DOC.
47
307
identical clock located
at
the coordinate
origin.
Suppose
an
observer located
somewhere
in
space
perceives
the
indications
of
the
two
clocks in
a
certain
way,
e.g.,
optically.
As
the time
Ar
that
elapses
between
the instants
at
which
a
clock indication
occurs
and at which
this indication is
perceived
by
the
observer is
independent
of
r,
for
an
observer
situated
somewhere
in
space
the clock in
point P
runs
(1
+
\)
times faster than the clock
at
the
c2
coordinate origin.
In this
sense we
may
say
that the
process
occurring
in the
clock, and,
more
generally,
any
physical
process,
proceeds
faster the
greater
the gravitational potential
at
the position of the
process
taking
place.
There
exist "clocks" that
are
present
at
locations
of
different
gravita-
tional
potentials and
whose
rates
can
be
controlled with
great precision;
these
are
the
producers
of spectral
lines. It
can
be
concluded
from
the
aforesaid1 that the
wave
length
of
light
coming
from
the
sun's surface,
which
originates from such
a
producer,
is
larger
by
about
one
part in
two
millionth
than that of light
produced
by
the
same
substance
on
earth. [100]
$20.
The
effect
of
gravitation
on
electromagnetic
phenomena
If
we
refer
an
electromagnetic
process at
some
point
of time
to
a non-
accelerated reference
system
S'
that is
instantaneously
at rest
relative
to
the reference
system E
accelerated
as
above,
then the
following
equations
will hold
according to
(5)
and (6):
1
c
and
p'ux +
W
1 dL1
dV
cJT
~
W
etc
dZ
etc.
In
accordance with the
above,
we
may
readily
equate
the S'-referred
quantities
p',
u',
X',
L', x',
etc.,
with the
corresponding
E-referred
1While
assuming
that
equation (30a)
holds for
an
inhomogeneous
gravitational
field
as
well.