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83
Relativity: The Special and General Theory
Albert Einstein: Relativity
Appendix
Appendix
IV
The Structure
of Space According
to the General Theory
of
Relativity
(Supplementary
to Section
32)
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:
(1) There exists an average density of matter in the whole of space which is everywhere the same
and different from zero.
(2) The magnitude (" radius ") of space is independent of time.
Both these hypotheses proved to be consistent, according to the general theory of relativity, but
only after a hypothetical term was added to the field 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 motion of the system 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.