484 DOCUMENT
362
JULY
1917
[10]To
lowest
order,
the
geodesic equation
for
a
test
particle
at rest
is
d2x‘/dt2
=
^dgu/dx'.
[11]The
coordinates
r
(also
written
as
b),
d,
and
cp
are
related to the
Cartesian
coordinates via:
x =
rsindcosp,
y
=
rsindsinp,
and
x =
rcosd.
[12]As
can
be
verified
by
inserting
the
second of
the three
expressions
for
g44
in
the
xz-plane,
given
above,
into the
geodesic equation
for
a
test
particle
at rest
(see
note
10 above).
[13]This
equivalence
is also noted in
Thirring 1918,
p.
37.
[14]In Thirring
1918,
p.
33 and
p.
38,
the
author
explained-contrary
to his
remarks
in this docu-
ment-that
no
matter which
mass
distribution is chosen to
represent
the actual
mass
distribution
of
the
universe,
his calculations will not establish
the
equivalence
of
systems
“(I)”
and
“(II)”
above. The
reason
is
that Minkowskian
boundary
conditions
are
used in all these calculations.
Citing
De
Sitter
1916d and Einstein 1917b
(Vol. 6,
Doc.
43), Thirring
pointed
out that this
means
that there is distant
matter
at rest with
respect to
the chosen
coordinate
system
in addition to the
rotating
hollow
sphere.
[15]The
topic
of
Lense
and
Thirring
1918. In
1913,
Einstein and Michele
Besso
had
already
done
similar
calculations
on
the basis
of
the “Entwurf”
theory (see
Doc. 178,
note
9,
for
more details).
[16]Einstein 1917b
(Vol. 6,
Doc.
43).
[17]In
Cartesian
coordinates,
the
spatial
part
of
the metric field
of
Einstein’s
cosmological
model is
gij
-
sij
xixj
R2-r2.
The line element in these coordinates
can easily
be rewritten in terms
of
spher-
ical
coordinates,
which
gives
the
expression
below
(the
minus
sign
in
the
expression
in
parentheses
should be
a plus sign).
On
pp.
38-39 of
his
notebook
on rotating
masses, Thirring
arrived at this form
of
the
line element (without the
sign
error)
by
transforming
each
component
of
the metric tensor from
Cartesian to
spherical
coordinates.
362.
To
Paul Ehrenfest
Arosa.
[22
July
1917]
Lieber Ehrenfest!
Herr
Grommer,
ein famoser
Mathematiker,
den Du
von
Göttingen
her
kennst[1]
(zur Unterstützung
des Gedächtnisses
erinnere
ich Dich
an
die
riesigen
Dimensio-
nen
seines
Kopfes
und
seiner
Hände),
wünscht
sehr eine
wenn
auch bescheidene
Mathematikerstelle in Russland.
Der Mann
ist
Jude
und
ächter
Russe.
Er
hat
eine
anerkannt
hervorragende
Dissertation
über
ganze
transzendente Funktionen
ver-
fasst[2]
und
beherrscht die
allg.
Rel.
Theorie. Ich habe
ihn
autorisiert, jetzt
während
meiner Abwesenheit
eine
Ergänzung zu
meinem
Kolleg
über
Rel. Th.
zu
lesen.[3]
Es wäre
schön,
wenn
Du den Mann Deinen
russischen Freunden
empfehlen
wür-
dest.-[4]
Ich verlebe
glückliche
Tage
mit
meinen
Buben hier in
der
Schweiz und bin
auf
dem
Wege,
mich
wieder
ordentlich
zu
erholen.[5] Glückliche
Ferien
wünscht
Dir
Dein
A. Einstein
Herzliche Grüsse
an
die Deinen & Lorentz.
AKS.
[9 406].
The
verso
is addressed
“Herrn
Prof. Dr.
P.
Ehrenfest Witte Roozen
str.
Leiden
(Holland),”
with return address “Abs. A.
Einstein
Brambergstr.
16
A.
Luzern.,”
and
postmarked
“Inner Arosa
(Graubünden)
22.VII.17.-3.”