Introduction to Classical Mechanics · Problem 11.59

Relativity (Kinematics) — Morin

Physics — Mechanics · invariant-interval

Problem

Passing a train ** Person

A

stands on the ground, train

B

with proper length

L

moves to the right at speed

3c/5

, and person

C

runs to the right at speed

4c/5

C

starts behind the train and eventually passes it. Let event

E_1

be ``

C

coincides with the back of the train,'' and let event

E_2

be ``

C

coincides with the front of the train.'' Find the

\Delta t

and

\Delta x

between the events

E_1

and

E_2

in the frames of

A

B

, and

C

, and show that

c^2\Delta t^2 - \Delta x^2

is the same in all three frames.