mass-energy equivalence is the concept that all mass has an energy equivalence, and all energy has a mass equivalence. Special relativity expresses this relationship using the mass-energy equivalence formula
E = mc2
where
* E = the energy equivalent to the mass (in joules),
* m = mass (in kilograms), and
* c = the speed of light in a vacuum (celeritas) (in meters per second).
In physics, E = mc2 is the equation that expresses an equivalence between energy (E) and mass (m), in direct proportion to the square of the speed of light in a vacuum (c2). Several definitions of mass in special relativity may be validly used with this equation.
The equation was first published by Henri Poincare in 1900[citation needed], and later rederived (in a slightly different formulation) in 1905 by Albert Einstein in what are known as his Annus Mirabilis ("Wonderful year") Papers.
Thus c² is the conversion factor required to convert from units of mass to units of energy, i.e. the energy per unit mass. In unit-specific terms, E (joules or kg·m²/s²) = m (kilograms) multiplied by (299,792,458 m/s)2.
This formula proposes that when a body has a mass, it has a certain energy equivalence, even "at rest". This is opposed to the Newtonian mechanics, in which a massive body at rest has no kinetic energy, and may or may not have other (relatively small) amounts of internal stored energy (such as chemical energy or thermal energy), in addition to any potential energy it may have from its position in a field of force. That is why a body's rest mass, in relativity theory, is often called the rest energy of the body. The E of the formula can be seen as the total energy of the body, which is proportional to the mass of the body.
Conversely, a single photon traveling in empty space cannot be considered to have an effective mass, m, according to the above equation. The reason is that such a photon cannot be measured in any way to be at "rest" and the formula above applies only to single particles when they are at rest, and also systems at rest (i.e., systems when seen from their center of mass frame). Individual photons are generally considered to be "massless," (that is, they have no rest mass or invariant mass) even though they have varying amounts of energy and relativistic mass. Systems of two or more photons moving in different directions (as for example from an electron-positron annihilation) will have an invariant mass, and the above equation will then apply to them, as a system, if the invariant mass is used.
This formula also gives the quantitative relation of the quantity of mass lost from a resting body or a resting system (a system with no net momentum, where invariant mass and relativistic mass are equal), when energy is removed from it, such as in a chemical or a nuclear reaction where heat and light are removed. Then this E could be seen as the energy released or removed, corresponding with a certain amount of relativistic or invariant mass m which is lost, and which corresponds with the removed heat or light. In those cases, the energy released and removed is equal in quantity to the mass lost, times the speed of light squared. Similarly, when energy of any kind is added to a resting body, the increase in the resting mass of the body will be the energy added, divided by the speed of light squared.
