DOCUMENT 619 SEPTEMBER 1918
879
hat).
Das wird die nächste
Aufgabe
sein,
daß ich hier
zur
Klarheit komme.[16]
Au-
ßerdem habe ich die
strengen Gleichungen
für
ein statisches
rotationssymmetri-
sches
Feld
ausgerechnet;
aber sie sind
so
kompliziert,
daß ich
vorläufig
nichts
mit
ihnen
anzufangen
weiß,
daraus müsste sich die Konstitution des Elektrons und sei-
ne
Möglichkeit
ergeben.[17]
Hilbert
war
einige
Wochen hier und hat sich
unbedingt
für mich
erklärt;
auch
von
Sommerfeld hatte ich einen sehr zustimmenden
Brief.[18]
Er schrieb
noch,
daß
neue sorgfältigste Messungen
auf
dem Mt. Wilson keine
Spur von
der astralen Rot-
verschiebung ergeben
haben;
wie steht’s
damit?[19]
Augenblicklich
erhole ich mich im
Engadin;
mein Gesundheitszustand hat mich
genötigt,
die Annahme des Rufs nach Breslau wieder
rückgängig
zu
machen.[20]
Hätten wir
nun
auch
nur
noch Sie wieder in Zürich! Sie können sich
denken,
wie
glücklich
ich darüber wäre. Wenn’s denn
aber nicht
dauernd sein
soll, so
hoffe ich
wenigstens,
daß
Sie in nächster Zeit
wenigstens
auf
einige
Wochen
zu uns
kom-
men.[21]
Mit den
besten
Grüßen Ihr
Herm.
Weyl
ALS.
[24 044].
[1]The unified
theory
of
gravity
and
electromagnetism
in
Weyl
1918b
(for
a
brief
characterization,
see
Doc.
472, note 3).
Einstein had
argued against
this
theory
in letters
to
Weyl
earlier
in 1918
(see,
e.g.,
Docs.
512, 551,
and
579).
[2]Weyl
1918d.
[3]The
gravitational
field is
represented
by
the affine connection.
[4]The
same imagery
of
God’s
plan
for creation is
used
in Docs. 544 and 551.
[5]The
core
of
Einstein’s main
objection
to
Weyl’s theory was
that
one
would have
to
give
up
the
notion that rods and clocks
directly measure
the line element
(see
Docs. 507 and
512).
[6]For
the definition
of
the notion
of
the
weight
of
a
tensor,
see
Doc.
499, note
3.
[7]The curvature
scalar for the affine connection in
Weyl’s theory,
which
depends
not
only on
the
metric field
but also
on
the
electromagnetic
four-vector
potential
(Weyl
1918b,
p.
477).
[8]The
quantity
is both
generally
covariant and
gauge
invariant.
[9]As
can
be
gathered
from Doc.
659,
essentially
the
same suggestion was
made
by
David
Hilbert,
who also formulated
a
differential
equation
for the scalar
of
weight
-1
multiplying
the
metric.
[10]Weyl 1918b, the manuscript
of
which
was
sent at
the
same
time
as
Doc.
497.
[11]This
is the
first time
Weyl
mentions
this result.
Initially
(see
Doc.
472),
he wrote
to
Einstein
that his
new
theory reproduces
the
field
equations
of
general relativity
in the
absence
of
electromag-
netic fields
(whether
with
or
without
cosmological
term,
he did
not
specify).
In his first
paper on
the
new theory,
he
explained
that the field
equations
of
his
theory
would be
of
fourth order
(Weyl
1918b,
p. 477; see
Doc.
472,
note 4,
for
discussion).
He added that it
was highly unlikely
that Einstein’s
second-order
equations
would hold
exactly,
thus
suggesting
that
they
would
at
least
hold
approxi-
mately
in the
new theory.
In his second
paper,
he mentioned that in
a
linear
approximation
the
new
theory
reproduces
Newton’s
gravitational theory
(Weyl
1918d,
p. 411;
in
June,
Walter Dällenbach had
mentioned
to
Einstein that
Weyl
had
found this
result
[see
Doc.
564]).
It
was only
in
Weyl
1919c
(pp.
121-124)
that
Weyl
would
publish
a
derivation-without
the
restriction
to
static fields
or
first-order
approximation
mentioned in this
document,
but with
a
particular choice
of
a
gauge-showing that
a
simple Lagrangian
for his
theory
does indeed lead
to
the Einstein field
equations,
including
the
cos-
mological
term.
This derivation
was
incorporated
in the revised third edition
of
Weyl’s
book
on
gen-
eral
relativity
(Weyl
1919d,
sec.
35)
and further
improved upon
in later editions
(Weyl
1921a,
sec.
36;
Weyl
1923a,
sec.
40;
see
also
Weyl
1921b,
and
one
of
the
notes
the author added to the
reprint
of
Weyl