Question

Timelike trajectories are said to allow for causality, meaning that it is possible for an event at one position in the interval to be caused by something at the other position in the interval. Explain why this is true for timelike intervals, but not for spacelike intervals.

Answer 1

Consider two events: event A taking place at position and at time , and event B taking place at position and at time . Let a light signal is sent from position A at time , towards position B. If the relative distance between the positions and is such that light signal falls short in reaching it in time interval , then the event A and B are said to be Spacelike separated. If the light signal can just reach the position B at time then the Events A and B are called lightlike events. And if the light signal can reach position B before time , the events A and B are called timelike events.

When a signal travels from Event A to Event B , and cause something to happen at B at the moment it reaches B, then we say that Event A has caused Event B.

Any signal (even the fastest one the light signal) cannot travel between two spacelike separated events A and B, so event A cannot cause anything to occur at event B. Therefore, spacelike separated events do not allow causality.

Signals can travel between two timelike separated events A and B, event A can therefore cause something to happen at the event B. Hence, timelike events allow causality.