DOC.
23
PROPAGATION
OF
LIGHT
385
is
nothing
that
compels us
to
assume
that
the
clocks
U,
which
are
situated in
different
gravitational
potentials,
must
be
conceived
as
going
at
the
same
rate.
On the
contrary,
we
must
surely
define
the time in
K
in such
a manner
that the number of
wave
crests
and
troughs
between
S2
and
S1
be
independent
of the absolute
value
of the
time,
because
the
process
under consideration
is stationary
by
its nature.
If
we
did not
satisfy
this
condition,
we
would
arrive
at
a
definition of
time
upon
whose
application
time would
enter
explicitly
the
laws
of
nature,
which would
surely
be unnatural and
inexpedient.
Thus,
the
clocks in
S1
and
S2
do not
both
give
the "time"
correctly.
If
we measure
the
time at
S1
with
the
clock
U,
then
we
must
measure
the time
at
S2
with
a
clock
that
runs
1
+
9/c2 times slower than the clock U when
compared
with
the latter
at
one
and
the
same
location.
Because,
when
measured
with such
a clock,
the
frequency
of the
light ray
considered
above
is,
at its emission at
S2,
L
1
+
I
and
is
thus, according
to
(2a),
equal
to
the
frequency
v1
of the
same
ray
of
light on
its
arrival
at
S1.
From
this follows
a
consequence
of fundamental
significance
for this
theory. Namely,
if the
velocity
of
light
is
measured
at
different
places
in
the
accelerated, gravitation-free
system
K'
by means
of
identically
constituted
clocks
U,
the
values
obtained
are
the
same
everywhere.
According
to
our
basic
assumption,
the
same
holds also
for
K.
But,
according
to what has
just
been
said, we
must
use
clocks
of unlike constitution
to
measure
time
at
points
of different
gravitational potential.
To
measure
time
at
a
point
whose
gravitational
potential is
$
relative to
the coordinate
origin,
we
must
employ
a
clock
which,
when
moved to
the coordinate
origin, runs
(1 + O/c2)
times slower
than the
clock with which
time
is
measured
at
the coordinate
origin.
If
c0
denotes the
velocity
of
light
at
the
coordinate
origin,
then the
velocity
of
light c
at
a point
with
a
gravitational
potential
$
will
be
given by
the relation
[10]
(3)
c
=
c1[1
+
c2].
The
principle
of
the
constancy
of
the
velocity
of
light
does
not
hold
in this
theory
in
the
formulation
in which it
is
normally
used
as
the
basis
of the
ordinary theory
of
relativity.
§
4. Bending
of
Light Rays
in the Gravitational Field
From the
proposition just proved,
that the
velocity
of
light
in
the
gravitational
field
is
a
function of
place, one can easily
deduce,
via
Huygens'
principle,
that
light rays
propagated
across a gravitational
field must
undergo
deflection.
For let
c
be
a
plane