Relativistic Energy: Matter & Photon

[serverxeon]

Homework Statement

Energy of a particle may be of the form:

$$E = \gamma mc^{2}$$
$$E = \sqrt{p^{2}c^{2} + m^{2}c^{4}}$$

Are both valid for every particle? matter and photon?
Can they be equated?

 

[tiny-tim]

Hi serverxeon!

(have a gamma: γ and a square-root: √ )

The first one doesn't work for m = 0 (a photon), since γ is not defined for v = c,

but apart from that, yes, they're both valid for every particle.

For m ≠ 0, you can prove the equivalence by using p = mvγ.