8Special relativity

IA Dynamics and Relativity

8.2 Spacetime diagrams

It is often helpful to plot out what is happening on a diagram. We plot them on

a graph, where the position

x

is on the horizontal axis and the time

ct

is on the

vertical axis. We use ct instead of t so that the dimensions make sense.

x

ct

world line

P

Definition

(Spacetime)

.

The union of space and time in special relativity is

called Minkowski spacetime. Each point

P

represents an event, labelled by

coordinates (ct, x) (note the order!).

A particle traces out a world line in spacetime, which is straight if the particle

moves uniformly.

Light rays moving in the x direction have world lines inclined at 45

◦

.

x

ct

light raylight ray

We can also draw the axes of

S

0

, moving in the

x

direction at velocity

v

relative to

S

. The

ct

0

axis corresponds to

x

0

= 0, i.e.

x

=

vt

. The

x

0

axis

corresponds to t

0

= 0, i.e. t = vx/c

2

.

x

ct

x

0

ct

0

Note that the

x

0

and

ct

0

axes are not orthogonal, but are symmetrical about

the diagonal (dashed line). So they agree on where the world line of a light ray

should lie on.