# 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

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

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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