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 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: image001 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_ → _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 flashes (as 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.