Introduction to Classical Mechanics · Problem 13.10
General Relativity — Morin
Physics — Mechanics · doppler-effect-4-vectors
Problem
Consider a photon traveling in the x direction. Ignoring the y and z components, and setting c=1, the 4-momentum is (p,p). In matrix notation, what are the Lorentz transformations for the frames traveling to the left and to the right at speed v? What is the new 4-momentum of the photon in these new frames? Accepting the fact that a photon's energy is proportional to its frequency, verify that your results are consistent with the Doppler results in Section 11.8.1.