290 DOCUMENT
222
MAY 1916
I
d(T‘ps)
dw¡
=
0
für
eine
beliebige
Wahl
von
ps. Hieraus würde aber nicht
nur
das Verschwinden
sowohl
der
zdTls/dwl
(sondern
auch
der
Tls
selbst
folgen.
Wie
klärt
sich dies auf?
Mit der Bitte
um
freundlichen Aufschluss und den besten
Grüssen Ihr
A.
[E]instein
AKSX
(GyGöU,
Cod. Ms. D. Hilbert
92b). [13 099].
There
are perforations
for
a
loose-leaf
binder at
the left
margin
of
the document. The
postcard
is
addressed
“Herrn Prof. Dr. D. Hilbert Wilhelm We-
ber-Str.
Göttingen,”
and
postmarked
“Berlin-Wilmersdorf
1
26.5.16.
2-3N[achmittags].”
[1]Hilbert 1915.
[2]Heinrich
Rubens’s
physics colloquium was
held
every Wednesday evening
(see
Berlin
Ver-
zeichnis 1916a,
p. 48).
[3]Hilbert’s
eq. (6)
is the theorem
dj/dxs
ps
=
PJ,
with
ws
the
space-time
coordinates, ps
an
arbi-
trary vector,
J
=
J(guv,
guvi,
guvij,
qu,
qui)
any
invariant function
of
the metric
guv
and its first and
second derivatives and
of
the
four-potential
qu
and its first derivatives.
P
is
a
differential
operator
containing
differentiations with
respect
to the variables
occurring
in
J
(see
the
following
document
for
its
explicit
form,
as given on p.
399
of
Hilbert’s
paper).
On
p.
398 and
preceding
eq.
(6),
Hilbert
gives an identity
that
is
equivalent
to
eq.
(6),
but
is written out in
a
different
way.
Einstein had
pre-
sumably
checked the
correctness
of
eq.
(6)
starting
from this
expression.
Hilbert
proves
his theorem
in
a more general way.
He
notes
that
it
holds
trivially
for constant ps,
since,
in that
case,
the
operator
P
reduces to
gsuvd/dguv+guvis/dgiuv+guvlksd/dquvl+q1sd/dql+qilkd/dqil
ps
.
He then concludes from the
invariance
of
both sides
of
the
equation
that it
holds for
arbitary
ps.
[4]H
is Hilbert’s world-function
(see
Doc.
140, note
3).
[5]On
p. 403,
Hilbert
shows that the
world-function
contains the derivatives
of
the
four-potential
only
in the
form
of
the
components
of
the
electromagnetic
six-vector.
[6]In
the
conservation
law el is the
“energy
vector.”
[7]Tls below is
the
energy-momentum
tensor.
222.
From David
Hilbert
Göttingen,
den 27.
5.
16.
Lieber Herr
Kollege.
Vor
Allem
besten Dank
für Ihren freundlichen
Brief
vom
letzten
März,[1]
auf
den
ich
so
lange
schon
einmal schreiben
wollte.
"Freundlich“
auch noch im
wörtlichen
Sinne;
doch
über
diese
Angelegenheit
"Freundlich“
sprechen
wir
hoffentlich bald
mündlich.[2]-
Ostern
war
ich 4
Wochen
in
Lugano
und habe dort
Fleisch
u.