First of all, we have to think of the distance between two events, not
between two bodies. This follows at once from what we have found as
regards time. If two bodies are moving relatively to each other—and
this is really always the case—the distance between them will be
continually changing, so that we can only speak of the distance
between them at a given time. If you are in a train traveling towards
Edinburgh, we can speak of your distance from Edinburgh at a given
time. But, as we said, different observers will judge differently as
to what is the “same” time for an event in the train and an event in
Edinburgh. This makes the measurement of distances relative, in just
the same way as the measurement of times has been found to be relative.
We commonly think that there are two separate kinds of interval between
two events, an interval in space and an interval in time: between your
departure from London and your arrival in Edinburgh, there are 400
miles and ten hours. We have already seen that another observer will
judge the time differently; it is even more obvious that he will judge
the distance differently. An observer in the sun will think the motion
of the train quite trivial, and will judge that you have traveled the
distance traveled by the earth in its orbit and its diurnal rotation.
On the other hand, a flea in the railway carriage will judge that you
have not moved at all in space, but have afforded him a period of
pleasure which he will measure by his “proper” time, not by Greenwich
Observatory. It cannot be said that you or the sun dweller or the
flea are mistaken: each is equally justified, and is only wrong if he
ascribes an objective validity to his subjective measures. The distance
in space between two events is, therefore, not in itself a physical
fact. But, as we shall see, there is a physical fact which can be
inferred from the distance in time together with the distance in space.
This is what is called the “interval” in space-time.
Public-domain text, read in full here on John Shaqi.
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