260
DOC.
272 NOVEMBER
1916
272. From
Willem
de
Sitter
Leyden,
1
November
1916
Dear Mr.
Einstein,
I
am sending you
today
a
separate
offprint
of
a
little
popular
exposition
of
the
general
theory of relativity which
I
have
published
in
an
English
astronomical
journal.[1]
I
have been
thinking
much
about the
relativity
of
inertia
and
about
distant
masses,[2]
and
the
longer
I
think about
it,
the
more
troubling
your
hypothesis
becomes for
me.[3] I
mean
the
hypothesis
that
(a)
at
infinity
the
gij's are
such
that
the
Minkowski
cones
become
planes
(i.e.,
three-dimensional flat
spaces),
and
that
(b)
far
beyond
all known
material
bodies,
as-yet-unknown masses
exist which
produce
the
effect
that,
in
regions
of
space
and time
we
know
about,
the
special
theory
of
relativity is
valid in
the
absence of
mass,
thus
that the
Minkowski
cones
have
a
finite
aperture. First,
a
question.
As I
understand the
hypothesis,
not
only
does it
predict
that the
gij's
degenerate
in
the
way
mentioned for infinite values
of the
space
variables
x1 x2
x3,
but
also
for
infinite values of
the
time variables
x4.
Is
this
correct,
or
do
the
gij's remain
Galilean-or
approximately
Galilean-for
x4
=
oo
but
x1, x2,
x3
finite? If
I
am
right,
the
hypothesis
would
thus
make
the
universe finite
not
only
in
space
but
also in time.
We
know
nothing
about
the
infinitely
distant
past
and
about the
infinitely
distant
future-therefore,
no
observations
can
tell
us
that there
has
always
been
a
universe and
that there
always
will
be
a
universe.
It
is not
the
finiteness,
in
principle,
in
space
and
time
which
bothers
me,
but
the
conviction
that the
boundary,
the
“envelope,”
will
always
remain
hypothetical
and
will
never
be observed.
Now
we can
say:
the
sources
of inertia
lie
beyond
the
Milky
Way,
but
when
our
grandchildren
make
an
invention
that
enlarges
the
known world in
the
same
proportion
that
it
was
enlarged
300
years ago
through
the
invention of
the
telescope,
then the
envelope
will
simply
have
to
shift
farther
outwards
again.
From
this
I conclude
that
the
envelope
is
not
a
physical reality.
If
the
hypothesis
is
accepted,
one
would first want
to
get
a
[crude]
idea
of
where these
distant
masses are
and of what
they
are
composed; second,
how
the
inertia
comes
over
here from there. An
artificial
mechanism will be
invented. The
coordinate
system
with reference to
which
the
envelope
and
this
mechanism
are
at rest
will
also be defined.
Although
the
principle
of
relativity will
still hold
formally, effectively, we
shall have
the
old absolute
space
with the ether
back.
And
another
thing
as
well.
At
infinity, only
transformations
in which
t'
is
just
a
function of t
are permissible,[4]
hence,
no
Lorentz transformations,
for
ex.
Thus in
the
finite
realm,
no
exact Lorentz
transformations
may
be
performed
either, only
one
that,
as
far
as our
universe
extends,
coincides
very precisely
with