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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 109 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.
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Relativity: The Special and General Theory
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.
Relativity: The Special and General Theory
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