In the foregoing remarks, however, we have neglected one important
aspect of Eddington's theory. In addition to the fact that the
whole general theory of relativity can be deduced from a few simple
assumptions, interest attaches to the manner of the deduction and the
considerations by which the substantial import of mathematical formulæ
is made less, or at least other, than would naturally be supposed.
A good example is afforded by a paragraph headed "Interpretation
of Einstein's Law of Gravitation."[30] The law concerned is not[Pg 90]
, which is not supposed to be quite accurate where
stellar distances are concerned; it is the modified law:
where must be very small, so small that within
the solar system the new law gives the same results, within
the limits of observation, as . The new law
is shown to be equivalent to the assumption that, in empty
space, the radius of curvature in every direction is everywhere
But this is interpreted as a law about
our measuring rods—namely, that they adjust themselves to the radius
of curvature at any place and in any direction. It is interpreted as
meaning:
"The length of a specified material structure bears a constant ratio to
the radius of curvature of the world at the place and in the direction
in which it lies." And the following gloss is added:
"The law no longer appears to have any reference to the constitution
of an empty continuum. It is a law of material structure showing what
dimensions a specified collection of molecules must take up in order
to adjust itself to equilibrium with the surrounding conditions of the
world."
Public-domain text, read in full here on John Shaqi.
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