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. ***

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

* 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.]

**B 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.

*** 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.

SPACE AND TIME IN CLASSICAL MECHANICS

The purpose of mechanics is to describe how bodies change their position in space with “time.”  I should load my conscience with grave sins against the sacred spirit of lucidity were I to formulate the aims of mechanics in this way, without serious reflection and detailed explanations.  Let us proceed to disclose these sins.

It is not clear what is to be understood here by “position” and “space.”  I stand at the window of a railway carriage which is travelling uniformly, and drop a stone on the embankment, without throwing it.  Then, disregarding the influence of the air resistance, I see the stone descend in a straight line.  A pedestrian who observes the misdeed from the footpath notices that the stone falls to earth in a parabolic curve.  I now ask:  Do the “positions” traversed by the stone lie “in reality” on a straight line or on a parabola?  Moreover, what is meant here by motion “in space” ?  From the considerations of the previous section the answer is self-evident.  In the first place we entirely shun the vague word