DOC.
71
PRINCETON LECTURES 363
THE
GENERAL THEORY
Although
all of these effects
are
inaccessible
to
experi-
ment,
because
k
is
so
small,
nevertheless
they certainly
exist
according to
the
general theory
of
relativity.
We
must
see
in
them
a
strong support
for Mach’s ideas
as
to
the
relativity
of
all
inertial
actions.
If
we
think
these ideas
consistently through to
the end
we
must
expect
the
whole
inertia,
that
is,
the
whole guv-field, to
be
determined
by
the
matter
of
the
universe,
and
not mainly
by
the
boundary
[135]
conditions
at
infinity.
For
a
satisfactory
conception
of
the
guv-field
of
cosmical
dimensions,
the fact
seems
to
be of
significance
that the
relative
velocity
of
the
stars
is
small
compared to
the
velocity
of
light.
It
follows
from
this
that,
with
a
suit-
able choice
of
co-ordinates,
g44
is nearly
constant
in
the
universe,
at
least,
in
that
part
of the
universe in
which
there
is
matter.
The
assumption appears
natural,
more-
over,
that there
are
stars
in
all
parts
of
the
universe,
so
that
we
may
well
assume
that the
inconstancy
of
g44
depends
only
upon
the
circumstance that
matter
is
not
distributed
continuously,
but
is
concentrated in
single
celestial bodies
and
systems
of bodies.
If
we are
willing
to
ignore
these
more
local
non-uniformities
of
the
density
of
matter
and of the
guv-field,
in order
to
learn
something
of the
geometrical properties
of
the
universe
as a
whole,
it
appears
natural
to
substitute
for
the actual distribution
of
masses a
continuous
distribution,
and furthermore
to
assign
to
this
distribution
a
uniform
density
a.
In
this
imagined
universe
all
points
with
space
directions
will
be
geometrically equivalent;
with
respect to
its
space
extension
it
will
have
a
constant
curvature,
and
will
be
[136]
cylindrical
with
respect to
its
x4-co-ordinate.
The
pos-
sibility
seems
to
be
particularly satisfying
that the universe
is spatially
bounded and
thus,
in
accordance with
our
[103]