The Mathematical Theory of RelativityEddington, Arthur Stanley, Sir
Science
The Mathematical Theory of Relativity
Eddington, Arthur Stanley, Sir
Relativity (Physics)
A possible indication that there is no real mass in de~Sitter's world is
afforded by a calculation of the gravitational flux~\Eq{(63.4)}. By~\Eq{(63.6)} this is
\[
4\pi r^{2} \left(-\delta y - \frac{2}{r}\, \delta\gamma\right) dt,
\]
since $dt$~can no longer be replaced by~$ds$. On substituting for~$\gamma$ it is found
that the flux vanishes for all values of~$r$. It is true that as we approach the
boundary $dt/ds$~becomes very great, but the complete absence of flux right up
to the boundary seems inconsistent with the existence of a genuine mass-horizon.
I believe then that the mass-horizon is merely an illusion of the observer
at the origin, and that it continually recedes as we move towards it.
\Section{71.}{Properties of Einstein's cylindrical world}
\index{Einstein's cylindrical world}%
Einstein does not regard the relation~\Eq{(69.5)}
\[
M = \tfrac{1}{2}\pi R = \tfrac{1}{2}\pi \lambda^{-\frac{1}{2}}
\Tag{(71.1)}
\]
as merely referring to the limiting case when the amount of matter in the
world happens to be sufficient to make the form cylindrical. He considers it
to be a necessary relation between $\lambda$ and~$M$; so that the constant~$\lambda$ occurring
in the law of gravitation is a function of the total mass of matter in the world,
and the volume of space is conditioned by the amount of matter contained
in it.
The question at once arises, By what mechanism can the value of~$\lambda$ be
adjusted to correspond with~$M$? The creation of a new stellar system in a
distant part of the world would have to propagate to us, not merely a gravitational
field, but a modification of the law of gravitation itself. We cannot
trace the propagation of any such influence, and the dependence of~$\lambda$ upon
distant masses looks like sheer action at a distance.
\PageSep{167}
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