500
DOC.
485
MARCH
1918
course (Z[eit]s[chrift]
für
Math.
+
Phys.
62,
226ff.),[5]
and
then,
even
if
this
were
so, if,
therefore,
the
case
of constant guv's
existed,
one
would
obtain
through
transformation
to
the
orthogonal
form
dAu/dxv
+
dAv/dxu0.
=
The
Ai’s
would
then
be
linear
functions of the form
Eaikxk,
with
aik
=
-aki,
likewise
the
vector
potential
gp
=
gpaAa;
the
field
would be
constant and
homogeneous,
the
current
Iu
=
0.
If
there
are no electromagnetic
masses
at
infinity,
then the
el.m.
field must
disappear
completely.
This condition cannot
bring
down
my assumption,
though;
for
one
obviously
cannot
easily
dismiss
the
fact
that the
presence
of
an
electrom.
field
influences
the
guv’s
already by
the
field
energy.
The
usual
requirement
that,
under the
assumption
gii =
1, gi#k
=
0, electromagnet.
fields
can
be
assumed,
is
only
a
first
approximation.
6)
Furthermore,
I
would also
like to
make
you
aware
of
a
factor
which alto-
gether
does not suit
my purpose, namely,
the
assumption
for
your
tao’s
repeated
in
your
latest article
(Sitzungsberichte
of
14
February
[19]18),[6]
as
well
as
the
quasi-
requirement
of
limiting
the
coordinate choice
by
the
conditions V'dy'ux-
=
0,
in
order
to
arrive at
the retarded
potentials.
Regarding
the
former,
I
believe
that
we
shall succeed in
putting
the
right-hand
sides of
the
equations
dTaa/dxa
=
-dtaa/[d]xa
into
a
form in which
a
real tensor takes
the
place
of
tao,
but the latter
gives me
pause. For,
as
it
seems
to me,
in connection with
Schläfli’s
theorem,[7]
which
I
al-
ready
introduced in
my
first
letter,
this
factor
of
your
theory,
which
Kretschmann
designates as an
absolute
theory,[8]
would
thus
appear
in
a manner
extending
far
beyond previous
interpretations
insofar
as
not
only
the
inner,
natural
geometry
(g
intrinseca)
of
the
manifold defined
by
the
equation
ds2
=
X41guvdxudxv
would
have
physical significance,
but also
the
coincidental
shape
in which
this
manifold
(:in
the
sense
of the
theory of
the
unraveling
[Abwickelung]
of
spatial
structures:)
would be
bent
into
shape
in its
linear
10-dimensional
space.
7)
Have
you already
thought
of
applying
to
the
theory of gravitation
the
integral
equations
Hilbert
had
used with such
astonishing success on gas
theory?[9]
(:I
am
thinking of
this because
the
guv's
will
not be able to be
uniquely
determined
through
differential
equations
alone.:)
8)
Regarding
my profession,
I
can
just
inform
you
that
I
am
very
satisfied
with it
and do not wish to
exchange
it for
a
teacher’s,
not
even
for
an
academic
teacher’s,
even
disregarding
the
unworthily
meager
salary.
At
best,
a
position
at
a
research
institute
could
attract
me.
The results of
my
work here
are
connected
only very
remotely
to
the
mass-genocide.[10]
I
do
not
design cannons
but
occupy