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

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.