778 DOCUMENT 552 MAY 1918
[1]Month
corrected
on
the
assumption
that
Einstein's
compliment paid
to
Weyl
in this document
on
his latest
findings concerning
the static
form of
the De Sitter solution occurred before 20
June,
the
date
of
Einstein’s
acknowledgment
in
a
letter
to
Felix Klein
(see
Doc.
567)
that the
singularity
in this
form
of
the solution
can
be transformed
away.
[2]See
Doc. 544.
[3]In particular, as
Einstein
wrote to
Felix Klein
a
few
days
later
(see
Doc.
556), Weyl’s
latest anal-
ysis
seemed
to
support
the idea that there is
a mass
horizon in De Sitter
space-time.
Einstein had
sug-
gested
this
earlier
to Willem
de Sitter
(see
Docs.
363
and
370)
and
in
Einstein 1918c
(Vol. 7,
Doc.
5).
Reading page proofs
of
Weyl
1918c, Einstein
quickly
became convinced and wrote
De Sitter in
mid-
April (see
Doc.
506)
that
Weyl
had
provided
proof
for this
suggestion. Shortly
thereafter, however,
Einstein and
Weyl
discovered
problems
in the
original analysis
that
cast
doubt
on
this conclusion.
These
problems were
resolved in Doc. 544.
[4]Einstein made the
request
in
a phone
call
to
the
publisher (see
Doc.
535).
[5]Weyl 1918c.
[6]Almost two weeks
earlier,
Weyl
had reiterated his
preference
for
an elliptic topology
(see
Doc.
544),
though
he
accepted
Einstein's
criticism
(in
Doc.
511)
that
an argument
in
page proofs
of
Weyl
1918c in
support
of
this
preference
was
fallacious.
[7]Weyl
1918b,
in which the author outlined
a
unified
theory
of
gravity
and
electromagnetism
based
on a generalization
of
Riemannian
geometry
(see
Doc.
472, note 3,
for
more
details).
[8]For
a
characterization
of
the
alleged "inconsequence," see
Doc.
544,
note
16.
[9]The
following argument
is based
on
Einstein’s
"brief characterization" of
Weyl’s theory
in
Doc. 529.
[10]Einstein
presumably
intended
to
write
"allgemeiner als."
As
long as
the
connection
is
linear,
as
it is both in Riemann’s and in
Weyl’s geometry, parallel
displacement
preserves
similarity.
From
Weyl’s
point
of
view
therefore,
the
alternative
presented
here
would
seem a
radical
departure
from
ordinary
Riemannian
geometry
rather than
a
natural extension
of
it.
[11]Einstein
feared
a relapse
of
his
gastric
condition
(see
Doc.
548)
and the
delays
at the German-
Swiss
border,
which he had last encountered
in
summer
1917
(see
Doc.
377). Instead,
he
planned
to
go
to
Ahrenshoop (see
Doc.
558).
552. From Felix Klein
Göttingen
31.
V.
18.
Sehr
geehrter
Hr.
Kollege!
Versprochener
Weise schreibe ich Ihnen
noch,
ehe ich meine
Beschäftigung
mit
Ihren letzten Arbeiten
für
einige
Wochen abbreche. Heute
nun
erst
zu
Ihren
"kos-
mologischen"
Betrachtungen.[1]
1.
Wenn man das ds2
so
definiert, wie Sie
es
1917 getan haben,
so
finde ich, in
Uebereinstimmung mit Ihrer Auffassung, keine Hinderung, den
"Raum"
nach
Be-
lieben sphärisch oder elliptisch
anzunehmen.[2]
2.
Nicht so, wenn man von einer "Welt" konstanter Krümmung ausgeht (wie ich
es, ohne den Unterschied gegen Ihre Annahme zu bemerken, in meiner Hedemün-
dener Ausarbeitung tat und es de Sitter’s "Hypothese B" zu Grunde
liegt).[3]
Es ist
jedenfalls am einfachsten, zu
dem
Zwecke
von
dem
"pseudosphärischen"
Gebilde in
5
Variabelen:
B2 +
rj2
+
B2
-
v2
+
w2
=
R2
auszugehen
und ds2
als