I've only just begun reading about relativity, and am finding Einstein's popular level book "Relativity: The Special and General Theory" quite satisfying. This particular example, from Section X (ON THE RELATIVITY OF THE CONCEPTION OF DISTANCE) has me a bit confused, though:(adsbygoogle = window.adsbygoogle || []).push({});

It is a different matter when the distance has to be judged from the railway line. Here the following method suggests itself. If we callA'andB'the two points on the train whose distance apart is required, then both of these points are moving with the velocityvalong the embankment. In the first place we require to determine the pointsAandBof the embankment which are just being passed by the two pointsA'andB'at a particular timet-- judged from the embankment. These pointsAandBof the embankment can be determined by applying the definition of time given in Section VIII. The distance between these pointsAandBis then measured by repeated application of the measuring-rod along the embankment.

A prioriit is by no means certain that this last measurement will supply the same result as the first^{1}.^{1}the first measurement being the distance between the pointsA'andB'on the train, judged from the train as reference body, simply by the "repeated application of the measuring-rod."

Any hints as to why it is "by no means certain" that the distances would be the same? I'm trying to picture the setup of the example, but am having a hard time. The definition of time of an event was given as "the reading (position of the hands) of that one of these clocks^{2}which is in the immediate vicinity (in space) of the event."

^{2}"clocks of identical construction placed at points D, E, and F of the railway line (co-ordinate system)" which were started with identical settings, simultaneously.

I'm picturing something like an A clock and a B clock, which are stopped as pointsA'andB', on the train, pass by, and would have identical settings (identical times) when stop. Is that even close? I guess you'd need plenty of clocks. In any case, the distance between the could be measured, as he says, but why wouldn't they necessarily be the same distance apart asA'andB', as measured from the train as reference body?

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# Einstein on the relativity of distance.

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