DOC.
465
FEBRUARY
1918
477
principle?
I
believe it would be
of great
importance
for science to
obtain this
integral,
but
it
simply
cannot be done. There
you
see
quite
clearly
that the
principle
of
general
transformability is not
a
principle
of
general
relativity.[10]
It
is
exactly
this that
I
considered
necessary
to
express
once,
because
some
actually
have
gained
the
impression
from
your
presentation
that
with
the
new
principle
the
fields of
arbitrarily
moving
electrons could
now
be
obtained. I heard
this
view
mentioned
even
in
Göttingen
at
the
discussion.[11]
If
this
were so,
if
there
really
were a
principle
of
general relativity,
then
this
principle
would
absolutely
have
to
read
as
it
was
recently
formulated in
the
Annalen
by
Dr.
Kretschmann,
and
I
consider
it
of
great
merit
that
he has
demonstrated
for
once
in full
detail that
such
a general
principle
of
relativity absolutely
cannot exist.[12]
Nevertheless, I
am a
very
enthusiastic
supporter of
your
theory of gravitation.
I
can only explain
your mystification
at this
by
the
probably
somewhat
incomplete
presentation
of
my
ideas. Most
importantly,
in
my
Göttingen
lectures
I
expressed
merely
in words
the
principle
that,
in
my opinion,
is
the
core
of
your
theory
of
gravitation;[13]
I did not
yet express
it in mathematical
formulas, though.
These
formulas
can
also
be
formed, however,
without the
least
difficulty
in
principle,
and
I
intend
to
do
so as soon as
I
have
free
time
for
these
investigations.
I would
also be
very pleased
if
my
ideas could
offer
you
some
inspiration,
just
as
you
have
stimulated
me so
much
already.[14]
19 February 1918[15]
In
the
meantime
I
have been
thinking
a
bit
more
about
your
curved
space.
You
are entirely right
with
your
assertion
p
=
2/k.R2;
I
was
mistaken.[16]
On
the other
hand, I
now
have
severe
doubts about whether
your
interpretation of
this
equation
really
is
correct.
Surely
the
field
equations
Guv
-
Aguv =
-k(Tuv-1/2guvT)
should
not
just
have
statistical
validity, so
to
speak?
For then
they
would
not
be funda-
mental
equations.
But
if they
are
valid in
every space element,
the
integral
you
have found would
surely
have
to
be
interpreted
such
that the
entire
space,
wher-
ever
there
are no
ordinary
accumulations
of matter, must
be
permeated
evenly
by
a
continuous, extremely
fine
material
haze
of
density
p.
For in
regions
that
are
at
an
“infinitely
remote” distance from
any
matter,
thus in
the
expansive empty
spaces
between
the
fixed stars,
the
gravitational potential must
satisfy
the
condi-
tion that the
space
exhibits
the
same
geometry throughout.
It
can
be
flat,
for this
the
condition
is
A
=
0,
then
p
=
0;
or on
the
other
hand,
it
can
have
a
constant
radius of curvature
R,
then
A
must
differ
from
zero
and then,
as
you
have
proven,
k.p
=
2A.
Hence
the
point
is
simply this,
that
in the flat
space
the
atmosphere
of