DOCUMENT 493 MARCH 1918
699
tion,
as expressed
in
eq.
(2) below,
can
be derived without
using
the field
equations
at
all
(see
Ein
stein’s comments in Doc.
480).
In
Klein, F.
1917
and in Doc.
487,
Klein
had,
in
fact,
used both the
field
equations
and the invariance
of
the action
integral
under
general
coordinate transformations to
derive
energymomentum
conservation. The relation
between
energymomentum
conservation and
the invariance
of
the action
integral
is also discussed in
Weyl
1917. The issue
was
resolved with the
formulation
of
Noether’s
theorem,
first
published
in
Noether
1918b. For historical
discussion,
see
Pais
1982,
pp.
274276.
[3]Einstein first
identified the Christoffel
symbols as representing
the
gravitational
field
in
Einstein
1915f
(Vol.
6,
Doc.
21).
For further
discussion, see
Doc.
153,
note 12.
[4]Einstein 1918a
(Vol.
7,
Doc.
1).
[5]In
the
equation below,
Eva
should be
aEva.
[6]A
reference
to
Carl
Runge’s
ideas
(see
Doc.
487, note
20).
[7]Two
months
later,
on
3 June,
Runge gave a
lecture
on
Einstein 1918a
(Vol.
7,
Doc.
1)
to
the
Mathematical
Society
of
Gottingen, expressing
doubts about Einstein’s considerations
concerning
energy
loss due to
gravitational waves (see
Jahresbericht der
Deutschen
MathematikerVereinigung
27
(1919),
Part
2,
pp.
4344).
[8]Schwarzschild’s solution
contains
the
De
Sitter
solution
(with
variable
g44) as a special case,
not, as
Klein
mistakenly
thought
(see
Doc.
487,
note
24),
the solution
describing
Einstein’s
cosmo
logical
model
(with
g44 =
1).
[9]For
the resolution
of
the numerical
discrepancy
found
by
Klein in Doc.
487,
see
Doc.
566, note
13.
[10]Four
days earlier,
Klein
promised to
send
Einstein
the lecture notes
for
one
of
his
courses (see
Doc.
487).
[11]Weyl
1918c.
[12]Both
in
Klein, F.
1917 and in
Weyl
1918c, sec.
27
(as
in
Weyl
1917), energymomentum conser
vation is derived
by considering
the
variation
of the
action
integral
under the
Lie
variation
8*g^v
=
g'mv(xp)

gmv(xp),
induced
by some
diffeomorphism
xm

x'V
=
xP
+
AxP
(the
notation
5*
is introduced in
Weyl
1918c,
p.
186),
whereas
in
Einstein 1916o
(Vol. 6,
Doc.
41) only
variation
under sgmv
=
g'^v(x'P)
 gmv(xp)
is considered.
Einstein
discussed this work
by Weyl
and Klein in
lectures
on general relativity
in Berlin in
summer
semester 1919
(see Vol.
7, Doc.
20).
On
the
verso
of
Doc.
670,
there
is
a
short calculation in Einstein’s
hand of
the Lie variation
of
some
unspecified
Lagrangian
G which
is
a
function
of
gpv
and its first and second order derivatives
(the
notation 8 is
used instead
of
8*).
[13]A
week
earlier,
Einstein had been notified that he had
won
the Vahlbruch Prize in the
amount
of
11,000
marks.
Officially
awarded
on
28
March,
the
prize
was
conferred
by
the
philosophical
fac
ulty
of
the
University
of
Göttingen
with
funding
from the Otto Vahlbruch Foundation
of
Hamburg
(see
entries
of
17
March and 23 March 1918 in
Calendar).
493.
To
Gustav Mie
[Berlin,]
24. III.
18.
Lieber
Herr
Kollege!
In der
freudigen Erwartung
Ihres
in
Aussicht
gestellten
Besuches beantworte ich
Ihren ausführlichen
Brief
vom 1.[1] nur
kurz. Nach meiner
Auffassung
braucht die
Verteilung
der
Materie nicht
so zu
sein,
dass
p
in Wirklichkeit konstant ist. Es
ge
nügt,
dass Räume
existieren,
die
gross
sind
gegen
den Abstand
benachbarter
Fix
sterne,
aber
so
klein,
dass die metrische
Abweichung
vom
euklidischen Verhalten