Relativity - The Special and General Theory | Page 9

this manner a
time-value is associated with every event which is essentially capable of observation.
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).
Notes
*) We suppose further, that, when three events A, B and C occur in different places in
such a manner that 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 the 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.

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 a vantage view the train as a rigid reference-body
(co-ordinate system); they regard all events in
Fig. 01: file fig01.gif
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 arrow 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 arrow 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.
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 7) disappears.
We were led to that conflict by the considerations of Section 6, which are now