Lectures on Physics has been derived from Benjamin Crowell's Light and Matter series of free introductory textbooks on physics. See the editorial for more information....

The correspondence principle for mass-energy

Show that the equation E = mγc2 obeys the correspondence principle.

As we accelerate an object from rest, its mass-energy becomes greater than its resting value. Classically, we interpret this excess mass-energy as the object's kinetic energy,

Expressing γ as (1 - v2/c2)-1/2 and making use of the approximation (1 + ε)p ≈ 1 + pε for small ε, we have γ ≈ 1 + v2/2c2, so

which is the classical expression. As demanded by the correspondence principle, relativity agrees with classical physics at speeds that are small compared to the speed of light.

Last Update: 2010-11-11