Introduction to Electrodynamics · Problem 12.20

Electrodynamics and Relativity — David J. Griffiths

Physics · invariant-interval

Problem

(a) Event

A

happens at point

(x_A = 5, y_A = 3, z_A = 0)

and at time

t_A

given by

ct_A = 15

; event

B

occurs at

(10, 8, 0)

and

ct_B = 5

, both in system

\mathcal{S}

. (i) What is the invariant interval between

A

and

B

? (ii) Is there an inertial system in which they occur simultaneously? If so, find its velocity (magnitude and direction) relative to

\mathcal{S}

. (iii) Is there an inertial system in which they occur at the same point? If so, find its velocity relative to

\mathcal{S}

. (b) Repeat part (a) for

A = (2, 0, 0)

ct = 1

; and

B = (5, 0, 0)

ct = 3