DOC.
313
MARCH
1917
303
313. From Willem
de
Sitter
Leyden,
20
March
1917
Dear Mr.
Einstein,
I
have found
that the
equations
Guv
=Ag
fLV
0,
thus
(13a)
without
matter,[1]
can
be satisfied
by
the
guv’s,
which
are
given
by[2]
ds2
-fir2
-
dy2
-
dz2
+
c2dt2
(1
-
/ah2)2
(1)
A
h2
=
c2t2
-
x2
-
y2
-
z2. x,
y, z,
t
can
become
oo.
At
infinity
(either spatial
or
temporal
or
both)
the
guv’s
become
0
0
0
0
0 0
0 0
0
0
0 0
0
0
0
0
Here
we
thus
have
a
system
of
integration
constants,
or
boundary
values at
infinity,
which
is
invariant
under
all transformations. For
relatively
small values
of
h,
i.e.,
in
our
spatial
and
temporal
proximity,
we
have
the
guv’s
of the old
theory
of
relativity
if
only
u(A)
is
small
enough.
This
is achieved without
supernatural
masses only
through
the introduction
of
the
undetermined and undeterminable
constant
A
in the
field
equations.[3]
I
do
not
know if it
can
be said
that
“inertia
is
explained”
in
this
way.
I
do
not
concern
myself
with
explanations.[4]
If
a
single
test
particle
existed in
the
world,
that
is,
there
were
no
sun
and
stars,
etc.,
it would have inertia.
Also
in
your
theory,
as
I
see
it,
if
physical
masses (sun, etc.) were
not
there.
Conjecturing
that
supernatural
masses
did not exist
is just
as
impossible
in
your
theory
as saying
“assume
the
world did not
exist.”[5]
(1)
can
also be
interpreted
in such
a way
that
the
four-dimensional
world
is
finite,
with
a
given
by
A =
3/R2.
The
analogy
with
your
solutions
emerges
from
the
following
comparison:[6]
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