An Introduction to Modern Astrophysics · Problem 4.18

The Interaction of Light and Matter — Carroll & Ostlie

Physics — Astrophysics · relativistic-kinetic-energy

Problem

Show that the relativistic kinetic energy of a particle can be written as

K = \frac{p^2}{(1 + \gamma)m},

where

p

is the magnitude of the particle's relativistic momentum. This demonstrates that in the low-speed Newtonian limit of

v/c \ll 1

K = p^2/2m

(as expected).