382
DOC.
23
PROPAGATION
OF
LIGHT
According
to
our
assumption, exactly
the
same
relation
will
hold
in
the
case
where
this
same
process
takes
place
in
the
system
K that
is
not
accelerated but
is provided
with
a
gravitational
field.
In that
case we can
replace yh
by
the
potential
$ of the
gravitation
vector in
S2,
if
the
arbitrary
constant
of $
in
S1
is
set
equal
to
zero.
We
thus
have
(1a)
E1
= E2
+
cr
This
equation
expresses
the
energy
principle
for
the
process
under consideration. The
energy
E1
arriving
in
S1
is greater
than the
energy
E2
(measured
by
the
same
kinds
of
instruments),
which
was
emitted
in
S2,
by
the
potential energy
of the
mass
E2/c2
in
the
gravitational
field.
Thus,
for the
energy
principle
to
be
satisfied, a
potential
energy
of
gravitation corresponding
to
the
(gravitational) mass
E/c2
must be
ascribed
to
the
energy
E
before
its emission at
S2.
Our
assumption
of the
equivalence
of K
and
K'
thus
removes
the
difficulty
mentioned
at
the
beginning
of
this
section,
which
the
ordinary
theory
of
relativity
leaves
unresolved.
The
meaning
of
this
result becomes
especially
clear
upon
consideration of the
following cyclic process:
1.
Energy
E
(measured
at
S2)
is
sent in
the
form
of radiation from
S2
to
S1,
where,
according
to
the result
we
have
just
obtained,
the
energy E(1
+ yh/c2)
is
absorbed
(as
measured
at
S1).
2.
A
body
W
of
mass
M
is
lowered
from
S2
to
S1,
in
which
process
an
amount
of
work
Myh is
released.
3.
The
energy
E
is
transferred
from
S1
to
the
body
W while W
is
in
S1.
This
changes
the
gravitational
mass
M
such
that
its
new
value will
be M'.
4.
W
is
lifted
back
to
S2,
which
requires
the
application
of
work M'yh.
5.
E
is
transferred from
W back to
S2.
The
only
effect
of
this
cyclic
process
is
that
has
undergone an
energy
increase
of
E(yh/c2)
and
that the
quantity
of
energy
M'yh
-
Myh
has
been
conveyed
to
the
system
in
the
form
of
mechanical work.
According
to the
energy principle,
we
must
then
have
Elh.
=
M'yh
-
Myh
c2
or