446 DOC.
439
JANUARY
1918
because
I
do not
see why
the
above condition
is
invariant
(provided
that
the other
Bik,lm’s
have
some
value
or other).
For
that,
a
tensor would
obviously
have to
exist
that
has
no
components
other
than
those mentioned above.
I also
was
occupied
for
a long
time with
proceeding
from
a
nonsymmetrical
guv;
but
I
have
almost
given up hope
of
getting
to
the
bottom of
this
(gravitation-
electromagnetism)
unification
mystery
in
this
way.
Various
reasons
arouse
serious
doubts:
1)
Electricity
has
the
two
constants,
the
electron’s
charge e
and
mass
u,
which
cannot be
invented
or
drawn out of
a
purely
mathematical
consideration.
2)
The mathematical
investigations
show
me,
time
and
again,
that the
symmet-
rical
and
antisymmetrical
components
of
guv
(=
suv
+
auv)
always
separate
like
oil
and
water.
I
draw
my examples
from
your
own interesting
reports:
Let
us
consider
the
two
equation
systems you propose
to be
electromagnetic[4]
,
Mt
{
oWß
l
+
».
ƒ
dx(a)a 1
a
)s 1
^
=
(0)F
(1)
f\uva
-
ßU
vp
a a
If in
the
first
system you
insert
gua, gav,
suv
+
auv,
etc.,
for
guv,
then the
portion
stemming
from
suv
disappears,
so
that
in fact
only
the
divergence
of
auv
remains
(in
the
sense
of absolute differential
calculus).
If
the
same
is
done
analogously
in
the
second
system,
there
remains
daß7
+
da
OV +
dxu
dXfj,
dxa
(2)
The
fact
that
auv
is
the
antisymmetrical
portion
of
guv
does
not
play
the
slightest
role in
(1) or (2).
The
hypothesis
of
interest
to
us
at
the
outset therefore
truly
plays
no
role in
the
result;
rather,
the
latter
agrees exactly
with
my
earlier electr.
equations
for
the
vacuum.-
Your
generalization
of
the
Riemann tensor would be
interesting
if
a
transpar-
ent
geometrical or
analytical
way
to its derivation could be
given
that
does not
make
use
of
the resolution
guv
=
suv
+
auv.
But it
does
seem
suspicious
that
saB
appears
as a
factor
of
the
second term.
3)
A study
of
the
gravitational
waves
has shown
me
that
something formally
different to
light
waves
is
involved. The
guv’s
themselves do
not
occur
in
the
energy
but
essentially
their
first
derivatives;[5]
this
I
cannot reconcile
either with
the fact
that
auv
signifies
the
electromagnetic
field.