Spacetime Diagram

As an example of a spacetime diagram consider the following situation; a man holds his arm out straight. The distance from his shoulder to his elbow is 35 cm and the distance from his wrist to his elbow is also 35 cm. As measured in the man’s rest frame a pulse of light leaves his shoulder in the direction of his elbow and a pulse of light leaves his wrist and is also directed to his elbow. Model this situation by assuming that the shoulder, elbow and wrist all lay on a straight line. The three events of concern here are

E₁ = Light leaves shoulder = (0 cm, 0 cm)

E₂ = Light arrives at elbow = (35 cm, 35 cm)

E₃ = Light leaves wrist = (0 cm, 70 cm)

These events, and the wordlines of the light pulses, as shown below in Fig. 1

The spacetime interval between events in the (ct, x) plane is defined as

Observing Fig. 1 we see three spacetime intervals of interest. They are