Relativity - The Special and General Theory | Page 8

you whether there is sense in this statement, you will
answer my question with a decided "Yes." But if I now approach you with the request to
explain to me the sense of the statement more precisely, you find after some
consideration that the answer to this question is not so easy as it appears at first sight.
After some time perhaps the following answer would occur to you: "The significance of
the statement is clear in itself and needs no further explanation; of course it would require
some consideration if I were to be commissioned to determine by observations whether in
the actual case the two events took place simultaneously or not." I cannot be satisfied
with this answer for the following reason. Supposing that as a result of ingenious
considerations an able meteorologist were to discover that the lightning must always

strike the places A and B simultaneously, then we should be faced with the task of testing
whether or not this theoretical result is in accordance with the reality. We encounter the
same difficulty with all physical statements in which the conception " simultaneous "
plays a part. The concept does not exist for the physicist until he has the possibility of
discovering whether or not it is fulfilled in an actual case. We thus require a definition of
simultaneity such that this definition supplies us with the method by means of which, in
the present case, he can decide by experiment whether or not both the lightning strokes
occurred simultaneously. As long as this requirement is not satisfied, I allow myself to be
deceived as a physicist (and of course the same applies if I am not a physicist), when I
imagine that I am able to attach a meaning to the statement of simultaneity. (I would ask
the reader not to proceed farther until he is fully convinced on this point.)
After thinking the matter over for some time you then offer the following suggestion with
which to test simultaneity. By measuring along the rails, the connecting line AB should
be measured up and an observer placed at the mid-point M of the distance AB. This
observer should be supplied with an arrangement (e.g. two mirrors inclined at 90^0)
which allows him visually to observe both places A and B at the same time. If the
observer perceives the two flashes of lightning at the same time, then they are
simultaneous.
I am very pleased with this suggestion, but for all that I cannot regard the matter as quite
settled, because I feel constrained to raise the following objection:
"Your definition would certainly be right, if only I knew that the light by means of which
the observer at M perceives the lightning flashes travels along the length A arrow M with
the same velocity as along the length B arrow M. But an examination of this supposition
would only be possible if we already had at our disposal the means of measuring time. It
would thus appear as though we were moving here in a logical circle."
After further consideration you cast a somewhat disdainful glance at me -- and rightly so
-- and you declare:
"I maintain my previous definition nevertheless, because in reality it assumes absolutely
nothing about light. There is only one demand to be made of the definition of
simultaneity, namely, that in 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 arrow M as for the path B arrow 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 * (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