370 DOC.
42
SPECIAL AND GENERAL RELATIVITY
THIRTY-TWO
The
Structure
of
Space
According
to
the
General
Theory
of
Relativity
According
to
the
general
theory
of
relativity,
the
geo-
metrical
properties
of
space
are
not
independent,
but
they
are
determined
by matter.
Thus
we can
draw
conclusions
about the
geometrical
structure
of the universe
only
if
we
base
our
considerations
on
the
state
of the
matter
as
being something
that
is
known. We know
from
experience
that, for
a
suitably
chosen co-ordinate
system,
the velocities of
the
stars
are
small
as
compared
with the
velocity
of transmis-
sion
of
light.
We
can
thus
as a
rough approximation
arrive
at
a
conclusion
as
to
the
nature
of the universe
as a
whole,
if
we
treat
the
matter
as
being
at rest.
We
already
know
from
our
previous
discussion that the
behaviour of
measuring-rods
and clocks
is
influenced
by grav-
itational
fields, i.e.
by
the distribution of
matter.
This
in itself
is
sufficient
to
exclude the
possibility
of the
exact validity
of
Euclidean
geometry
in
our
universe. But
it
is
conceivable that
our
universe differs
only
slightly
from
a
Euclidean
one,
and
this notion
seems
all
the
more
probable,
since calculations
show
that the metrics of
surrounding space
is
influenced
only
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