956
DOCUMENT
661 NOVEMBER 1918
Weitaus
am
Wesentlichen scheint mir mein
erster
Einwand: Die Aichinvarianz
führt
zu
einer Modifikation der
Gesetze,
für
die kein
einzigen
Faktum
spricht,
so-
wie
zu
einer nach
unserem heutigen
Wissen
bedeutungslosen
neuen
Naturkonstan-
ten.
Dazu
kommt,
dass die Existenz
von Spektrallinien,
d. h.
von
der
Vorgeschichte
unabhängiger Uhren,
es
als das
einzig
Natürliche erscheinen
lässt,
das ds
von
An-
fang
als eine Invariante
zu
behandeln.
Ich
freue
mich schon
sehr
darauf,
im Februar mit Ihnen
plaudern
und-streiten
zu
können. Einstweilen herzliche Grüsse
von
Ihrem
Einstein.
ALS
(SzZE
Bibliothek, Hs.
91:549). [24 051].
[1]The
year
is
provided by
the
reference
to an early
version
of
Weyl
1919c.
[2]The
manuscript
enclosed
with Doc.
657, a
revised version of which would
be
published as Weyl
1919c. In
this
manuscript,
the author further
elaborated the
physical aspects
of
the
unified
theory
of
gravity
and
electromagnetism
based
on a generalization
of
Riemannian
geometry
first
presented
in
Weyl
1918b
(see
Doc.
472,
note
3,
for
more
details
on
this
theory).
[3]The political
situation
in
Germany
continued
to
deteriorate
as
the future form
of
government
was fiercely
debated
(see
Doc. 655,
note 3).
[4]Weyl
received
very encouraging
reactions from other
colleagues (as
pointed
out
in
Doc.
619).
Directly
contradicting Einstein’s assessment, Sommerfeld wrote that
the
successes
of
the
theory
"scarcely
leave
room
for
doubt that
you are
on
the
right
track
and
not
on a
road
to
nowhere"
("lassen
kaum einen Zweifel
zu,
dass Sie
auf
dem
richtigen Wege
und nicht
auf
einem
H[o]lzwege
sind." See
Arnold Sommerfeld to Hermann
Weyl,
7
July
1918,
SzZE
Bibliothek,
Hs.
91:751).
Gustav Mie also
had
high hopes
for
Weyl’s theory.
He wrote: "It looks
to
me as
if
the
key
to
the
mystery
of
matter will
now really
be found.
Previously,
I
did
not
think that I would live
to
see
the
day,
but
now my hope
is
renewed" ("Mir
scheint,
als ob
jetzt
wirklich
der
Schlüssel
zum
Geheimnis der Materie
gefunden
werden wird. Ich
glaubte
vorher
nicht,
dass ich
es
noch erleben
würde,
aber
nun schöpfe
ich
neue
Hoffnung."
Gustav Mie
to
Hermann
Weyl,
26 October
1918,
SzZE
Bibliothek,
Hs.
91:674).
[5]Einstein
probably
took this
term
from
Weyl’s manuscript.
In the revised version
of
this
manu-
script,
the
phrase "measuring
rod invariance"
("Maßstab-Invarianz")
used in
Weyl
1918b,
1918d is
replaced
by
"gauge
invariance"
("Eichinvarianz,"
Weyl
1919c,
p.
114).
[6]See
Doc. 619,
note 12,
for discussion
of
Weyl’s treatment
of conservation laws in his
new
theory.
[7]The
result
that the
electromagnetic
four-vector
potential
is determined
only up
to
the
gradient
of
some arbitrary
function,
which had
originally suggested
the link between
Weyl’s generalization
of
Riemannian
geometry
and
electrodynamics
(see
Doc.
472,
note
3,
for
details) goes
back
to Wiechert
1900b, pp.
552-553.
[8]See
Doc. 512.
[9]See
Doc.
472, note 3,
for discussion
of
the role
of
the linear differential form
dQ
in
Weyl’s
geometry.
[10]If
the
quantity
Qu
in
Weyl’s geometry
is
interpreted as
the
electromagnetic
four-vector
poten-
tial,
dQ gets
the dimension
of
an
electric
charge.
The
factor
y
is needed
to
keep dQ
dimensionless.
[11]The
Hamiltonian
function
and the
equation
referred
to
above
can
also be found in the revised
version
of
Weyl’s manuscript
(Weyl
1919c, p.
122-123).
For
a
discussion
of
how
Weyl
arrived
at
a
Lagrangian
for his
theory, including
the
term QiQiv-g,
see
Doc. 619,
note 11.
Variation
of
Qi
in the
integral over
this
term,
with the additional factor
y2,
gives
rise to the
right-hand
side
of
the electro-
magnetic
field
equations
above. The
electromagnetic
field tensor
density
fuv
on
the left-hand side is
defined
as v-ggupgvo(doQp-dpQo).
[12]Under
consideration here is the
special case
of
the
static field
of
an
electron,
in which the fourth
component
of
the
left-hand side
of
the
equation
above reduces
to -AQ,
where Q=Q4.
Thus,
the
con-
stant
in the
equation
below
must
be
equal
to
-3y2/2Y.
[13]Inserting
this solution into
AQ,
one
arrives
at
AQ
=
Q/l2.
[14]If
Weyl’s theory
is
to
be
compatible
with Coulomb’s
law,
Q
must
have this form.