21 November 1905: Albert Einstein‘s paper that leads to the mass–energy equivalence formula, E = mc², is published in the journal Annalen der Physik. (Source)

# Mass–energy equivalence

In physics, mass–energy equivalence is the relationship between mass and energy in a system’s rest frame, where the two values differ only by a constant and the units of measurement.[1][2] The principle is described by the physicist Albert Einstein‘s famous formula:  E = m c 2 {\displaystyle E=mc^{2}} .[3]

The formula defines the energy E of a particle in its rest frame as the product of mass (m) with the speed of light squared (c2). Because the speed of light is a large number in everyday units (approximately 3×108 meters per second), the formula implies that a small amount of rest mass corresponds to an enormous amount of energy, which is independent of the composition of the matter. Rest mass, also called invariant mass, is the mass that is measured when the system is at rest. It is a fundamental physical property that is independent of momentum, even at extreme speeds approaching the speed of light (i.e., its value is the same in all inertial frames of reference). Massless particles such as photons have zero invariant mass, but massless free particles have both momentum and energy. The equivalence principle implies that when energy is lost in chemical reactions, nuclear reactions, and other energy transformations, the system will also lose a corresponding amount of mass. The energy, and mass, can be released to the environment as radiant energy, such as light, or as thermal energy. The principle is fundamental to many fields of physics, including nuclear and particle physics.

Mass–energy equivalence arose from special relativity as a paradox described by the French polymath Henri Poincaré.[4] Einstein was the first to propose the equivalence of mass and energy as a general principle and a consequence of the symmetries of space and time. The principle first appeared in “Does the inertia of a body depend upon its energy-content?”, one of his Annus Mirabilis (Miraculous Year) papers, published on 21 November 1905.[5] The formula and its relationship to momentum, as described by the energy–momentum relation, were later developed by other physicists.