DOC. 24 RESPONSE TO
QUESTION
BY REIßNER 277
be another
symmetric
four-dimensional
expression
for the conservation
laws,
other
than
(9b).
But
equation (9b)
can
indeed elicit the doubts
expressed by
Mr. Reißner.
According
to
(9b),
the
equations
for the
momentum
of the static
gravitational
field
in the absence of material
processes
have the
following
form:
d
fp-j
+
d
^2
+
_
Q
dx
dy
dz
The
equilibrium
of
the static
gravitational
field
is
reduced here to
an equilibrium
exclusively
of
surface forces, whereas, indeed,
a
kind of
volume
forces should exist
in
the
gravitational
field, since,
according
to
the basic
assumptions
of the
theory,
the
gravitational
field would be
expected
to act
on
its
own
"energetic components"
tov
just
as
it
acts
on
the
corresponding energetic components
3!ov
of
matter.
It should be
noted, however,
that the
possibility
of such
a
representation
does
not
imply anything
about the
physical
nature
of the
effects under consideration.
All that
the
possibility
of such
a
representation
does
say
is
that the
momentum
law
is
valid.
When Mr. Reißner
says
that,
for the basic idea of the
theory
not to
be
abandoned,
the
existence
of
an
energy
density
of
a
static
gravitational
field
must
have
as a
consequence
a
transfer
of
momentum
from the
gravitational
field
to
itself,
then
I
agree
with him.
But this
momentum
transfer
must
be
compensated
by
the effects
(momentum
transfer)
of
pressure forces,
because otherwise the
momentum
law would
be
violated. Volume forces and surface forces
are
not
separable
in the
momentum
conservation
law for the
gravitational field,
and the
momentum
law
requires
that all
forces be reducible
to
surface
forces.3
But
on
the other
hand,
one
must
demand of the
theory
that the
energetic
components
of
a gravitational
field
belonging
to
a
closed
system
make
exactly
the
same
contribution
to
the
gravitational
mass
of the whole
system
as
do the
energetic
components
of the
matter
constituting
the
system.
The
theory actually
satisfies this
condition,
as
is evident
from the
following.
In
a
formerly gravitation-free
space
(
dguv/dxo
=
0
)
a
we place a
static material
system
X
,
the
energetic components
of which
belong
in
part
to
the
gravitational
field
produced
by
the
parts
of
X
.
If
one
sets
3In
electrostatics,
for
example,
the fact that all forces
acting on
matter
can
be
represented by
Maxwellian stresses does not
permit
the conclusion that
no
volume forces
actually
act
on
the
matter; rather,
this is
merely a
mode
of
representation
that makes the
validity
of
the
principle
of
reaction evident.
[6]