The Mathematical Theory of RelativityEddington, Arthur Stanley, Sir
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The Mathematical Theory of Relativity
Eddington, Arthur Stanley, Sir
Relativity (Physics)
It may seem strange that we should be able to deduce the contraction of
a material rod and the retardation of a material clock from the general
geometry of space and time. But it must be remembered that the contraction
and retardation do not imply any absolute change in the rod and clock. The
``configuration of events'' constituting the four-dimensional structure which
we call a rod is unaltered; all that happens is that the observer's space and
time partitions cross it in a different direction.
\PageSep{27}
Further we make no prediction as to what would happen to the rod set
in motion in an actual experiment. There may or may not be an absolute
change of the configuration according to the circumstances by which it is set
in motion. Our results apply to the case in which the rod after being set in
motion is (according to all experimental tests) found to be similar to the rod
in its original state of rest\footnotemark.\footnotetext
{It may be impossible to change the motion of a rod without causing a rise of temperature.
Our conclusions will then not apply until the temperature has fallen again, i.e.\ until the temperature-test
shows that the rod is precisely similar to the rod before the change of motion.}
When a number of phenomena are connected together it becomes somewhat
arbitrary to decide which is to be regarded as the explanation of the
others. To many it will seem easier to regard the strange property of
the fundamental velocity as \emph{explained} by these differences of behaviour of
the observers' clocks and scales. They would say that the observers arrive
at the same value of the velocity of light because they omit the corrections
which would allow for the different behaviour of their measuring-appliances.
That is the relative point of view, in which the relative quantities, length,
time, etc., are taken as fundamental. From the absolute point of view, which
has regard to intervals only, the standards of the two observers are equal and
behave similarly; the so-called \emph{explanations} of the invariance of the velocity
of light only lead us away from the root of the matter.
Moreover the recognition of the FitzGerald contraction does not enable
us to avoid paradox. From~\Eq{(5.3)} we found that $S'$'s~longitudinal measuring-rods
were contracted relatively to those of~$S$. From~\Eq{(5.1)} we can show similarly
that $S$'s~rods are contracted relatively to those of~$S'$. There is complete
reciprocity between $S$ and~$S'$. This paradox is discussed more fully in \Title{Space,
Time and Gravitation}, p.~55.
\Section{11.}{Simultaneity at different places}
\index{Simultaneity at different places}%
It will be seen from the fourth equation of~\Eq{(5.1)}, viz.\
\[
dt = -\beta (t' - ux'/c^{2}),
\]
that events at different places which are simultaneous for~$S'$ are not in general
simultaneous for~$S$. In fact, if $dt' = 0$,
\[
dt = -\beta u\, dx'/c^{2}.
\Tag{(11.1)}
\]
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