DOCS.
661,
662 NOVEMBER-DECEMBER
1918 701
in
cm,
a
very large
number
indeed!).
The order of
magnitude
of
1/r
is
hence in
any
case
well
over
1/A ~
1013.
This universal
constant
has
the dimension of
an
electricity
quantity and must be
of
immense
size if
the
theory is
not to violate
the
known laws of electrostatics. Not
the
slightest
hint
of
this
can
be
found in
the
known laws of nature.
It
therefore
seems downright
insane to introduce
such
a
thing
for
the
sake of
the
gauge
invariance! This
surely
is
a
very
serious
objection.
Moreover,
I
absolutely
cannot
concede
that
your
theory
leads to
the
equation
of motion
d{mui)
ds
1
dgaß
2 dxi
muau13
=
0
because
this
expression,
in which
m
is
supposed
to be
constant,
of
course,
is
invariant neither
against
coordinate
nor gauge
transformation.[15] In
your
consid-
eration
you
cannot
assume a
priori
that the
Qi’s
do not
yield any moving
forces.
The
special
role of
the
electrically uncharged point-mass
consists in
that
its
path
does not
depend on
the
electrical
field
fik.
I
am
convinced,
now as
before,
that
from
the
aspect of invariance and
gauge invariance,
the
geodesic
line
is
the
only
one
that
can come
into consideration at
all.-[16]
Furthermore, I
do
not
see
how
the introduction
of
a gauge according
to
F
=
a
is
possible,
even
though
one can
make free
use
of
a
gauge
factor.[17]
It
may very
well
be
possible,
for
inst.,
that
any
attempt
at
imposing
such
a
gauge
would
bring
about
singularities.-
My
first
objection
seems
to
me
by
far
the
most
substantial: the
gauge
invari-
ance
leads to
a
modification
of
the
laws,
which not
a
single
fact
supports,
and
also
leads to
a new
natural
constant
that
is
meaningless, according
to
current
knowledge.
Added
to
this
is
that
the
existence
of
spectral lines, i.e.,
of clocks
independent of their
prehistory,
makes the
only
natural
way
seem
to
be
treating
ds
as an
invariant
from
the
beginning.
I
am
already looking
forward
to
being
able to
chat-and
argue-with
you
in
February.
Until
then, cordial
regards, yours,
Einstein.
662. From Arnold Sommerfeld
[Munich,] 3
December
1918
Dear
Einstein,
For
a
particular
purpose (a
popular
book
on
atomic
models)
I
need
a
simple
description
of
the
foundations
of
quantum
statistics.[1] For
that
I
must make
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