The Mathematical Theory of RelativityEddington, Arthur Stanley, Sir
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The Mathematical Theory of Relativity
Eddington, Arthur Stanley, Sir
Relativity (Physics)
Our system of coordinates is a \emph{static system}, that is to say the $g_{\mu\nu}$ do not
change with the time. (An arbitrary coordinate-system has not generally this
property; and further when we have to take account of two or more attracting
bodies, it is in most cases impossible to find a strictly static system of coordinates.)
Taking an observer at rest in the system $(r, \theta, \phi, t)$ a wave emitted
by one of the atoms will reach him at a certain time~$\delta t$ after it leaves the
atom; and owing to the static condition this time-lag remains constant for
subsequent waves. Consequently the waves are received at the same time-periods
as they are emitted. We are therefore able to compare the time-periods
$dt$ of the different atoms, by comparing the periods of the waves received from
them, and can verify experimentally their dependence on the value of~$\sqrt{\gamma}$ at
the place where they were emitted. Naturally the most hopeful test is the
comparison of the waves received from a solar and a terrestrial atom whose
periods should be in the ratio $1.00000212 : 1$. For wave-length $4000$~Å, this
amounts to a relative displacement of $0.0082$~Å of the respective spectral
lines. The verdict of experiment is not yet such as to secure universal assent;
but it is now distinctly more favourable to Einstein's theory than when \Title{Space,
Time and Gravitation} was written.
The quantity~$dt$ is merely an auxiliary quantity introduced through the
equation~\Eq{(38.8)} which defines it. The fact that it is carried to us unchanged
by light-waves is not of any physical interest, since $dt$~was \emph{defined} in such a
way that this must happen. The absolute quantity~$ds$, the interval of the
vibration, is not carried to us unchanged, but becomes gradually modified as
the waves take their course through the non-Euclidean space-time. It is in
transmission through the solar system that the absolute difference is introduced
into the waves, which the experiment hopes to detect.
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