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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]
Total energy is the sum of rest energy = and relativistic kinetic energy: = = + Invariant mass is mass measured in a center-of-momentum frame. For bodies or systems with zero momentum, it simplifies to the mass–energy equation E 0 = m 0 c 2 {\displaystyle E_{0}=m_{0}c^{2}} , where total energy in this case is equal to rest energy.
The mathematical by-product of this calculation is the mass–energy equivalence formula, that mass and energy are essentially the same thing: [14]: 51 [15]: 121 = = At a low speed (v ≪ c), the relativistic kinetic energy is approximated well by the classical kinetic energy.
The relativistic mass is the sum total quantity of energy in a body or system (divided by c 2).Thus, the mass in the formula = is the relativistic mass. For a particle of non-zero rest mass m moving at a speed relative to the observer, one finds =.
Mass is also equivalent to a certain amount of energy, and likewise always appears associated with it, as described in mass–energy equivalence. The formula E = mc 2, derived by Albert Einstein (1905) quantifies the relationship between relativistic mass and energy within the concept of special
By mass–energy equivalence, the electronvolt corresponds to a unit of mass. It is common in particle physics, where units of mass and energy are often interchanged, to express mass in units of eV/c 2, where c is the speed of light in vacuum (from E = mc 2).
In particle physics, the invariant mass m 0 is equal to the mass in the rest frame of the particle, and can be calculated by the particle's energy E and its momentum p as measured in any frame, by the energy–momentum relation: = ‖ ‖ or in natural units where c = 1, = ‖ ‖.
With respect to classical physics, conservation laws include conservation of energy, mass (or matter), linear momentum, angular momentum, and electric charge. With respect to particle physics, particles cannot be created or destroyed except in pairs, where one is ordinary and the other is an antiparticle.