DOC.
21
THEORY OF RELATIVITY
261
From this
point
of
view,
there
is
no
substantial difference between
inertia and
gravitation;
for
it
depends
on
the coordinate
system,
i.e., on
the
point
of
view,
whether, at
a
certain
instant,
a
body
is
under the exclusive influence of inertia
or
under the combined influence of inertia and
gravitation.
Thus, widely
known
physical
facts lead
us
to
the
general relativity
principle, i.e.,
to
the
conception
that the laws of
nature
are
to
be formulated
in
such
a
way
that
they
hold with
respect
to
arbitrarily
moving
coordinate
systems.
[22]
The
Theory
of
the Gravitational
Field
From
what has been said
so
far,
one sees
immediately
that the
general relativity
principle
must
lead
to
a theory
of the
gravitational
field. For if
one
starts
out
from
the
gravitation-free
inertial
system
K and introduces
a
coordinate
system
K' that
moves
arbitrarily
with
respect
to
the
former, then,
with
respect
to
K',
there exists
a
precisely
known
gravitational
field,
and
one can
find the
general properties
of
gravitational
fields from the
general properties
of those
gravitational
fields
at
which
one
arrives in this
way.
However,
one
must
be careful
not to
assume
that,
conversely, every gravitational
field
can
be made
to vanish,
i.e.,
can
be turned into
a
gravitation-free region, by
means
of
a
suitable choice of the coordinate
system.
For
example,
it
is
impossible
to
make the
gravitational
field of the Earth vanish
by means
of
a
suitable choice of the
coordinate
system.
In
fact,
for
a
region
of
finite
extension this
is
only possible
with
gravitational
fields of
a very special
kind.
But for
an infinitely
small
region
the
coordinates
can
always
be chosen such that
no
gravitational
field will be
present
in
it.
With
respect
to
such
an
infinitely
small
region
one
may
then
assume
that the
special theory
of
relativity
is
valid. That
way
the
general theory
of
relativity
is
connected with the
special theory
of
relativity,
and the results of the latter
can
be
utilized for the former.
The
Bending
of
Light
Rays
A
simple argument
shows that
a
ray
of
light
that
propagates rectilinearly
and
uniformly
with
respect
to
the inertial
system
K
must
describe
a
curved
trajectory
with
respect
to
the coordinate
system
K'
that is
in
accelerated translational motion. From
this
we
conclude that
light rays are
bent
by
gravitational
fields,
which
means,
according
to
Huygens's principle,
that the
velocity
of
light
in
gravitational
fields
depends
on
the location. This
consequence
was
confirmed for the first time
on
the
occasion of the solar
eclipse
in 1919.
[23]