296
DOC.
308 MARCH
1917
have
hit
upon
essentially
the
right
thing
and also
that
I
can
convince
you
of it in
person,
if
necessary,
when I
come
to visit
you again.
First the
main
issue:
Take Newton’s
theory
as a
basis.
You
suggest
it should
be assumed
that
a mass
filling
the
space
uniformly
into
infinity
does
not
pro-
duce
a
field
(for reasons
of
symmetry).
This is not
correct, though.
Let
there
be
no
field at
point
P.
Even
so,
there
has
to
be
a
flux of
gravitation running
from
the
spherical
surface
K
according
to
Gauss’s
theorem, arising
from
the
masses
enclosed
by
K.
According
to Gauss’s
theorem, every
mass
is
a
point of
convergence
for lines
of force! Even if
the
world
outside of
K
is filled
with
mass,
even
into
infinity,
the
matter
must,
nevertheless,
fall
toward
P;
to
be
more
precise,
the
acceleration
is greater,
the
greater
the
distance
is
from P. Jehovah did
not
found
the
world
on
such
a crazy
basis.
If
the
world is
to
be
permanently
stable,
motion has
to
obstruct the
fall
(centrifugal forces).
That
is
how
it
is
in
the
solar
system,
of
course.
But this
only
works when
the
average density
of
the
matter
is
brought
to
zero
at
infinity
in
the
appropriate
manner;
otherwise
infinitely large
differences in
potential
occur.
Such
an
interpretation
is
unsatisfactory
even according
to
Newton[6]-problem
of
reduction
of matter and
energy.
Dispersal
at infinity-and
is
even more un-
satisfactory
according
to
relativity
theory,
because the
relativity
of
inertia
is not
satisfied.
The
latter would be determined for
the
most part
by
the
guv's
in
infi-
nite
space and, to
a
very
small
part,
by
interaction with the
other
masses.
This
interpretation is
intolerable
to
me.
The
only
alternative
I
find
is
the
hypothesis
of
spatial closure,
the
feasibility
of
which
I
have
proven.
I
do not
seriously
consider
believing
that
the
universe
is statistically
and
me-
chanically
at
equilibrium, even
though I
argue as
I
do.[7]
The
stars would all
have to
conglomerate,
of
course (if
the
available volume
was finite).
But
closer
reflection
reveals
that statistics
can
be
legitimately applied
to
the
problems
of
importance to
me.
It
could also be done
without statistical
considerations, by
the
way.
It
is
certain
that
infinitely large
differences in
potential
would have to
yield
stellar
velocities of
very significant magnitude
that
probably would have
ceased
long ago.
Small differences in
potential,
in
conjunction
with
infinite
ex-
tension
of
the
world, require emptiness
in
the
universe
at
infinity
(constancy
of
the
guv’s
at
infinity
for
a
suitable
choice of
coordinates),
in
contradiction
to
a
sensible
interpretation
of
relativity. Only
the
closure
of
the
universe
frees
us
from
this
dilemma;
this
also
suggests
itself in
that
the curvature has the
same
sign
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