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17
Relativity: The Special and General Theory
every real case it must supply us with an empirical decision as to whether or not the conception
that has to be defined is fulfilled. That my definition satisfies this demand is indisputable. That light
requires the same time to traverse the path A
M as for the path B
M is in reality neither a
supposition nor a hypothesis about the physical nature of light, but a stipulation which I can make
of my own freewill in order to arrive at a definition of simultaneity."
It is clear that this definition can be used to give an exact meaning not only to two events, but to as
many events as we care to choose, and independently of the positions of the scenes of the events
with respect to the body of reference ¹
)
(here the railway embankment). We are thus led also to a
definition of " time " in physics. For this purpose we suppose that clocks of identical construction
are placed at the points A, B and C of the railway line (co?ordinate system) and that they are set in
such a manner that the positions of their pointers are simultaneously (in the above sense) the
same. Under these conditions we understand by the " time " of an event the reading (position of the
hands) of that one of these clocks which is in the immediate vicinity (in space) of the event. In 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).
Next: The Relativity of Simultaneity
Footnotes
1
)
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.
Relativity: The Special and General Theory