Introduction to Electrodynamics · Problem 12.24

Electrodynamics and Relativity — David J. Griffiths

Physics · proper-velocity

Problem

(a) Equation 12.40 defines proper velocity in terms of ordinary velocity. Invert that equation to get the formula for

\mathbf{u}

in terms of

\boldsymbol{\eta}

. (b) What is the relation between proper velocity and rapidity (Eq. 12.34)? Assume the velocity is along the

x

direction, and find

\eta

as a function of

\theta