346
DOC.
31
VARIATIONAL PRINCIPLE
[2]See
Einstein
1916o (Doc. 41)
for
a
published paper
on
the
same topic
that shows
some
similarities with this
manuscript (see note
6
for
a
major
difference).
See also Cattani and De
Maria
1993
and
Kichenassamy
1993
for historical discussion of variational
principles
in
gen-
eral
relativity.
[3]At this
point
in
the
original text
Einstein indicates
a
note
he has
appended at
the foot of
the
page:
"Die
von
Hilbert
im
Anschluss
an
Mie
eingeführte Voraussetzung,
dass sich die
Funktion
D
durch
die
Komponenten
eines Vierervektors
und
dessen
erste
Ableitungen
darstellen
lasse,
halte
ich für
wenig
aussichtsvoll."
Einsteinqp
refers
to
the
theory developed
by
Hilbert in Hilbert
1915.
It
is based
on
Gustav Mie's
theory
of
matter,
which
implied
in
partic-
ular that the
energy-momentum
tensor
of
matter
should be
a
function
of
electromagnetic quan-
tities
only.
Later
in 1916
Einstein criticized Hilbert's
theory
rather
vehemently, calling
his
assumptions
for the Hamiltonian
"infantile, in
the
sense
of
the
child,
who
is innocent
of the
guile
of
the
external world"
("kindlich,
im Sinne des
Kindes,
das
keine
Tücken der Aussenwelt
kennt." Einstein
to
Hermann
Weyl,
23
November
1916).
See
also Mehra
1973
and Earman and
Glymour
1978b for historical discussions of Hilbert's
and
Einstein's theories.
[4]At this
point
in
the
original text
Einstein indicates
a
note
he has
appended at
the foot
of
the
page:
"Hilbert und Lorentz haben
zuerst
diesen
Weg
eingeschlagen." In
the
corresponding
passage
in
Einstein 1916o
(Doc. 41),
there
is
a
reference
to
Hilbert
1915
and Lorentz
1915,
1916b, 1916c,
and
1916d.
[5]All references
to equations
with numbers lower than
47
are
to equations
in
Einstein 1916e
(Doc. 30).
[6]In contrast to
the
discussion
in this
manuscript,
Einstein
left
completely unspecified
the
form of the Hamiltonian
in
Einstein 1916o
(Doc. 41).
The choice made here
was
already
dis-
cussed
by
Einstein
in
January
1916 in
two
letters
to
Lorentz
(see
Einstein
to
H. A. Lorentz,
17
January
1916
and
19 January 1916).
[7]"m"
should
be
"0."
[8]In
Einstein 1916o
(Doc.
41),
eq.
(90) is
used
to
derive the
energy-momentum
conserva-
tion laws. The
same
could
be
done
here,
starting
from
eq.
(90)
and the
explicit
form of
0,
but
as
Einstein admitted
a
few
months later
he
did
not
carry
out
the calculation
(see
Einstein
to
Theophile
de Donder, 23
July
1916).