An observer in frame wants to measure how long something takes to occur

PHYSICS · Multi-part · A Level · Physics · Turning points in physics · Turning points in physics

Problem

An observer in frame

S

wants to measure how long something takes to occur. They will measure the start time of an event,

t_1

, at a place

x_1

, measure the end time of the event,

t_2

, at a place

x_2

and then say that the event took a time of

\Delta t = t_2 - t_1

. Another observer in frame

S'

, moving at a speed,

v

, relative to

S

, wants to measure how much time the event has taken. (1) a** Using the Lorentz transformation, write expressions for

t_1'

and

t_2'

. (2) b** If

\Delta t' = t_2' - t_1'

, show that

\Delta t' = \gamma \left( \Delta t - \frac{v}{c^2} \Delta x \right)