Einstein’s 1905 Derivation of the Mass-Energy Equivalence: Is It Valid? Is Energy Always Equal to Mass and Vice Versa?

Abstract

In 1905, Einstein gave his first derivation of the mass-energy equivalence by studying, in different reference frames, the energy balance of a body emitting electromagnetic radiation and assuming special relativity as a prerequisite. Here, we reassess the logical soundness of Einstein’s approach and the validity of one assumption crucial for his derivation. That assumption has nothing to do with special relativity. If we accept that assumption as valid, the essence of the mass-energy equivalence (but not its exact formula) can be reached without special relativity or any full-fledged physical theory. However, that assumption is unsupported from a physics viewpoint, and with its use, Einstein was begging the question. We also show why a consequence of the widely received interpretation of \(E = m{{c}^{2}}\) (i.e., every kind of energy has a mass) can be problematic.