380 DOC.
382
SEPTEMBER
1917
In
this
way
the
approximate expression
for
U1
is
obtained
a
/
a
\
a
a 1
a2
-
1--
r2
V
ArJ
p 2
p2 2
r3
This
clearly
is
valid
at
a
point
with
x2
=
x3
=
0.
For
an
arbitrary
point,
we
find
the
B-components
axß
la2xß
~ r3
2
r4
'
(B
=
1,
2,
3)
(26)
The
divergence
of this
is
0?
div2l
=
-
(27)
2r4
and
equations
(1)
and
(10)
yield
t4
=
I^
4
4 r4
'
(28)
This
is
indeed
an energy
density
of the order of
magnitude one
would
expect
in
a
theory of
gravitation
that
excludes action
at
a
distance.
What
is
most
peculiar,
though, is
that-assuming
my
calculations above
are
correct-this
energy
can
be
transformed
away
to
zero
in the entire
field
outside
of the
body by
means
of
a
very
small
change
in the
coordinate
system.[25]
The
reason
for this
is
obviously
that
the
tuv’s
are
not
tensor
components.
I
must
say,
though,
that the
interpretation
of
t44
as
the
energy
density
does
not
seem
as
useful
to
me now as
it did
earlier.[26]
Now
what
remains to be examined
is
whether
expression
(28)
agrees
with
your
expression
(11)
in
“Approxim. Integr.”
When
your
values
r'44
= -kM/2Tr
(remaining
y'uv
=
0)
are
inserted
in
this
expression,
one
obtains,
as
far
as
I
see,
for
t44
a
value twice
that
of
(28)
with
an
opposite
sign.[27]
This
contradiction
may possibly
stem
from
an
incorrect
approximation.[28]
Well,
please
excuse me
for
conveying
to
you
all these
fairly boring
computa-
tions. Perhaps
you
will
find
something
of
interest in it
nevertheless,
and
at
all
events
you can see
that
I
am
occupying myself continually
with
your
theory.-
It
has
now
just
been
a
year
since
you
were here,[29]
and
we are
all
hoping keenly
that there
will
soon
be
a
repetition.
There
is
very,
very
much
to
discuss of
a
scientific
nature,
and science
aside,
your
visit would
bring
great
joy.
So
consider
the
matter.-
Here
courses
begin
next
week.
Lorentz
will
be
lecturing on
quantum
theory
this
year
as
well.