170
DOC.
13
GENERALIZED THEORY OF RELATIVITY
Here, too,
the material
process
of
an
arbitrary
kind is characterized
by
a
stress–
energy
tensor
Tuv.
But with this
conception
it is
a
scalar
that determines the
interaction between the
gravitational
field and the material
process.
As
Mr.
Laue
pointed
out to me, this
scalar
can
only
be
ETm-r,
[43]
which
I
will call the "Laue
scalar."17
Here
too
one can
then
do
justice
to
the
law
of
the
equivalence
of inertial and
gravitational
mass
up
to
a
certain
degree.
For
Mr.
Laue drew
my
attention
to
the fact that for
a
closed
system
fPdV =
f
Tudr.
[44]
From
this,
one can see
that
according
to
this
conception
too
the
gravity
of
a
closed
system
is
determined
by
its total
energy.
But the
gravity
of
systems
that
are
not
closed would
depend
on
the
orthogonal
stresses
T11
etc.
to
which
the system is subjected.
This leads
to
consequences
that
seem
to
me
unacceptable,
as
shall be demonstrated with the
example
of
cavity
radiation.
As
we
know,
for radiation in
a
vacuum,
the scalar P vanishes. If the radiation
is
enclosed in
a
massless
reflecting box,
then its walls
experience
tensile
stresses,
as
the result of which the
system-taken
as
a
whole-possesses
a
gravitational
mass
JPdr
corresponding
to
the
energy
E of the radiation.
/
S
But instead of
enclosing
the radiation in
a
hollow
box, I
now
imagine
that
it is
bounded
1.
by
the
reflecting
walls of
a
firmly
fixed shaft
S,
2.
by
two
reflecting
walls
W1
and
W2
that
can
be
displaced
vertically
and that
are
rigidly
tied
to
each other
by
a
rod.
In that
case,
the
gravitational
mass
JPdr
of the movable
system
amounts
only
to
one-third of the value obtained
in
the
case
of
a
box
moving
as a
whole.
Thus,
in order
to
lift the
radiation
against a gravitational
field,
one
would have
to
apply only
one-third of the
work that
one
would have
to
apply
in
the
previously
considered
case
of the radiation
enclosed in
a
box. This
seems unacceptable
to
me.
Of
course,
I
must
admit
that,
for
me,
the
most
effective
argument
for the
rejection
of such
a theory
rests
on
the conviction that
relativity
holds
not
only
with
respect
to
17Cf. Part
II, §1,
last
formula.