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Einstein

Relativity: The Special and General Theory
three perpendiculars can be determined by a series of manipulations with rigid measuring−rods
performed according to the rules and methods laid down by Euclidean geometry.
In practice, the rigid surfaces which constitute the system of co−ordinates are generally not
available ; furthermore, the magnitudes of the co−ordinates are not actually determined by
constructions with rigid rods, but by indirect means. If the results of physics and astronomy are to
maintain their clearness, the physical meaning of specifications of position must always be sought
in accordance with the above considerations. 3)
We thus obtain the following result: Every description of events in space involves the use of a rigid
body to which such events have to be referred. The resulting relationship takes for granted that the
laws of Euclidean geometry hold for "distances;" the "distance" being represented physically by
means of the convention of two marks on a rigid body.
Notes
1) Here we have assumed that there is nothing left over i.e. that the measurement gives a whole
number. This difficulty is got over by the use of divided measuring−rods, the introduction of which
does not demand any fundamentally new method.
[A] Einstein used "Potsdamer Platz, Berlin" in the original text. In the authorised translation this was
supplemented with "Tranfalgar Square, London". We have changed this to "Times Square, New
York", as this is the most well known/identifiable location to English speakers in the present day.
[Note by the janitor.]
2) It is not necessary here to investigate further the significance of the expression "coincidence in
space." This conception is sufficiently obvious to ensure that differences of opinion are scarcely
likely to arise as to its applicability in practice.
3) A refinement and modification of these views does not become necessary until we come to deal
with the general theory of relativity, treated in the second part of this book.
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