340
DOC.
351
JUNE
1917
351. To
Willem
de
Sitter
[Berlin,]
14
June
1917
Dear de
Sitter,
From
your
postcard
and
from
your
correction
proof
I
see
that
you
have mis
understood
my paper
on one point.[1]
According
to
my conception,
apart
from
the stars
there
is
no
“world matter,”
or
at
least,
there
does
not have
to
be
any.
The
density
p
in
my paper
is
the
density
of matter which would
result
if the
mat
ter condensed in
the
stars
were
spread evenly
throughout
the interstellar
spaces.
“World
matter”
in
my
sense
is
thus
definitely
present
in
reality.[2]
This
density
yields
a
cosmic radius
of
about
107 lightyears.
At
most,
it could be
a
question
of
whether its
density
does not vanish
in
parts
of
the universe.
I
have
merely
examined
the
simplest
case
conceivable, namely,
the
one
where
p
is constant
throughout.
(This
can
naturally
be valid
only as a mean
value for
p
in
spaces
that
are
large compared
to
the
average
distance
of
neighboring
fixed
stars.)
I cannot
make
sense
of
your
fourdimensional structure[3]
ds2
=
f(h)[dx2

dy2

dz2
+
dt2]
mainly
for
the
following reasons:
1)
It
could
only
exist
without
“world
matter,”
that
is,
if
there
were no
stars.
2)
Your
fourdimensional
continuum does
not
have
the
property
that
all its
points
are
equivalent;
rather,
it has
a
spatiotemporal center
x
=
y
=
z
=
t
=
0.
This
is
the
center
of
the
conic section
1
+
h2
=
0
(with
the
above coordinate
choice[4]).
The
spatial
extension of
your
universe
(in
natural
measure) depends
in
a
peculiar way
on
t.
For
sufficiently
negative
[t],[5]
a
rigid
circular
hoop
can
be
placed
in
your world,
for which
there
is
no room
in
your
world at t =
0.[6]
3)
It
seems
to
me
that
a
reasonable
interpretation of
the
present
universe
neces
sarily requires
the
approximate
spatial
constancy
of
g44,
owing
to
the
fact of
the
small relative motion of
the
stars.[7]
I would
also
like
to
emphasize
particularly
that
the
identifiability
of
the
lines
of
the
visible
stars does not
prove
the
approximate constancy
of
the
g11...g33’s
but
only
the
approximate constancy
of
g44.[8]
With
cordial
regards
and best wishes for
your
health,
yours,
A.
Einstein.