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Relativity: The Special and General Theory
Albert Einstein: Relativity
Part I: The Special Theory of Relativity
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
advantage uew 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 :
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 M1 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 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:
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.