The Relativity of Simultaneity

Up to now our considerations have been referred

to a particular body of reference, which we have styled a "railway embankment." We suppose a very long train travelling along the rails with the constant velocity $v$ and in the direction indicated in [fig:1]Fig. 1. People travelling in this train will with advantage use the train as a rigid reference-body (co-ordinate system); they regard all events in

025 reference to the train. Then every event which takes place along the line also takes place at a particular point of the train. Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment. As a natural consequence, however, the following question arises:

Are two events (e.g. the two strokes of lightning $A$ and $B$ ) which are simultaneous with reference to the railway embankment also simultaneous relatively to the train? We shall show directly that the answer must be in the negative.

When we say that the lightning strokes $A$ and $B$ are

simultaneous with respect to the embankment, we mean: the rays of light emitted at the places $A$ and $B$ , where the lightning occurs, meet each other at the mid-point $M$ of the length $A ⟶ B$ of the embankment. But the events $A$ and $B$ also correspond to positions $A$ and $B$

on the train. Let $M^{'}$ be the mid-point of the distance $A ⟶ B$ on the travelling train. Just when the flashesAs judged from the embankment. of lightning occur, this point $M^{'}$ naturally coincides with the point $M$ , but it moves towards the right in the diagram with the velocity $v$ of the train. If an observer sitting in the position $M^{'}$ in the train did not possess this velocity, then he would remain permanently at $M$ , and the light rays emitted by the flashes of lightning $A$ and $B$ would reach him simultaneously, i.e. they would meet just where he is situated. Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from $B$ , whilst he is riding on ahead of the beam of light coming from $A$ . Hence the observer will see the beam of light emitted from $B$ earlier than he will see that emitted from $A$ . Observers who take the railway train as their reference-body must therefore come

to the conclusion that the lightning flash $B$ took place earlier than the lightning flash $A$ . We thus arrive at the important result:

Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity). Every

reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event.

Now before the advent of the theory of relativity it had always tacitly been assumed in physics that the statement of time had an absolute significance, i.e. that it is independent of the state of motion of the body