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.
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