DOC.
32
INTEGRATION OF FIELD
EQUATIONS
209
A
=
I-
(21)
{10}
24ir
aß
df
This
expression
would
get
an
additional factor
1-c4
if
we
would
measure
time in
seconds and
energy
in
Erg. Considering
furthermore that
k
=
1.87
•
10-27,
it is
obvious that
A has,
in all
imaginable
cases, a
practically vanishing
value.
Nevertheless,
due to the inneratomic movement of
electrons,
atoms would have
[p.
696]
to radiate not
only electromagnetic
but also
gravitational energy,
if
only
in
tiny
amounts. As this
is
hardly
true
in
nature,
it
appears
that
quantum theory
would have
to
modify
not
only
Maxwellian
electrodynamics,
but also the
new theory
of
gravitation.
Supplement.
There is
a simple
way
to
clarify
the
strange
result that
gravitational
waves
(types a,
b,
c),
which
transport no
energy,
could exist. The
reason
is
that
they
[12]
are
not "real"
waves
but rather
"apparent"
waves,
initiated
by
the
use
of
a system
of
reference whose
origin
of
coordinates is
subject
to wavelike
jitters.
This is
easily
seen
in the
following manner.
If
one
selects from the
beginning
a
coordinate
system
in the
usual
manner
such that
/-g
=
1,
one gets
instead
of
(2)
as
field
equations
in the
{11}
absence
of
matter
£
+
d2Vv«
_
^Ymv
=
0
a
dxvdxa
dxßxa
fal
Substituting
into this
equation
Yuv
=
(x1
+
ix4),
one
obtains
10
equations
between the constants
auv
from which it
can
be
seen
that
only
a22,
a33,
and
a23
can
differ from
zero
(where
a22
+
a33 =
0). With this choice
of
system
of
reference
only
the
wave types (d,
e,
f)
exist,
which do
transport
energy.
The other
types
of
waves
are
eliminated
by
this choice of
coordinates;
in this
sense
they
are
not
"real"
waves.
Even
though
it turned out
to
be
advantageous
for this
investigation
not to
restrain
the choice
of
coordinate
system
for the calculation
of
a
first
approximation, our
last
result
shows, nevertheless,
that the
choice
of
coordinates under
the restriction
/-g
=
1
has
a
deep-seated physical
justification.
[13]