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:

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 $\longrightarrow$ 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 (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 incompatible with the most natural definition of
simultaneity; if we discard this assumption, then the conflict between
the law of the propagation of light in vacuo and the principle of
relativity (developed in Section VI) disappears.

We were led to that conflict by the considerations of Section VI,
which are now no longer tenable. In that section we concluded that the
man in the carriage, who traverses the distance $w$ *per second* relative
to the carriage, traverses the same distance also with respect to the
embankment *in each second* of time. But, according to the foregoing
considerations, the time required by a particular occurrence with
respect to the carriage must not be considered equal to the duration
of the same occurrence as judged from the embankment (as
reference-body). Hence it cannot be contended that the man in walking
travels the distance $w$ relative to the railway line in a time which is
equal to one second as judged from the embankment.

Moreover, the considerations of Section VI are based on yet a second assumption, which, in the light of a strict consideration, appears to be arbitrary, although it was always tacitly made even before the introduction of the theory of relativity.

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