278
DOC. 24 RESPONSE TO
QUESTION
BY REIßNER
E
J~8Yaß =
G«aV
then
the
equations
of the
gravitational
field
(7b)
read:
[7]
clC1
T
=
K($ov + tov).
«
dxa
In
a
certain
sense,
the
quantities Gaov
can
be
designated
here
as
the
components
of
the
gravitational
field
strength.
Since
all
time
derivatives
are
to
vanish
in
our
case,
integration
over
the inside of
a
closed surface
yields
the
following system
of
equations,
which
correspond
to
Gauss's theorem:
J
(G1ovcos(nx)
+
G2ovcos(ny)
+
G3ovcos(nz))do
=
k
J (Sov + tov)dV,
where
n
denotes the
direction
of
the normal drawn outward
on
the surface
element
do,
and
dV
the volume element. If
a
surface
enclosing
the
system
E
along
with
its
gravitational
field
is
chosen
as
the
boundary
of the
integration space,
so
that it
includes,
up
to
a
neglible amount,
all
of the
gravitational energy,
then
one sees
that
the
number of the "lines of force of
gravitation" crossing
an
infinitely
distant surface
depends
solely on
the
integral
on
the
right-hand
side of the
equation
in
question. By
the
way,
one can see
from the
momentum
conservation laws
that,
given an
appropriate
choice of the reference
system,
the
right-hand
side
in
the
case
of interest
to
us
is
different from
zero
only
in the
case o
=
v
=
4.
From what has been
said it follows that the
strength
of
a
gravitational
field
at
a
great
distance from
E
depends, apart
from the
distance, only
on
/
$44
+
*44)
dV,
i.e.,
only
on
the total
energy
of
E
(energy
of the
matter +
gravitational energy).4
A
corresponding
conclusion
applies
to
the
ponderomotive
action that the
gravitational
field
generated by
E
exerts
on a mass
point
P that
is
sufficiently
far removed from
E.
But such
a
material
point
P
reacts,
in
turn, upon
E,
because of
(9b),
in such
a
manner
that the
equality
of action and reaction be
preserved.
Thus,
the total effect of
the force that P
exerts
on
E
through gravitation depends,
aside from the relative
position
of E and P and the
mass
of
P, only
on
the total
energy
of E.
Thus,
we
have
the
required
proof.
Furthermore,
the foundation of the
theory
does
not
incorporate only
the demand
4To be
sure,
the radial
symmetry
of
the field in the infinite is here
tacitly
assumed.
This
can
be attained
if
one
chooses the reference
system
such that the
principle
of
the
constancy
of
the
velocity
of
light
is
preserved
in
the infinite
(justified
reference
system
in
the
sense
of
the
original theory
of
relativity).