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Mass–energy equivalence

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In physics, mass–energy equivalence defines 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. The principle is described by Albert Einstein's famous formula: E = m c 2 {\displaystyle E=m\,c^{2}} 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 ( c 2 ). Equivalently, the mass of a particle at rest is equal to its energy E divided by the speed of light squared ( c 2 ). 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. The rest mass is a fundamental physical property that remains independent of mome...
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Extension for systems in motion

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Unlike a system's energy in an inertial frame, the relativistic energy ( E r {\displaystyle E_{r}} ) of a system depends on both the rest mass ( m 0 {\displaystyle m_{0}} ) and the total momentum of the system. The extension of Einstein's equation to these systems is given by:note E r 2 − | p → | 2 c 2 = m 0 2 c 4 E r 2 − ( p c ) 2 = ( m 0 c 2 ) 2 {\displaystyle {\begin{aligned}E_{r}^{2}-|{\vec {p}}\,|^{2}c^{2}&=m_{0}^{2}c^{4}\\E_{r}^{2}-(pc)^{2}&=(m_{0}c^{2})^{2}\end{aligned}}} or where the ( p c ) 2 {\displaystyle (pc)^{2}} term represents the square of the Euclidean norm (total vector length) of the various momentum vectors in the system, which reduces to the square of the simple momentum magnitude, if only a single particle is considered. This equation is called the energy–momentum relation and reduces to ...
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Efficiency

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In some reactions matter particles can be destroyed and their associated energy released to the environment as other forms of energy, such as light and heat. One example of such a conversion takes place in elementary particle interactions, where the rest energy is transformed into kinetic energy. Such conversions between types of energy happen in nuclear weapons, in which the protons and neutrons in atomic nuclei lose a small fraction of their original mass, though the mass lost is not due to the destruction of any smaller constituents. Nuclear fission allows a tiny fraction of the energy associated with the mass to be converted into usable energy such as radiation, in the decay of the uranium, for instance, about 0.1% of the mass of the original atom is lost. In theory, it should be possible to destroy matter and convert all of the rest-energy associated with matter into heat and light, but none of the theoretically known methods are practical. One way to harness all the energy assoc...
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