DOC.
317
MARCH
1917 309
It
certainly
would be most
natural
to describe this world
as
spatially
closed and
finite.
2)
The
hyperboloid
surface
1
-
uh2
=
0
is
a
singularity.
On
crossing it,
the
guu's
jump
from
-oo
to +oo, and
the
g44’s
from +oo to
-oo,
resp.[5]
3)
Such
singularities
are
to be ruled out in
the
physically
finite. The intersection
of
the
positive
t-axis with
the
singul[arity's]
surface
is
at t
= 1/uc.
The
naturally
measured
(time-like)
distance
of
the
intersection
point
from
the
origin
x1
=
x2
=
x3
=
t
=
0
(measured
on
the
time
axis)
is
Sis=So
v^c 1
cdt
--(finite).[6]
1
-
¡jlcH2
\fß
2
The surface
with
singular qualities
(discontinuities)
thus
lies
in
the
physically
finite.
It
seems
to
me
for
this
reason
that
your
solution does
not
correspond
to
a
physical possibility.
The
guv's
and
guv’s
(together
with
their
first
derivatives)
must be continuous
everywhere.
In
my
opinion,
it would be
unsatisfactory
if
a
world
without
matter
were
possible.
Rather,
the
guv-field
should
be
fully
determined
by
matter and not
be
able to
exist
without
the
matter.
This is the
core
of what
I
mean
by
the
requirement
of
the
relativity of inertia.[7]
One could
just
as
well
speak
of
the
“matter
conditioning geometry.”
To
me,
as
long
as
this
requirement
had
not
been
fulfilled,
the
goal
of
general relativity was
not
yet completely
achieved. This
only
came
about
with
the
A
term.
Cordial
greetings, yours,
Einstein.
P.
S.
The
fact of
low
stellar velocities
is
an
argument
whose
cogency
exceeds
that
of
the
nonexistence of
the
violet shift
only
insofar
as one
is not
limited here
exclusively
to
the
effect of
the visible
portion of
the
stars.[8]
Under the
assumption
of
a
mechanically
quasi-stationary
behavior
of
matter,[9]
the
low
stellar velocities
prove
that
great
differences in
gravitational potential
do
not
occur
at all in
the
universe.
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