definition of time. We have to imagine each of these clocks fixed at a
point on the non-rigid reference-body. These clocks satisfy only the
one condition, that the readings which are observed simultaneously on
adjacent clocks (in space) differ from each other by an indefinitely
small amount. This non-rigid reference-body, which might appropriately
be termed a reference-mollusc , is in the main equivalent to a
Gaussian four-dimensional co-ordinate system chosen arbitrarily. That
which gives the mollusc a certain comprehensibility as compared with
the Gauss co-ordinate system is the (really unjustified) formal
retention of the separate existence of the
space co-ordinates as opposed to the time co-ordinate. Every point on
the mollusc is treated as a space-point, and every material point which
is at rest relatively to it as at rest, so long as the mollusc is
considered as reference-body. The general principle of relativity
requires that all these molluscs can be used as reference-bodies with
equal right and equal success in the formulation of the general laws of
nature; the laws themselves must be quite independent of the choice of
mollusc.
The great power possessed by the general principle of relativity lies
in the comprehensive limitation which is imposed on the laws of nature
in consequence of what we have seen above.
XXIX.
THE SOLUTION OF THE PROBLEM OF GRAVITATION ON THE BASIS OF THE GENERAL
PRINCIPLE OF RELATIVITY
If the reader has followed all our previous considerations, he will
have no further difficulty in understanding the methods leading to the
solution of the problem of gravitation.
We start off on a consideration of a Galileian domain, _i.e._ a domain
in which there is no gravitational field relative to the Galileian
reference-body _K_. The behaviour of measuring-rods and clocks with
reference to _K_ is known from the special theory of relativity,
likewise the behaviour of isolated material points; the latter move
uniformly and in straight lines.
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