On the macroscopic verifications of Klein's theorem and the proof of $E_0=mc^2$

TL;DR

This paper presents alternative macroscopic verifications of Klein's theorem and the proof of Einstein's mass-energy equivalence, demonstrating their robustness across models with different boundary conditions and electromagnetic considerations.

Contribution

It provides new macroscopic models that verify Klein's theorem and the relation E_0=mc^2, highlighting the minimal impact of Poincaré stresses on these results.

Findings

Models confirm E_0=mc^2 for macroscopic bodies.

Robustness of the relation across different boundary conditions.

Electromagnetic radiation considerations do not alter the core result.

Abstract

Alternative verifications of Klein's theorem and the proof of $E_0=mc^2$, for a relativistic macroscopic body are presented, using models with boundary conditions of varying complexity, together with some refinements for the case containing electromagnetic radiation for the simplest model. The robustness of these models to the final result of $E_0=mc^2$, attests to the minor role played by the Poincar\'e type stresses introduced in some of these models for mechanical stability. Finally we caution the reader that while internal consistency of the $E_0=mc^2$ relation for a macroscopic body in special relativity is proved, it does not in any way furnish a proof of the relation for a single point particle, for this would imply that one is able to prove the postulates of special relativity from the premises of the theory itself.