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In physics, mass–energy equivalence is the relationship between mass and energy in a system's rest frame, where the two quantities differ only by a multiplicative constant and the units of measurement. [1] [2] The principle is described by the physicist Albert Einstein's formula: =. [3]
The equations were published by Albert Einstein in 1915 in the form of a tensor equation [2] which related the local spacetime curvature (expressed by the Einstein tensor) with the local energy, momentum and stress within that spacetime (expressed by the stress–energy tensor).
Einstein's paper on the photoelectric effect is sixth on this list. The article "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt" ("On a Heuristic Viewpoint Concerning the Production and Transformation of Light") [einstein 1] received 18 March and published 9 June, proposed the idea of energy quanta.
1928 – Paul Dirac describes the general energy–momentum relation, extending the equivalence of mass and energy. 1932 – Kennedy–Thorndike experiment confirms the Lorentz transformations in a new way, complementary to the Michelson–Morley experiment. [31] These two results, if combined, prove some form of time dilation.
The Einstein field equations (EFE) are the core of general relativity theory. The EFE describe how mass and energy (as represented in the stress–energy tensor) are related to the curvature of space-time (as represented in the Einstein tensor).
The theory of special relativity was initially developed in 1905 by Albert Einstein. However, other interpretations of special relativity have been developed, some on the basis of different foundational axioms. While some are mathematically equivalent to Einstein's theory, others aim to revise or extend it.
The stress–energy tensor is the source of the gravitational field in the Einstein field equations of general relativity, just as mass density is the source of such a field in Newtonian gravity. Because this tensor has 2 indices (see next section) the Riemann curvature tensor has to be contracted into the Ricci tensor, also with 2 indices.
The equation is often written this way because the difference is the relativistic length of the energy momentum four-vector, a length which is associated with rest mass or invariant mass in systems. Where m > 0 and p = 0, this equation again expresses the mass–energy equivalence E = m.