594
DOCS.
566,
567
JUNE
1918
has
to set
xa
=
n/2,
c
=
2,
R
=
Kp0/3_
in formula
(35)
there
in order
to have de
2
V
3
Sitter’s
ds2.[12]
Formula
(35)
relates,
of
course,
to
the
interior
of
the
sphere
at rest
considered
by
Schwarzschild of
gravitating liquid
of
constant
density.
Formula
(30)
is
thus
applicable,
which
yields p
=
-p0,
hence
a
steady
pull.[13]
Obliging regards
from
yours
most
truly,
Klein.
P.S.
I
think
I
can
set
your
letter
of
9 June[14] straight
now.
The
ÄB's
are
strictly
equal
to
zero
for
a
#
4,
the
corresp.
Axa’s
are
arbitrarily
small
against
Ax4.[15]
567. To
Felix
Klein
[Berlin,
20
June
1918]
Esteemed
Colleague,
You
are
entirely right.
De
Sitter’s world
is,
in and of
itself,
free of
singulari-
ties
and its
space-time points
are
all
equivalent.[1]
A
singularity
comes
about
only
through
the
substitution
providing
the
transition to the static form of
the
line el-
ement. This
substitution
changes
the
analysis-situs
relations. Two
hypersurfaces
t
=
t1
and
t
= t2
intersect
each
other
in
the
original represention,
whereas they do not
intersect
each
other
in
the
static
one.[2]
This
is
related
to
the fact
that, for
the
physi-
cal
interpretation,
masses are
necessary
in
the static
conception
but
not
in
the
former
one.[3]
My
critical remark about
de Sitter’s solution needs
correction;
a
singularity-free
solution for
the
gravitation
equations
without
matter
does in
fact
exist.[4]
However,
under
no
condition could
this
world
come
into
consideration
as
a
physical possibility.
For in
this
world,
time t cannot be defined in such
a
way
that the
three-dimensional slices t
=
const. do not intersect
one
another and
so
that
these slices
are
equal
to
one
another
(metrically).[5]
With
sincere
thanks
for
your
fine
and
illuminating
letter,
yours truly,
A.
Einstein.
Recipients
note
on
the
verso:
“Did
Weyl
appear? Appointment regarding
the
building
plans
of
the Math. Inst.”