# Energy, Momentum, and Mass

Almost everyone is familar with Einstein's famous equation *E=mc ^{2}*. It indicates the energy content of a particle of mass m at rest. This is a special case. More generally, particle energy depends on particle motion as well as its mass. The energy of a particle (mass m moving with momentum p) is given by

*E ^{2} = (pc)^{2} + (mc^{2})^{2}*

or:

*E ^{2} = p^{2}c^{2} + m^{2}c^{4}*.

^{2}, respectively. If you put these units in to the equation, you get:

[eV]^{2} = [eV/c]^{2}c^{2} + [eV/c^{2}]^{2}c^{4}.

Take a look at what happens. All the c's cancel out:

.

That is why particle physicists someitmes render this equation as

*E ^{2} = p^{2} + m^{2}*.

The c's are not exactly *dropped*; it is more like they are *implied* and it is understood that, given the proper units, they cancel.

Another thing: *if* the mass of a particle is very small and it has high momentum (p>>m, ignoring c's as we do above) - as in the case of many muons and electrons that come from decays of more massive particles in CMS - then the energy and the magnitude of the momentum are, in GeV units, *almost * the same (*E≈p* or *E≈pc*). Of course, for photons, which have no mass, *E = p* or *E = pc* is an exact equality and always true.Take a look at the screencast to see an example of how this can work out.

Learn more:

- construct the E-p-m relationship from data
- about those MeV and GeV units
- calculate the Z boson mass from CMS or ATLAS events