DOCUMENT 314
MARCH
1917
417
tribution,
had
also
been used for the
distant
masses
in the
earlier
proposal
(De
Sitter
1916e,
p.
183).
In De Sitter
1917a, p.
1270
(p.
1219 in the
English
translation),
the term “world-matter” is introduced
for Einstein’s uniform
mass
distribution. For De
Sitter,
this world-matter exists in addition to
ordinary
matter,
just as
Einstein’s distant
masses.
[4]De
Sitter had made
it clear
before that he would
rather
have
no explanation
of the
origin
of
inertia
at
all than
an explanation
that
required
the
introduction of
unobservable elements into the
theory
(see
Doc.
272).
[5]See
De
Sitter
1917a,
p.
1273
(p.
1222 in the
English
translation)
for
a
more
elaborate
version
of
this
argument.
[6]In
Einstein’s solution
of
the field
equations
with
cosmological term
and
a
static
uniform
mass
distribution
(see
Einstein 1917b
[Vol.
6,
Doc.
43],
pp.
149-150),
the
spatial geometry
is
that of
the
hypersphere
x21
+
x22
+
x23
+
u2
=
R2 in
a
four-dimensional
Euclidean
space (where (xi,u) are
Car-
tesian coordinates in
the
embedding
space).
In De Sitter’s
vacuum solution,
the
space-time
geometry
is
that of
the
hypersphere
x21
+
x22
+
x23
+
u2 +
x24
=
R2
(with
x4
=
ict
)
in
a
five-dimensional Euclid-
ean
space
(if
the
imaginary
time coordinate
it
is
used)
or
that of
a hyper-hyperboloid
in
a
4+1-dimen-
sional Minkowski
space-time
(if the real time coordinate t is
used).
The
following side-by-side com-
parison
of
Einstein’s and De Sitter’s solutions in three different coordinate
systems
is
given
in
more
detail in De
Sitter
1917a. The
components
of
the metric tensors in coordinate
system
“I,”
which
are
the coordinates used in Einstein 1917b
(Vol. 6,
Doc.
43),
can
be read
off
from the line elements in the
Euclidean
embedding spaces (expressed
in
Cartesian
coordinates)
after
substitution
of
xidxi/vR2-zx2i
for
du
(where
i
runs
from
1
through
3
for
Einstein’s solution and from
1
through
4
for
De
Sitter’s
solution).
The
relations
between
X
and
R
given
at
the
beginning
of
the
comparison are
derived
later
on
in
the
document. For
an
illuminating
discussion
of
the
geometry
of
the De Sitter
solution,
see
Schrödinger
1956. As is
acknowledged
in
a
footnote in
De Sitter
1917a, p.
1270
(p.
1219 in
the
English translation),
the
idea of
conceiving
of
four-dimensional
space-time as
being
spherical
had
been
suggested
several months
before
by
Paul Ehrenfest in
a
conversation with De Sitter.
[7]See
Kerszberg
1989b,
pp.
184-186,
for
diagrams illustrating
the
stereographical
projection
of
a
hyperboloid.
[8]At
this
point
in the
original
text,
De
Sitter has
designated
the insertion
of
the
following
sentence
with
an
arrow:
“Physisch
weiss
ich
nur
dass ich im endlichen sehr nahe die guv
der
alten Rel. Theor.
finden muss.”
[9]In
Doc.
311,
Einstein
had alluded
to
a gallstone
ailment.
314.
To
Moritz Schlick
[Berlin,]
21. III.
17.
Sehr
geehrter
Herr
Kollege!
Bei
nochmaligem
Durchlesen
Ihres schönen Aufsatzes
in
den
"Naturwissen-
schaften“ finde ich noch eine kleine
Ungenauigkeit.
Ich teile Ihnen dieselbe mit für
den
Fall,
dass Ihr Artikel
anderweitig zum
Abdruck
käme.[1]
Die
Auf
Seite 184
gegebene Ableitung
des Gesetzes
der
Punktbewegung geht
davon
aus, dass,
im lokalen
Koordinatensystem
betrachtet,
die
Punktbewegung
eine Gerade sei. Hieraus
kann
aber nichts
abgeleitet
werden. Das lokale Koordina-
tensystem
hat seine
Bedeutung
im
Allgemeinen nur
im
Unendlich-Kleinen,
und
im
Unendlichkleinen ist
jede
stetige
Linie eine Gerade. Die
richtige Ableitung
geht