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 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 $$A \longrightarrow B$$ 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 $$A \longrightarrow B$$ on the travelling train. Just when the flashes 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