E^2=(mc^2)^2+(pc)^2

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is a formula in special relativity that relates the relativistic energy, E, rest mass, , and momentum, p, of a particle. From it the momentum of a photon can be derived and so to the famous equation E=mc2.

Derivation

The relativistic equation for momentum is:

The equation for relativistic energy is:

These can be rearranged into the forms:

Subtracting the momentum equation from the energy equation an rearranging gives:

Other Formulae

The energy of a photon can be derived by setting the rest mass, , equal to zero, so:

Mass energy equivalence can be derived by setting the momentum, , to zero. This gives us one of the most famous equations in physics,