The Mathematical Theory of RelativityEddington, Arthur Stanley, Sir
Science
The Mathematical Theory of Relativity
Eddington, Arthur Stanley, Sir
Relativity (Physics)
The advance of $1''.94$ per century has not exclusive reference to the
\index{Absolute change!rotation}%
\index{Foucault's pendulum}%
\index{Inertial frame, precession of}%
\index{Perigee, advance of}%
\index{Precession of inertial frame}%
\index{Rotation, absolute}%
moon; in fact the elements of the moon's orbit do not appear in~\Eq{(44.6)}. It
represents a property of the space surrounding the earth---a precession of the
inertial frame in this region relative to the general inertial frame of the sidereal
system. If the earth's rotation could be accurately measured by Foucault's
pendulum or by gyrostatic experiments, the result would differ from the
rotation relative to the fixed stars by this amount. This result seems to have
been first pointed out by J.~A. Schouten. One of the difficulties most often
urged against the relativity theory is that the earth's rotation relative to the
mean of the fixed stars appears to be an absolute quantity determinable by
dynamical experiments on the earth\footnotemark;\footnotetext
{\Title{Space, Time and Gravitation}, p.~152.}
it is therefore of interest to find that
these two rotations are not exactly the same, and the earth's rotation relative
to the stellar system (supposed to agree with the general inertial frame of the
universe) \emph{cannot be determined except by astronomical observations}.
The argument of the relativist is that the observed effect on Foucault's
pendulum can be accounted for indifferently by a field of force or by rotation.
The anti-relativist replies that the field of force is clearly a mathematical
fiction, and the only possible \emph{physical cause} must be absolute rotation. It is
pointed out to him that nothing essential is gained by choosing the so-called
non-rotating axes, because in any case the main part of the field of force
remains, viz.\ terrestrial gravitation. He retorts that with his non-rotating
axes he has succeeded in making the field of force vanish at infinity, so that
the residuum is accounted for as a local disturbance by the earth; whereas,
if axes fixed in the earth are admitted, the corresponding field of force becomes
larger and larger as we recede from the earth, so that the relativist demands
enormous forces in distant parts for which no physical cause can be assigned.
Suppose, however, that the earth's rotation were much slower than it is now,
\PageSep{100}
and that Foucault's experiment had indicated a rotation of only $-1''.94$ per
century. Our two disputants on the cloud-bound planet would no doubt carry
on a long argument as to whether this was essentially an absolute rotation of
the earth in space, the irony of the situation being that the earth all the while
was non-rotating in the anti-relativist's sense, and the proposed transformation
to allow for the Foucault rotation would actually have the effect of introducing
the enormous field of force in distant parts of space which was so much objected
to.
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