[7] We suppose further that, when three events _A, B_ and _C_ occur in
different places in such a manner that, if _A_ is simultaneous with
_B_, and _B_ is simultaneous with _C_ (simultaneous in the sense of
the above definition), then the criterion for the simultaneity of the
pair of events _A, C_ is also satisfied. This assumption is a physical
hypothesis about the law of propagation of light; it must certainly be
fulfilled if we are to maintain the law of the constancy of the
velocity of light _in vacuo_.
This stipulation contains a further physical hypothesis, the validity
of which will hardly be doubted without empirical evidence to the
contrary. It has been assumed that all these clocks _go at the same
rate_ if they are of identical construction. Stated more exactly: When
two clocks arranged at rest in different places of a reference-body are
set in such a manner that a _particular_ position of the pointers of
the one clock is _simultaneous_ (in the above sense) with the _same_
position, of the pointers of the other clock, then identical settings
are always simultaneous (in the sense of the above definition).
IX.
THE RELATIVITY OF SIMULTANEITY
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
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