472
DOC.
463 FEBRUARY
1918
463. From Rudolf
Förster
Essen,
6
Kunigunda
St.,
16 February 1918
Esteemed
Professor,
I
thank
you kindly
for
your
nice
letter
of 17
January.[1]
Again
I
could not make
up my
mind to
answer
it
immediately,
since
very
many
questions I hoped to
clarify
were
passing
through
my
head.
Now
that the
full extent of
the
mathematical
difficulties has become evident
to
me, however,
I
cannot
postpone
it
any
longer.
Your
objections
to
the
expositions
in
my
earlier
letter[2] apparently
are
based
on
misunderstandings
for
which, owing
to
my
so
frugal
choice of
words,
I
myself
am
at fault.
1)
B12,34
=
B13,24 = B14,23 =
0
should
not
be
a
satisfactory
condition
but
only a necessary one
which allows
ds2 to
be
changed
into the
orthogonal
form.
2)
I
derived
directly
from
the transformation
formulas
my generalization
of
the
Riemann
tensor
Buv,Po
to
the
case
of
an
asymmetric
fundamental
tensor,
without
resorting
to
splitting
it into
a
symmetric
and
an
antisymmetric
component.
The
occurrence
of
the
connected
symmetric
contravariant
tensor suv
automatically
results
as a
requirement.
3)
If
guv
is
reduced in
the
specified
manner
to
suv
+
auv
and forms
the
guv's (or
suv's
or auv’s)
from
the determinant
of
the
guv's
(or
suv’s,
or auv)'s,
then under
no
circumstance
is
guv
= suv
=
auv.
Rather,
guv
- smv
depends
not
only
on
the
six
tensor
of the
auv's,
but
also
on
all the
suv’s
besides in
a
quite
complicated
way.
It
is
thus
not
correct
that
in
my
tentatively
suggested electromagnetic
field
equations
the
symmetric
and
antisymmetric components
separate like oil and
water.
This
separation
occurs,
in the form
I
have
used, only
in
the
2nd Maxwell
equation;
in
the
first
one,
the
guv's
enter
completely.
I
had
unfortunately
omitted
to
emphasize
this
explicitly.
4)
My
considerations
on
“gravitational
fields
that
are
derived
from
a
potential”
have of themselves
nothing
to do with those
on
the
asymmetric
fundamental
tensor; indeed,
they
are
in conflict with them to
a
certain extent. Whereas
the
introduction
of
the
asymmetric
tensor is
a
generalization,
that
of
the
potential
is
a
specialization.
Your
objection
that the
field
energy depends essentially
on
the
first derivatives
of
the
guv's
does
admittedly
apply
to
my
auv’s
but
not to
my
potential.[3]
I
have
abandoned
asymmetric
guv
again
for
another
reason
besides,
which
I
want to
go
into
now.
In
a
note
to
appear shortly
in
the
Astronomischen Nachrichten
under the
pseudonym Rudolf Bach,[4]
I
conduct
probability
considerations
on
the
attractive