Argument

Mass–energy equivalence

Overview

In physics, mass–energy equivalence is the relationship between mass and energy in a system's rest frame. The two differ only by a multiplicative constant and the units of measurement. The principle is described by the physicist Albert Einstein's formula:

{\displaystyle E=mc^{2}.}

The formula defines the energy,

{\displaystyle E,}

of a particle in its rest frame as the product of mass,

{\displaystyle m,}

with the speed of light,

{\displaystyle c,}

squared. Because the speed of light is a large number and it is squared, the formula implies that a small amount of mass corresponds to an enormous amount of energy. In a reference frame where the system is moving, its relativistic energy and relativistic mass (instead of rest mass) obey the same formula.

Rest mass, also called invariant mass, is a fundamental physical property of matter, independent of velocity. Massless particles such as photons have zero invariant mass, but massless free particles have both momentum and energy.

The equivalence principle implies that when mass is lost in chemical reactions or nuclear reactions, a corresponding amount of energy will be released. The energy can be released to the environment (outside of the system being considered) as radiant energy, such as light, or as thermal energy. The principle is fundamental to many fields of physics, including nuclear and particle physics.

Some relation between mass and energy was explored in the late 1800s under the term electromagnetic mass. Mass–energy equivalence arose from special relativity as a paradox described by the French polymath Henri Poincaré (1854–1912). 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 papers, published on 21 November 1905. The formula and its relationship to momentum, as described by the energy–momentum relation, were later developed by other physicists.

Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).

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The axiom can be explained as follows: Let {alpha} and {beta} be the names of two time-systems. The directions of motion in the space of {alpha} due to rest in a point of {beta} is called the '{beta}-direction in {alpha}' and the direction of motion in the space of {beta} due to rest in a point of {alpha} is called the '{alpha}-direction in {beta}.' Consider a motion in the space of {alpha} consisting of a certain…
Alfred North Whitehead, The Concept of Nature The Tarner Lectures Delivered in Trinity College, November 1919
States what Mass–energy equivalence is.
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For theoretical purposes, a mass is defined as being determined by the amount of force required to produce a given acceleration: The more massive a body is, the greater will be the force required to alter its velocity by a given amount in a given time. It takes a more powerful engine to make a long train attain a speed of ten miles an hour at the end of the first half-minute, than it does to make a short train do…
Bertrand Russell, The A B C of Relativity
States what Mass–energy equivalence is.
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If now instead of (_x_, _y_, _z_, _i t_), I use the method of writing with indices, certain essential circumstances will come into evidence; on this will be based a general use of the suffixes (1, 2, 3, 4). The advantage of this method will be, as I expressly emphasize here, that we shall have to handle symbols which have apparently a purely real appearance; we can however at any moment pass to real equations if it…
Albert Einstein, The Principle of Relativity
States what Mass–energy equivalence is.
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Philosophers who discussed Mass–energy equivalence

Leucippus

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Part of Deductive-nomological model.

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