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.
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