DOCUMENT 63
MARCH
1915
101
Die
Frage
ist,
ob das
über
die Materie
(z.
B.
Sonne)
erstreckte
Integral
^%\dxdydz
verschwindet. Mit der
hier
in Betracht
kommenden
Annäherung ist[2]
35?
35?
35?
35?
dx
+
3y
+
dz
+
dt
=
0
DE41/dt
verschwindet
im
statischen Falle.
Multipliziere
ich die
Gleichung
mit
x,
inte-
griere
über
den
ganzen
Körper,
so
geht
,
^35? 35? 35?
K^+a7+lF
dxdydz
=
0
durch
partielle Integration
über
in
ƒ5?
dxdydz
=
0,
wie bereits Laue erkannt
hat.[3]
Damit ist
der
Beweis
geliefert,
dass ein
g11
-Feld
für
das
Planetenproblem[4]
nicht in Betracht kommen
kann.[5]
Mit besten Grüssen Ihr
Einstein.
AKS
(NNPM,
MA 4725
(9)).
[11
208].
The
verso
is
addressed
“Herrn
Dr.
Freundlich Sternwarte
Neubabelsberg.,”
and
postmarked
“Berlin-Wilmersdorf
1
19.3.15.
2-3N[achmittags].”
[1]The
conclusion reached in this
document-that
for
a
weak static field the
only
nonconstant
com-
ponent
of
the metric tensor is
the
44-component-lends
support
to Einstein’s
earlier
presuppositions
on
this
point.
For
a
historical discussion
of
the
role Einstein’s
belief
concerning
the form
of
the
weak
static field
played
in the
development
of
general relativity,
see
Stachel
1989,
pp.
66-68;
Norton
1984,
sec.
4.2;
and
Vol. 4,
the editorial
note,
“Einstein’s Research Notes
on a
Generalized
Theory
of
Rela-
tivity,” p.
198.
[2]The
following equation
is the first
component
of
the
energy-momentum
conservation
law
in
a
first-order
approximation.
[3]This result,
sometimes
called
“Laue’s theorem”
(see, e.g.,
Einstein 1913c
[Vol.
4,
Doc.
17],
p. 1253), was
first
derived,
in
the
context of
special
relativity,
in Laue 1911a
(pp.
540-541;
see
also
Laue
1911b,
p. 169).
[4]A
reference to the anomalous advance
of
the perihelion
of
Mercury
and
perhaps
also to
other
well-known
anomalies
in the motion
of
the
perihelia
and the nodes
of
Venus and Mars.
Freundlich
had
just
written
a paper criticizing Hugo
von Seeliger’s
explanation
of
such anomalies
(Freundlich
1915b,
dated 27
February
1915).
[5]In
first-order
approximation,
the
11-component
of
the
“Entwurf” field
equations
for
a
static
field
is
Ag11 =
KI11.
Hence,
at
an arbitrary point
with coordinates
x
=
(x,y,z),
g11
is, up
to
a
constant,
equal
to
K/4nfI11(x')|x-x|d3x'.
For
the
problem
of
planetary
motion,
where the field is evaluated at
large
distances
from
a source
that is confined to
a relatively
small
region
of
space,
one
may
expand
the in-
tegrand
in terms
of
the
quantities
x'/|x|,
y'/|x|,
z'/|x|,
which
are
small
if
the
origin
of
the coordi-
nate
system
is chosen somewhere inside the
source.
The
leading
term in this
expansion
is
equal
to