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.
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 of reference. But we have just seen that this assumption is
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