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 I 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.
Notes
*) The field disappears at the centre of the disc and increases
proportionally to the distance from the centre as we proceed outwards.
**) 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 K1 a gravitational field prevails).
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