On the Relativity
of the Conception of Distance







Einstein: Let us consider two particular points on the train travelling along the embankment with the velocity v, and inquire as to their distance apart.






AAF: Let's consider 'em in earnest.





Einstein: 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.




AAF: And we call it 'co-ordinate system'.




Einstein: It is the simplest plan to use the train itself as reference-body (co-ordinate system).





AAF: It is; and we call it 'the moving co-ordinate system'.





Einstein: 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.




AAF: Very simple indeed!

How does Ernest feel about everyone using him to do their considering in?

Good question, Anonymous!


As for 'earnest' as in the phrase 'in earnest',
I guess, it should feel very proud, if the ID theory is correct;
and it must feel nothing at all, if Darwin's theory
is the correct one; correct?

Einstein: It is a different matter when the distance has to be judged from the railway line. Here the following method suggests itself.





AAF: It's a bit more complicated; I admit.





Einstein: 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.





AAF: True; both points are moving at the same speed in the same direction.





Einstein: 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.






AAF: You stated In Section 8: "For this purpose we suppose that clocks of identical construction are placed at the points A, B of the railway line (co-ordinate system) and that they are set in such a manner that the positions of their pointers are simultaneously (in the above sense) the same"; right, Albert?





Einstein: The distance between these points A and B is then measured by repeated application of thee measuring-rod along the embankment.





AAF: Of course!

Einstein: The distance between these points A and B is then measured by repeated application of thee measuring-rod along the embankment.





AAF: Of course!




Einstein: 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.




AAF: If the measurements are done correctly, the result must be exactly the same.




Einstein: This circumstance leads us to a second objection which must be raised against the apparently obvious consideration of Section 6.



AAF: What is it?



Einstein: 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.





AAF: This whole thing is a piece of cake for land surveyors, I presume!