Introduction to Classical Mechanics · Problem 12.1

Relativity (Dynamics) — Morin

Physics — Mechanics · relativistic-energy-momentum-derivation

Problem

Accepting the facts that the energy and momentum of a photon are

E = h\nu

and

p = h\nu/c

(where

\nu

is the frequency of the light wave, and

h

is Planck's constant), derive the relativistic formulas for the energy and momentum of a massive particle,

E = \gamma mc^2

and

p = \gamma mv

. Hint: Consider a mass

m

that decays into two photons. Look at this decay in the rest frame of the mass, and then in a frame where the mass has speed

v

. You'll need to use the Doppler effect.