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Einstein

Relativity: The Special and General Theory
Albert Einstein: Relativity
Part I: The Special Theory of Relativity
On the Idea of Time in Physics
Lightning has struck the rails on our railway embankment at two places A and B far distant from
each other. I make the additional assertion that these two lightning flashes occurred
simultaneously. If I ask 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 900) 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 M with the same velocity as
along the length B 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
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