The Einstein formula: E_0=mc^2 "Isn't the Lord laughing?"

TL;DR

This paper examines Einstein's original formulation of the energy-mass relation, highlighting misconceptions and clarifying the distinction between rest energy and total energy in special relativity.

Contribution

It provides a historical and conceptual analysis of Einstein's formulation, emphasizing the importance of the rest energy $E_0=mc^2$ over the popularized $E=mc^2$.

Findings

Einstein emphasized the rest energy $E_0=mc^2$ as fundamental.

The widespread belief that mass increases with velocity is a misconception.

The paper clarifies the difference between rest energy and total energy in relativity.

Abstract

The article traces the way Einstein formulated the relation between energy and mass in his work from 1905 to 1955. Einstein emphasized quite often that the mass $m$ of a body is equivalent to its rest energy $E_0$. At the same time he frequently resorted to the less clear-cut statement of equivalence of energy and mass. As a result, Einstein's formula $E_0=mc^2$ still remains much less known than its popular form, $E=mc^2$, in which $E$ is the total energy equal to the sum of the rest energy and the kinetic energy of a freely moving body. One of the consequences of this is the widespread fallacy that the mass of a body increases when its velocity increases and even that this is an experimental fact. As wrote the playwright A N Ostrovsky "Something must exist for people, something so austere, so lofty, so sacrosanct that it would make profaning it unthinkable."