Relativity
The Special and General Theory

disc, on dividing the one by the other, he will not obtain as quotient the familiar number π = 3.14···, but a larger number,^[2] whereas of course, for a disc which is at rest with respect to K, this operation would yield  π  exactly. This proves that the propositions of Euclidean geometry cannot hold exactly on the rotating disc, or in general in a gravitational field, at least if we attribute the length 1 to the rod in all positions and in every orientation. Hence the idea of a straight line also loses its meaning. We are therefore not in a position to define exactly the co-ordinates x, y, z relative to the disc by means of the method used in discussing the special theory, and as long as the co-ordinates and times of events have not been defined, we cannot assign an exact meaning to the natural laws in which these occur.

Thus all our previous conclusions based on general relativity would appear to be called in question. In reality we must make a subtle detour in order to be able to apply the postulate of general relativity exactly. I shall prepare the reader for this in the following paragraphs.

[2] Throughout this consideration we have to use the Galilean (non-rotating) system K as reference-body, since we may only assume the validity of the results of the special theory of relativity relative to K (relative to K' a gravitational field prevails).