DOC. 42 SPECIAL AND GENERAL RELATIVITY
393
The Structure
of
Space According
to the
General
Theory
of
Relativity
153
Hypothesis
(2)
appeared
unavoidable
to
me
at
the
time,
since
I
thought
that
one
would
get
into bottomless
specula-
tions if
one
departed
from
it.
However, already
in the
'twenties,
the
Russian mathema-
tician
Friedman
showed
that
a
different
hypothesis was
nat-
ural 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
Dop-
pler'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,
there-
fore,
be considered
to
some
extent
as
a
confirmation of the
theory.
There
does
arise, however,
a
strange difficulty.
The
inter-
pretation
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