DOCS.
321,
322
APRIL
1917 313
It
is
obvious
that
“my”
world
is
finite
like
yours;[8]
I have forced
it
into
a
Carte-
sian Euclidean coordinate
system merely
to show
that the
finiteness in
natural
measure
is
equivalent
to
the
requirement
of
the
guv’s becoming
zero
at
Euclidean
infinity.
As
concerns
the
singularity,
I
have
nothing
here,
no
books, etc.,
thus
I
cannot
do
the
calculations.
But
I
think that it
is just apparent
and
that
it stems from
my
description
of
my
actually
hyperbolic
world
as
spherical.[9]
Thus
the
hyperboloids’
infinity
is
dragged
into the finite
realm,
where
it
naturally
must
appear as a
singularity.
If
the
guv's
on
the
hyperboloid are
finite at
infinity,
the
g'uv's
must
necessarily
become infinite
there,
when
this
infinite
part of
the
hyperboloid
is
mapped
onto
a
finite
region
of
a
flat
space.[10]
I cannot
agree
with
the
second
part
of
your
letter.
I
must
emphatically
contest
your
assumption
that the
world
is
mechanically quasi-stationary.[11]
We
only
have
a
snapshot
of
the
worl,
and
we
cannot and must not conclude from
the
fact
that
we
do not
see
any large changes
on
this
photograph
that
everything
will
always
remain
as
at
that instant
when
the
picture
was
taken.
I
believe
that
it
is
probably
certain
that
even
the
Milky Way
is
not
a
stable
system.
Is
the
entire universe
then
likely
to
be stable? The
distribution
of
matter
in
the
universe
is
extremely inhomogeneous
[I
mean
of
the
stars, not
your
“world
matter”],
and it cannot be
substituted,
even
in
rough
approximation, by
a
distribution
of constant
density.
The
assumption you
tacitly
make
that the
mean
stellar
density
is
the
same
throughout
the
universe[12]
[naturally,
for vast
spaces
of,
e.g.,
(100,000 light-years)3]
has
no
justification whatsoever,
and
all
our
observations
speak against
it. I do not have
the data
here to do
anything
other
than
express my
conviction;
I do not intend to
try
to
prove
it
today.
With
cordial
greetings, yours truly,
W. de Sitter.
322. To Hendrik A. Lorentz
Berlin, 3 April 1917
Dear
Colleague,
Your
warm
words[1]
were
most
comforting
to
me.
In
you,
nature
was
seized
by
the
rare
impulse
of
combining
a
keen mind with
warm
sentiment. If
only
this
were more
often
the
case;
the
public
at
large
would be
considerably
better
off! My
condition
is
probably
not connected
appreciably
to
work;
it
is probably
attributable
to
a
constitutional
flaw.[2]
I
have
not
been
working
much
at
all,
and
that under
ideal
external
circumstances.