DOCUMENT 317
MARCH
1917 423
Verhaltens
der
Materie[9] beweisen die
geringen
Sterngeschwindigkeiten,
dass
grosse
Potentialdifferenzen der Gravitation in
der
Welt
überhaupt
nicht
Vorkom-
men.
Angenommen,
die
Richtigkeit
der
allgemeinen
Relativitätstheorie wäre sicher-
gestellt,
dann könnte durch
Beobachtung
der
Spektrallinien
ferner Sterne die
y-Fra-
ge
entschieden werden.
Denn
wenn
y
=
0
wäre,
so
würde die mittlere Sterndichte
hinreichen, um
eine Potentialdifferenz zwischen
uns
und fernen Sternen herbeizu-
führen,
die einen
erheblichen Violett-Effekt mit sich brächte.
ALS
(NeLO,
box
31). [20 547].
[1]Conveyed
in Doc. 313.
[2]De
Sitter’s tuberculosis and Einstein’s
gallstones
are
alluded
to in Doc. 311.
[3]The
calculations
in
this document
are
based
on
the line element for the De
Sitter solution in ste-
reographic
coordinates
given
in
eq. (1)
in Doc. 313.
[4]At this
point
in the
original
text,
De Sitter has inserted: “=
T/2Vu.”
[5]The
denominator in the line
element
in
eq.
(1)
in Doc. 313 is
(1-uh2)2
and does not
change
sign upon passing
the
singular hypersurface
1
-
uh2
=
0.
More
importantly, points on
the stereo-
graphic hyperplane beyond
this
hypersurface
do
not correspond
to
points
of
the
space-time
(see
Doc.
321,
note
9).
[6]De
Sitter
has deleted
"1/VuT/2
(endlich)”
and
replaced
it
by:
“=
°°.”
In the
margin
he has
noted
“see
Kluyver’s postcard”
(“zie
briefkaart
van
Kluyver”), a
reference
to
a postcard
from
Jan
Cornelis
Kluyver
(1860-1932),
Professor
of
Mathematics
at
the
University
of
Leyden,
of
2
April
1917
(see
NeLO,
box
31).
Three and
a
half
weeks
later,
De Sitter
informed
Einstein
of
the correct
result
for the
integral
under
“3)”
and
of
the
precise
value
of
the
integral
under
“1)”
above
(see
Doc.
327).
Both
re-
sults
can
also be found in
a
footnote
on p.
1271
of
De
Sitter 1917a
(p.
1220
of
the English translation).
[7]The
preceding
three sentences
of
this
paragraph are
cited
in
a “Postscript”
to De
Sitter
1917a.
In Docs. 321 and
325,
respectively,
De Sitter asked and
Einstein
gave permission
to
quote
this
passage.
In Einstein
1918f (Vol.
7,
Doc.
4),
the term “Mach’s
principle”
(“Machsches
Prinzip”)
would
be
introduced for
the
requirement
that the metric field be
fully
determined
by
matter.
For
historical
background to
and critical discussion
of
this
principle, see
Barbour and
Pfister
1995.
[8]This
is
a response
to De Sitter’s
argumentation
in Doc. 312.
[9]De
Sitter has drawn
an arrow
to this
phrase
in
Einstein’s
text and
appended
the
following com-
ment
[20 548] to
the document: “This
reasoning
is completely
wrong.
After
all, [this] assumes
that
the
average density
here
remains
the
same up
to
°°.
This is most
certainly not
true.
To the
contrary,
from
my
result,
M. N.
II,
p.
177,
it follows
that,
for
instance, m(R)
600R,
if
the observations
would
show the nonexistence
of
the shift
everywhere.
We have
p
=
3m/4TR3,
so
p
14/R2.
This is the correct
conclusion from the observations, not
something concerning X.
The
error
lies here.”
(“Deze
redeneer-
ing
is heelemaal fout.
Immers
veronderstelt
dat de
gemiddelde
dichtheid
hier,
tot in
't
°°
zoo blijft.
Dit
is
zeer
zeker niet
waar.
Integendeel,
uit
mijn
resultaat M. N.
II,
p.
177
volgt dat,
als de obs. overal
het
niet bestaan
van
de
verschuiving
aantoonde,
zeg m(R)
600R
Nu
is
p =
3m/4TR3
dus
p(R)14/R2
Dit
is de
juiste
conclusie
uit
de
obs.,
niet
iets
over X.
De
fout
zit
hier.”)
“M. N. II” refers to De
Sitter
1916e;
m(R)
is the
mass
in
a sphere
of
radius
R.
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