical context, an analysis is done of the derivation of the universal mass-energy relationship. It is found, contrary to the today accepted Physics knowledge, that a body's Rest Mass measures its Potential Energy in the 1905 context. After emphasizing the difference between 1905 Relativity (1905R) and Special Relativity (SR), the developing of a 1905R relativistic gravity is started for a small mass m material point moving in the central gravitational field of a great mass M one. A formula for the rest mass m_0 as a function of its distance r from M is obtained. Finally, those results are applied to an atomic clock in a gravitational field, reaching a factor to obtain the clock time rate change very close to the GR one. The factors from 1905R and GR are compared, emphasizing the absent of a singularity in 1905R. In the conclusions, a new road for the development of a 1905R relativistic mechanics is declared, related with the discovery that Rest Mass measures Potential Energy, done by 1905 Einstein even if not realizing it.