116
DOC. 4 THEORY OF
STATIC
GRAVITATIONAL FIELD
that
the
inertial
mass
of the
system equals
E.
Thus,
if
one
wishes
to
stick with the
proportionality
of
the
gravitational
and
the
inertial
mass
of such
structures,
which
can
be viewed
as
material
points, one
has
to
assume
that the
gravitational
mass
of
our
system
also
equals
E.
But
according
to
the
above
argument,
this
is
only
the
case
if
we
do
not
assume
that the forces of the
gravitational
field
act
on
massless walls
subjected
to stresses.
A
wholly analogous argument may
be
applied
to
the
equations
of
motion of
[23]
material
points
derived in the
previous paper.
That
is to
say,
let
us
consider
a
box in
which
material
points fly
to
and
fro,
and rebound
completely elastically
from the
walls
(model
of
a
monatomic
gas).
Just
as
in the
case
of
the radiation
box,
one
finds
that the
gravitational
and inertial
mass
of the whole
system
are
equal
only
in the
case
where the
gravitational
field
exerts
no
forces
on
the massless frameworks that
are
in
states
of
stress.
Thus,
the
violation of the reaction
principle
contained in
equations
(3a)
and
(4)
still stands. The
expression
(4)
for the force
acting on
masses
at rest
in the
gravitational
field follows
necessarily
from
our
equations
of motion for the material
point.
It
is
therefore
natural
to
question
the
correctness
of these
equations;
but the
latter
can
hardly
be
altered,
as
the
following
argument
shows.
If
the
momentum of
a
material
point
in
a
space
of
constant
c
is
given by
[24]
mX
l/l
-
v2/c2
dc
-as
the old
theory
of
relativity
requires-then
the
expression
for the
momentum
in the
general
case
must
differ from the above
expression solely by
a
factor that is
a
function of
c
alone.3
For
dimensional
reasons,
this factor will have
to
be
a
power
of
c
(ca).
The
equations
of motion
must
therefore have the form
d
mxca
dt
4
N
i-i!
c2
if
Rxs
denotes the
x-component
of the force exerted
on
the
point by
the
gravitational
field,
and
Rxa
the
x-component
of the resultant
of
the forces
of
other
origin.
The
question
now
arises,
by
what
sort
of
an
expression
can Rs
be
given.
If
we are
dealing
with
a point
for which
precisely q=0,
then the force will have
to
be
proportional
to
the
vector
-m
grad
c, provided one
assumes
that the static
gravitational
field is
characterized
by
c.
This force will be able
to
differ from
-
m
grade
c
only
by
a
factor
that
depends
on c
alone;
this factor will also have
to
be,
for dimensional
reasons,
a
3Actually, one
would also have
to admit that the momentum
also
depends on
the
spatial
derivatives
of
c.
But
we
will
assume
that
this
is
not
the
case.