Mass–energy connection without special relativity

In 1905, Einstein carried out 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. In this paper, we prove that a general mass–energy relationship can be derived solely from very basic assumptions, which are the same made in Einstein’s first derivation but completely neglecting special relativity. The general mass–energy relationship turns to a mass–energy equivalence when is applied to the case of a body emitting energy in the form of electromagnetic waves. Our main result is that if the core logic behind Einstein’s approach is sound, then the essence of the mass–energy equivalence can be derived without special relativity. We believe that our heuristic approach, although not capable of giving the exact mathematical formula for the mass–energy equivalence, may represent a useful addition to the general discussion on the matter at the graduate level. Our finding suggests that the connection between mass and energy is at a deeper level and comes before any full-fledged physical theory.