DOCUMENT
232
JULY 1916
309
ADft
(BBU,
95PP
2).
[71
403].
[1]The
preceding
document.
[2]The
equations are
in
sec.
7
of
De
Donder
1917a,
the
manuscript
of
which De
Donder
had sent
to
Einstein
(see
Doc.
228).
[3]In
the
identity
below,
eim
is the Kronecker delta
function;
the
symbol
0
represents a
differential
operator
involving
derivations
with
respect
to
gim
and its first and second
derivatives,
as
well
as
first
and
second derivatives to the
space-time
coordinates
(see
De
Donder
1917a,
eq. (351),
for
its defini-
tion);
and
l
-
kC
J^g,
with
2C
the curvature scalar and
k
a
constant. The
identity
below,
as
well
as
eqs.
(a) and
(ß) following
it, are
also discussed in
an
“Avertissement,”
dated
12
June
1916,
that
con-
cludes De
Donder
1917a.
There it
is
pointed
out that the calculations
leading
to the
identity
below
are
“extremely lengthy”
(“extrêmement
longs”).
[4] As
Einstein
points
out
in the
following document,
there
should be
no
factor
J-g
on
the left-
hand
side
of
the
equations
below
(which are
Einstein’s field
equations
for the
case
where the
trace
of
the
energy-momentum
tensor
vanishes).
[5]The
square
brackets here and in the
subsequent
text
are
in the
original.
[6]In
the
equation
below,
M is the
electromagnetic
field tensor and M* its dual.
a +
ß
in
the second
term should be
a.
[7]Einstein
and
Grossmann
1914a,
Einstein 1914o
(Vol. 6,
Doc.
9).
[8]Eq.
(341)
of
De
Donder 1917a
defines De Donder’s
gravitational energy-momentum
in terms
of
the curvature scalar and its derivatives.
[9]F-k
is the
electromagnetic
force
(see
De
Donder
1917a,
p.
97).
[10]Eq.
(8)
of
Einstein 1915i
(Vol.
6,
Doc.
25)
is the
energy-momentum
conservation law for matter
and
gravitational
field. The
quantity
tuA
is the
energy-momentum pseudo-tensor
of
the
gravitational
field.
[11]Eqs.
(2a)
of
of
Einstein 1915i
(Vol.
6,
Doc.
25) are
the
gravitational
field
equations.
[12]In
the
following equation, an integral sign
is
missing
after
5.
[13]In
De
Donder
1917a,
A
and B
represent
the electric and
magnetic energy, respectively,
of
the
electromagnetic
system
under
consideration.
232.
To
Théophile de Donder
[Berlin,]
8. VII.
16.
Sehr
geehrter
Herr
Kollege!
Ich beeile
mich,
Ihre
Fragen zu
beantworten.[1] Zuvor aber eine
allgemeine
Be-
merkung.
Es ist nach
meiner
Meinung
ein
Nachteil, wenn man
den Indizes eines
Tensors
nicht
ansieht,
ob
sie
kovarianten
oder
kontravarianten Transformations
Charakter
haben;
durch
diesen
Mangel
in der
Bezeichnung
erschweren Sie die
Übersicht
unnötigerweise.
Wenn Sie also
z.
B. meine
Feldgleichungen
bei
ver-
schwindendem
Energie-Skalar
der Materie
schreiben, so
dürfen Sie
nicht
schrei-
ben
lm)
=
XSkmTik
kl k
sondern
oder
k^Tg^gkl(ik,
Im)
=