*) We suppose further, that, when three events A, B and C occur in different places in such a manner that A is simultaneous with B and B is simultaneous with C (simultaneous in the sense of the above definition), then the criterion for the simultaneity of the pair of events A, C is also satisfied.  This assumption is a physical hypothesis about the the of propagation of light:  it must certainly be fulfilled if we are to maintain the law of the constancy of the velocity of light in vacuo.

THE RELATIVITY OF SIMULATNEITY

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.  People travelling in this train will with a vantage view the train as a rigid reference-body (co-ordinate system); they regard all events in

Fig. 01:  file fig01.gif

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 be 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 arrow B of the embankment.  But the events A and B also correspond to positions A and B on the train.  Let M1 be the mid-point of the distance A arrow B on the travelling train.  Just when the flashes (as judged from the embankment) of lightning occur, this point M1 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 M1 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: