structural:summarization
Momentum of light

Light particles, or photons, travel at the speed of c, the constant that is conventionally known as the speed of light. This statement is not a tautology, since many modern formulations of relativity do not start with constant speed of light as a postulate. Photons therefore propagate along a lightlike world line and, in appropriate units, have equal space and time components for every observer.

A consequence of Maxwell's theory of electromagnetism is that light carries energy and momentum, and that their ratio is a constant: E / p = c {\displaystyle E/p=c}. Rearranging, E / c = p {\displaystyle E/c=p}, and since for photons, the space and time components are equal, E / c must therefore be equated with the time component of the spacetime momentum vector.

Photons travel at the speed of light, yet have finite momentum and energy. For this to be so, the mass term in γmc must be zero, meaning that photons are massless particles. Infinity times zero is an ill-defined quantity, but E / c is well-defined.

By this analysis, if the energy of a photon equals E in the rest frame, it equals E ′ = (1 − β) γ E {\displaystyle E^{\prime }=(1-\beta)\gamma E} in a moving frame. This result can be derived by inspection of Fig. 3-9 or by application of the Lorentz transformations, and is consistent with the analysis of Doppler effect given previously.