196
DOCUMENT 140
NOVEMBER
1915
Soweit ich Ihre
neue
Abh.
verstehe,
ist die
von
Ihnen
geg.
Lösung
von
der meinen
völlig
verschieden,
zumal die
es
bei mir auch
nothwendig
das
elektrische
Potential
enthalten müssen.[8]
ALS
displayed on
two
postcards.
[13 052].
There is
a
perforation
for
a
loose-leaf
binder at the
left
margin
of
the
cards. The first is addressed “Herrn
Professor
Einstein
Mitglied
der.
Kgl.
Akademie
der
Wissenschaften in
Berlin
Wittelsbacherstr
13,”
and
postmarked
“Göttingen
1
14.11.15. 6-7V[ormit-
tags].”
The author has added:
“Fortsetzung
auf Blatt
I
mit
der
Einladung
auf
Dienstg
6 Uhr
her
zu
kommen. Viele Grusse H.”
Presumably
Hilbert
was referring
to
the second
card,
which is addressed
“Herrn Professor
Einstein
Mitglied
der
Kgl.
Gesellschaft
der Wissenschaften in Berlin Wittelsbacher-
str
13,”
and
postmarked
“Göttingen
1
14.11.15.
6-7V[ormittags].”
[1]Dated by
Hilbert’s announcement
of
the lecture.
[2]Hilbert’s
lecture
on
16
November to the Mathematical
Society
of
Göttingen was
entitled
“Grundgleichungen
der
Physik” (see
Jahresbericht der
Deutschen
Mathematiker-Vereinigung
24
(1915)
part
2, p. 111).
[3]On
20
November,
Hilbert
presented
a
paper
on
a
unified field
theory
of
gravitation
and electro-
magnetism
to
the
Royal Society
in
Göttingen,
which
was published
after extensive revision
on
31
March 1916
(see
Corry
et
al.
1997)
as
Hilbert
1915.
In
the
published paper,
Hilbert
bases
his
theory
on
two
axioms:
(i)
the
field
equations can
be derived
through
a
variational
principle
from
a
“world
function”
(“Weltfunktion”),
that is
a
function
of
the
metric
tensor and its first and second
derivatives
and
of
the
electromagnetic
vector
potential
and its first
derivatives;
and
(ii)
the
“world function” is
invariant under
arbitrary
transformations of the
space-time
coordinates
or
“world
parameters”
(“Welt-
parameter”) as
Hilbert calls them. The first axiom is
adapted
from the
theory
of
matter
presented
in
Mie
1912a, 1912b,
1913. See
Mehra
1973 and
Earman and
Glymour
1978 for
historical
discussions
of
Hilbert’s
theory; see
also Einstein’s harsh
criticism of
Hilbert’s
approach
in Doc. 278.
[4]This
result is
on p.
397
of Hilbert
1915.
Hilbert
derives
it
from
a
theorem that is
a special case
of
what would
later
be known
as
Noether’s theorem.
[5]The
expression
for E
given
here
can
be found
(in a slightly
different
notation)
in
a
set
of
proofs
of Hilbert
1915,
marked “first
proofs
of
my
first note”
(“Erste
Korrektur
meiner
ersten Note”)
and
bearing
a
stamp
with
the
date, 6 December 1915
(see GyGöU,
Cod. Ms. D.
Hilbert
634).
For
a
dis-
cussion
of
these
page proofs, see Corry et al.
1997.
The
quantity
E,
called the
“energy
form”
(“Ener-
gie
Form”),
is
constructed
out
of
the
tensor
JgPg
H,
where
Pg
is
an
operator
(see
Doc.
222,
note
13,
for
its
definition) acting
on
the world function H. In
these
page proofs,
Hilbert
argues,
in
a way
that
is
reminiscent of
Einstein’s “hole
argument”
(see
Doc.
43,
note
2,
for
discussion),
that
the
generally
covariant
Euler-Lagrange
equations
for the world
function
H
cannot
determine the fields
uniquely,
and that in order to avoid violation
of
what he calls the
“causality principle” (“Kausalitätsprinzip”)
four additional
equations are
needed that
are
not
generally
covariant. The
equations
added
by
Hilbert
are
es
=
0.
He then adds
a
third axiom to his
theory,
called the
“space-time
axiom”
(“Axiom von
Raum und
Zeit”).
This
axiom
restricts the covariance
of
the
theory
to
arbitrary
transformations
of
the
“space-time
coordinates”
(“Raum-Zeitkoordinaten”),
defined
as
those world
parameters
in terms
of
which the
“energy
theorem”
(“Energie
Satz”),
which
can
be written
as
es
=
0,
holds. This
way
of
avoiding a
conflict
with
the
causality principle
is similar
to
the
escape
from
the “hole
argument”
through
the introduction
of
adapted
coordinates
(see
Doc.
18,
note
5,
for
a
definition
of
this
notion)
presented
in Einstein 1914o
(Vol.
6,
Doc.
9), offprints
of
which Einstein
had
just
sent Hilbert
(see
the
preceding
document).
None
of
the above
considerations
appear
in the
published
version
of
Hilbert’s
paper. Instead, a generally
covariant
“energy
equation”
(“Energie Gleichung”)
is derived
(see
Hilbert
1915,
p. 402).
In
Hilbert
1917,
a new
definition
of
the
principle
of
causality
is introduced, which
re-
moves
the need to restrict the
general
covariance
of
the
theory
(see
Stachel
1992,
sec.
3,
for discussion
of
this
new definition).
[6]See
Hilbert
1915,
p.
404.