Clarifying Einstein's First Derivation for Mass-Energy Equivalence and Consequently Making Ives's Criticism a Void

TL;DR

This paper clarifies Einstein's original derivation of mass-energy equivalence, determines the value of the constant involved, and refutes Ives's criticism by showing the constant should be zero, offering a new perspective on Einstein's reasoning.

Contribution

The paper provides a detailed clarification of Einstein's first derivation, calculates the constant C as zero, and invalidates Ives's criticism.

Findings

The constant C in Einstein's derivation is zero.

Ives's criticism is rendered invalid by the zero value of C.

The clarification offers an alternative explanation for Einstein's derivation.

Abstract

We study physical situation considered by Einstein (Ann. Physik, 17, 1905) for his first derivation of mass-energy equivalence. Einstein introduced a constant $C$ in his derivation and reasoning surrounding $C$ and equations containing $C$ caused criticism by Ives. Here we clarify Einstein's derivation and obtain a value for constant $C$. The obtained zero value for $C$ suggests alternative explanation for Einstein's derivation and makes Ives's criticism a void and for which details are also presented in this paper.