DOCUMENT 502 APRIL 1918 713
die
philosophische
Forderung zu
stellen,
und also
meine
Lösung
abzulehnen. Aber
ich habe auch das Recht die
philosophische
Forderung
abzulehnen,
nicht aber die
phyisische.
Ob meine
Lösung
sich wirklich auffassen lässt als eine Welt worin alle
Materie
auf
die
Fläche
r
=
1/2^R
konzentriert
ist,[5]
wäre
auszurechnen-ich
weiss
nicht ob
es so
ist oder nicht.
Mit herzlichen Grussen Ihr
W.
de Sitter.
AKS.
[20 565].
The
verso
is addressed "Prof. Dr. A. Einstein Wittelsbacherstr.
13
Berlin Wilmers-
dorf.,"
then deleted and addressed "Haberlandstr.
5
bei
Einstein"
in another
hand,
and
postmarked
"Leiden
14
11.IV.1918 2
N[amiddag]."
[1]Einstein
1918c
(Vol.
7,
Doc.
5).
[2]In
Einstein 1918c
(Vol. 7,
Doc.
5),
the
following regularity
condition-or
"continuity
condition"
("Stetigkeitsbedingung”)-is
formulated
(the
need for such
a
recognized by July
1917
[see
Doc.
363]):
in the
neighborhood
of
any point
P
connected
to
an arbitrarily
chosen
origin
O
by a curve
of
finite
proper
length,
there has
to
be
a
coordinate
system
such that the determinant
g
of
the metric does
not
vanish
at P.
For the De Sitter solution in the static form used in the
paper (see,
e.g.,
Doc.
363),
g
=
-R2sin4(r/R)sin2t|rcos2(r/R). This
expression
vanishes for
r
=
0,
\|/
=
0,
and
r
=
kR/2. Einstein
recognized
that the first two
singularities can
be eliminated
through
a
change
of
coordinates,
but he claimed that the third singularity-a surface whose
points,
he
verified,
can
be connected
to
the
point r
=
t
=
0
by a curve
of
finite
proper length-cannot.
He concluded
that the De Sitter solution violates the
regularity
condition and that it therefore does
not
serve
as
a
counterexample
to
what in Einstein
1918f
(Vol.
7,
Doc.
4)
is called "Mach’s
principle."
See Eisens-
taedt
1993,
pp.
355-356, for
a
concise discussion
of
Einstein 1918c
(Vol. 7,
Doc.
5).
[3]On
pp.
17-18
of
De
Sitter
1917c,
it is shown that the coordinate time it would take
light
to travel
from
any point
at
time
zero
to
the
singular
surface mentioned here is infinite.
However,
the
impossi-
bility
of
reaching
the
surface,
which De Sitter inferred from this
result,
is
an
artifact
of
the coordinates
used
to
write the De Sitter solution in static form. It turns
out
that the
double-wedge-shaped region
of
De Sitter
space-time
covered
by
such coordinates lies outside the
light cones
of
the
points
of
the sin-
gular
surface
(see
the
figure
in Doc.
566, note 7).
[4]This
response
to
Einstein 1918c
(Vol. 7,
Doc.
5)
was
published
in De Sitter
1918,
submitted
to
the Amsterdam
26
April.
[5]As
suggested
in the conclusion
of
Einstein 1918c
(Vol. 7,
Doc.
5),
as
well
as
in Docs. 363 and
370.
502. To
Hugo
A.
Kruss
Berlin,
Haberlandstr. 5.
[before
11
April
1918][1]
Hoch
geehrter
Herr
Professor!
Bezugnehmend
auf
die
Unterredung,
die Sie neulich
mei[n]er
Cousine
gewährt
haben,
bezüglich
einer
meine
Anstellungsbedingungen
betreffenden
Bitte,
erlaube
ich
mir,
Ihnen die
Angelegenheit
nochmals schriftlich
zu
unterbreiten.[2] Es handelt
sich
um Folgendes.
Mit meiner
Anstellung
ist das
Recht auf
eine Witwen-Pension verbunden. Ich
beabsichtige
nun,
mich scheiden
zu
lassen,
um
darauf
wieder
zu