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.
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.
K = co-ordinate system x, y = two-dimensional co-ordinates x, y, z = three-
dimensional co-ordinates x, y, z, t = four-dimensional co-ordinates
t = time I = distance v = velocity
F = force
G = gravitational field