Talk:PlanetPhysics/Structure of Space According to the General Theory of Relativity Supplementary to Section 32

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%%% Primary Title: The Structure of Space According to the General Theory of Relativity (Supplementary to Section 32)
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\begin{document}

 \subsection{The Structure of Space According to the General Theory of Relativity
(Supplementary to Section 32)}
From \htmladdnormallink{Relativity: The Special and General Theory}{http://planetphysics.us/encyclopedia/SpecialTheoryOfRelativity.html} by \htmladdnormallink{Albert Einstein}{http://planetphysics.us/encyclopedia/AlbertEinstein.html}
Since the publication of the first edition of this little book, our
knowledge about the structure of space in the large (``cosmological
problem'') has had an important development, which ought to be
mentioned even in a popular presentation of the subject.

My original considerations on the subject were based on two
hypotheses:

\begin{enumerate}
\item There exists an average density of matter in the whole of space
which is everywhere the same and different from zero.

\item The \htmladdnormallink{magnitude}{http://planetphysics.us/encyclopedia/AbsoluteMagnitude.html} (``radius'') of space is independent of time.
\end{enumerate}

Both these hypotheses proved to be consistent, according to the
\htmladdnormallink{general theory}{http://planetphysics.us/encyclopedia/GeneralTheory.html} of relativity, but only after a hypothetical term was
added to the \htmladdnormallink{field}{http://planetphysics.us/encyclopedia/CosmologicalConstant2.html} equations, a term which was not required by the
theory as such nor did it seem natural from a theoretical point of
view (``cosmological term of the field equations'').

Hypothesis (2) appeared unavoidable to me at the time, since I thought
that one would get into bottomless speculations if one departed from
it.

However, already in the 'twenties, the Russian mathematician Friedman
showed that a different hypothesis was natural from a purely
theoretical point of view. He realized that it was possible to
preserve hypothesis (1) without introducing the less natural
cosmological term into the field equations of gravitation, if one was
ready to drop hypothesis (2). Namely, the original field equations
admit a solution in which the ``world radius'' depends on time
(expanding space). In that sense one can say, according to Friedman,
that the theory demands an expansion of space.

A few years later Hubble showed, by a special investigation of the
extra-galactic nebulae (``milky ways''), that the spectral lines
emitted showed a red shift which increased regularly with the distance
of the nebulae. This can be interpreted in regard to our present
knowledge only in the sense of Doppler's principle, as an expansive
\htmladdnormallink{motion}{http://planetphysics.us/encyclopedia/CosmologicalConstant.html} of the \htmladdnormallink{system}{http://planetphysics.us/encyclopedia/SimilarityAndAnalogousSystemsDynamicAdjointnessAndTopologicalEquivalence.html} of stars in the large---as required, according
to Friedman, by the field equations of gravitation. Hubble's discovery
can, therefore, be considered to some extent as a confirmation of the
theory.

There does arise, however, a strange difficulty. The interpretation of
the galactic line-shift discovered by Hubble as an expansion (which
can hardly be doubted from a theoretical point of view), leads to an
origin of this expansion which lies ``only'' about $10^9$ years ago,
while physical astronomy makes it appear likely that the development
of individual stars and systems of stars takes considerably longer. It
is in no way known how this incongruity is to be overcome.

I further want to rernark that the theory of expanding space, together
with the empirical data of astronomy, permit no decision to be reached
about the finite or infinite character of (three-dimensional) space,
while the original ``static'' hypothesis of space yielded the closure
(finiteness) of space.

\newpage

~\\
$K$ = co-ordinate system \\
$x, y$ = \htmladdnormallink{two-dimensional}{http://planetphysics.us/encyclopedia/CoriolisEffect.html} co-ordinates \\
$x, y, z$ = three-dimensional co-ordinates \\
$x, y, z, t$ = four-dimensional co-ordinates \\

~\\
$t$ = time \\
$I$ = distance \\
$v$ = \htmladdnormallink{velocity}{http://planetphysics.us/encyclopedia/Velocity.html} \\

~\\
$F$ = \htmladdnormallink{force}{http://planetphysics.us/encyclopedia/Thrust.html} \\
$G$ = gravitational field

\subsection{References}
This article is derived from the Einstein Reference Archive (marxists.org) 1999, 2002. \htmladdnormallink{Einstein Reference Archive}{http://www.marxists.org/reference/archive/einstein/index.htm} which is under the FDL copyright.

\end{document}