486
DOC.
470 FEBRUARY
1918
through
the
Lorentz
transformation;
the
importance
of
special
relativity
thus
ex-
tends
only
to
the
consideration
of
regions
that
are
small
enough
to
be
regarded
with
sufficient
precision
as
Euclidean
(Galilean).
From
the last
exposition
in
your
letter
I unfortunately
see,
as
in
many
other
instances
already,
that
my Academy paper
“Cosmol. Considerations”
is
being
totally
misunderstood.[7]
Apparently
I
did
not
express myself precisely enough.
The
equations
Guv
v
~
-g^T")
should be
exactly
valid
everywhere.
The
T44’s are
thus
supposed
to differ from
zero
only
in
the
interior
of
the
stars
but
vanish
everywhere
else.
If
I
imagine
the
universe divided into
regions
of
equal
size,
each of
which
contains
on
average
1,000
fixed
stars,
then
each
of
these
regions
will
contain
approximately
the
same
amount
of
mass.
I.e.,
I make
the
hypothesis
that
apart from
the
local concentration in
stars,
the matter
is
uniformly
distributed
on
the
large
scale.
This matter
I
replace,
for
the
sake of
convenience,
with
homogeneously
distributed
matter
of
the
same
mean
density.
In
this
way,
the
grav.
field’s
local structure
is admittedly
changed,
or
disturbed
compared
to
reality.
However,
the
metric
character
of
this
field
will
be
preserved
on
the
large scale,
so
I
am
correctly
informed
about the
geometric
nature of
the
universe
on
the
large scale. Thus,
in
this
consideration
I
abstract
totally
from
the
structure of
the
field
in
spaces
of
the
order of
magnitude
or
smaller
than the
distance
from
neighboring
fixed stars.-
Finally,
I note
that
Michelson’s
experiment
must
always
come
out
negatively
according
to
the
general
theory
as
well,
in the
case
where the mirror
structure
is
so
small and in such
a
state of
motion
that the
guv’s,
with
reference
to
the
structure
as a
coordinate
system,
are
constant
enough
in
the
relevant
space.-
Now I
believe
I
have addressed
everything you
mentioned in
your
letter.
I
think
we
shall
come
to
understand
each other’s
standpoint
by
this
means
of
“successive
approximation.”
With best
regards, yours truly,
A. Einstein.