Introduction to Electrodynamics · Problem 12.29

Electrodynamics and Relativity — David J. Griffiths

Physics · relativistic-momentum

Problem

(a) Repeat Prob. 12.2(a) using the (incorrect) definition

\mathbf{p} = m\mathbf{u}

, but with the (correct) Einstein velocity addition rule. Notice that if momentum (so defined) is conserved in

\mathcal{S}

, it is not conserved in

\bar{\mathcal{S}}

. Assume all motion is along the

x

axis. (b) Now do the same using the correct definition,

\mathbf{p} = m\boldsymbol{\eta}

. Notice that if momentum (so defined) is conserved in

\mathcal{S}

, it is automatically also conserved in

\bar{\mathcal{S}}

. [Hint: Use Eq. 12.43 to transform the proper velocity.] What must you assume about relativistic energy?