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Einstein

Relativity: The Special and General Theory
Albert Einstein: Relativity
Part I: The Special Theory of Relativity
On the Relativity of the Conception of Distance
Let us consider two particular points on the train 1) travelling along the embankment with the
velocity v, and inquire as to their distance apart. We already know that it is necessary to have a
body of reference for the measurement of a distance, with respect to which body the distance can
be measured up. It is the simplest plan to use the train itself as reference−body (co−ordinate
system). An observer in the train measures the interval by marking off his measuring−rod in a
straight line (e.g. along the floor of the carriage) as many times as is necessary to take him from
the one marked point to the other. Then the number which tells us how often the rod has to be laid
down is the required distance.
It is a different matter when the distance has to be judged from the railway line. Here the following
method suggests itself. If we call A1 and B1 the two points on the train whose distance apart is
required, then both of these points are moving with the velocity v along the embankment. In the first
place we require to determine the points A and B of the embankment which are just being passed
by the two points A1 and B1 at a particular time t — judged from the embankment. These points
A and B of the embankment can be determined by applying the definition of time given in Section 8.
The distance between these points A and B is then measured by repeated application of thee
measuring−rod along the embankment.
A priori it is by no means certain that this last measurement will supply us with the same result as
the first. Thus the length of the train as measured from the embankment may be different from that
obtained by measuring in the train itself. This circumstance leads us to a second objection which
must be raised against the apparently obvious consideration of Section 6. Namely, if the man in the
carriage covers the distance w in a unit of time — measured from the train, — then this distance —
as measured from the embankment — is not necessarily also equal to w.
Footnotes
1) e.g. the middle of the first and of the twentieth carriage.
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