In special relativity, the energymomentum relation is a relation between the energy, momentum and the mass of a body:
where c is the speed of light, is total energy, is invariant mass, and is momentum.
For a body in its rest frame, the momentum is zero, so the equation simplifies to
If the object is massless then the energy momentum relation reduces to
as is the case for a photon.
In natural units the energymomentum relation can be expressed as
where is angular frequency, is rest mass and is wave number.
In Minkowski space, energy and momentum (the latter multiplied by a factor of c) can be seen as two components of a Minkowski fourvector. The norm of this vector is equal to the square of the rest mass of the body, which is a Lorentz invariant quantity and hence is independent of the frame of reference.
When working in units where c = 1, known as the natural unit system, the energymomentum equation reduces to
In particle physics, energy is typically given in units of electron volts (eV), momentum in units of eV/c, and mass in units of eV/c^{2}. In electromagnetism, and because of relativistic invariance, it is useful to have the electric field E and the magnetic field B in the same unit (gauss), using the cgs (gaussian) system of units, where energy is given in units of erg, momentum in g.cm/s and mass in grams.
Energy may also in theory be expressed in units of grams, though in practice it requires a large amount of energy to be equivalent to masses in this range. For example, the first atomic bomb liberated about 1 gram of heat, and the largest thermonuclear bombs have generated a kilogram or more of heat. Energies of thermonuclear bombs are usually given in tens of kilotons and megatons referring to the energy liberated by exploding that amount of trinitrotoluene (TNT).
