Pagina 122 van 212

This proves that the propositions of Euclidean geometry cannot

hold exactly on the rotating disc, nor 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.

[19] Throughout this consideration we have to use the Galileian

(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).