Introduction to Electrodynamics · Problem 12.28

Electrodynamics and Relativity — David J. Griffiths

Physics · hyperbolic-motion

Problem

Consider a particle in hyperbolic motion,

x(t) = \sqrt{b^2 + (ct)^2}, \quad y = z = 0.

(a) Find the proper time

\tau

as a function of

t

, assuming the clocks are set so that

\tau = 0

when

t = 0

. [Hint: Integrate Eq. 12.37.] (b) Find

x

and

v

(ordinary velocity) as functions of

\tau

. (c) Find

\eta^\mu

(proper velocity) as a function of

\tau