700 DOC.
661
NOVEMBER
1918
I
have
studied
your paper
but
am more
than
ever
convinced
that
you
have
gotten
onto
a
very
dubious
track[4]
which
is
regrettably
costing you your
valuable
energy.
I
believe
you
are
placing
too much
importance
on
the beautiful
conserva-
tion
laws to which the
gauge
invariance[5] leads.[6]
It
is not
so surprising
that the
form of Maxwellian
electromagnetism
comes
out of it,
since
it
is
known
a
priori
that the
Maxwell
equations satisfy
the
gauge
invariance.[7]
The
question
is,
how-
ever,
whether the other
parts
of
the
action function
are gauge
invariant
as
well.
The
existence of
spectral
lines
(electrons
of
a
specific size), etc., speaks very
much
against it,
as
I
already
said
earlier.[8]
But
now
I
would
like
to
present you
with
another
counterargument
that
suggests
itself
from
your
latest
considerations.
I
make
the
following
preamble.
If
we
want to retain
the
common
units
for
mass
and
length
and
define
the
infinitesimal
displacement
in
your
geometric theory,
we
must
write,
instead
of
1
+
dQ,[9]
1
+
7dQ,
where
7
is
a
universal constant.
We
must do
this
if
we
set
dQ
=
Qvdxv,
where
Qv
signifies
the
four vector of
the
el[ectric]
potential
in
standard
units
(cm,
gr).[10]
In the Hamilton function
given on page
8
of
your paper,
which should be valid
at
least
outside
of electrons and
atoms,
we
must
then
write
72QiQi
instead of
QiQi,
and
on page (9), as
the
equation
for
the
electromagnetic
field,
dfik
_
3
Vff72
dxk 2
A
-p
.
In
this
connection
7
means
the
gravitational
constant.
(-
10-27.)[11]
This
field
equation is
easily
integrated
to determine
the
field
outside of
an
electron, whereby
it
is
legitimate
to select
guv
=
-1
0 0
0
0
-1
0
0
0
0
-1
0
0
0 0
1.
One
is
then
simply
led
to
the
equation[12]
AQ
=
-const
Q,
the
solution of which
is
e-r/r.[13]
For
Q4
to
come
out
practically
=
const/r,
[14]
l-
A-r
must
be
a
very large length (approximately
the
world
radius?) (measured