in this way, yet we may entertain the hope that the general law of
gravitation will be derivable from such gravitational fields of a
special kind. This hope has been realised in the most beautiful manner.
But between the clear vision of this goal and its actual realisation it
was necessary to surmount a serious difficulty, and as this lies deep
at the root of things, I dare not withhold it from the reader. We
require to extend our ideas of the space-time continuum still farther.
[17] This follows from a generalisation of the discussion in Section
XX.
XXIII.
BEHAVIOUR OF CLOCKS AND MEASURING-RODS ON A ROTATING BODY OF REFERENCE
Hitherto I have purposely refrained from speaking about the physical
interpretation of space- and time-data in the case of the general
theory of relativity. As a consequence, I am guilty of a certain
slovenliness of treatment, which, as we know from the special theory of
relativity, is far from being unimportant and pardonable. It is now
high time that we remedy this defect; but I would mention at the
outset, that this matter lays no small claims on the patience and on
the power of abstraction of the reader.
We start off again from quite special cases, which we have frequently
used before. Let us consider a space time domain in which no
gravitational field exists relative to a reference-body _K_ whose state
of motion has been suitably chosen. _K_ is then a Galileian
reference-body as regards the domain considered, and the results of the
special theory of relativity hold relative to _K_. Let us suppose the
same domain referred to a second body of reference _K _, which is
rotating uniformly with respect to _K_. In order to fix our ideas, we
shall imagine _K _ to be in the form of a plane circular disc, which
rotates uniformly in its own plane about its centre. An observer who is
sitting eccentrically on the disc _K _ is sensible of a force which
acts outwards in a radial direction, and which would be interpreted as
an effect of inertia (centrifugal force) by an observer who was at rest
with respect to the original reference-body _K_. But the observer on
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