478
DOC.
465
FEBRUARY
1918
highly
rarefied
energy,
which surrounds
the
mass
particles,
converges very
rapidly
toward
p
=
0,
while in
the
curved
space,
on
the other
hand,
it
converges very
rapidly
toward
p
=
2A/k.
This
seems
to
me
to
be
the
only
difference.
Nothing
can
be
stated,
however,
as
it
seems,
about the
amount
of
discrete
material
particles
in
the
world,
also not in
the
case
of curved
space.
In
the latter
case
there
would
be conceivable
a
world in which
there
were
only
1
electron
or 1
atom,
while
the
entire
remaining region
would be
permeated
continuously by
an
extremely
thin
material
haze of
density
p;
but there
could also be
an entirely
arbitrary
number
of atoms in
the
world.[17]
If
you
want to interpret
p
in
your
equation
k
.
p
=
2À
as
the
average density
of
the
celestial bodies’
distribution
of
mass
in
space,
then
in
my opinion you
must
first show
that
a
value for
the
gravitational potential
can
exist in
the
vast
empty
intermediate
spaces,
where
one
actually
has to
set
p
=
0,
which satisfies
the
condition of
the
continuous
uniformity
of these
spaces.
If
no
such
integral
solution for
the
equations
Guv
-
Aguv =
-k(Tuv-1/2guvT) can
be
found,[18]
then the
interpretation
that
I just
described
must
be
the
only
cor-
rect
one.
Then, however,
the
assumption
of
curvature
could
offer
no
apparent
advantage.
What
is
immediately conspicuous
about this
theory
and
speaks
little
for
it
is,
of
course,
that
the
principle of
relativity of
uniform
motions becomes
invalid
within
it. For with
the
cylindrical
curvature assumed
by you
for
the
four-
dimensional
space-time region,
the
time axis
as a
cylindrical
axis
is
preferred
over
the three
spatial
axes
(in
the
cylinder cross-section),
which
the three
cylinder
cir-
cles
form. If the
theory
of
cylindrically
curved
space-time
were
correct,
it would
have
to
be
possible
to
conduct
experiments
that did
not
yield
a
purely
negative
result,
as
did
the
Michelson
experiment, provided,
of
course,
that
we
could attain
the
necessary precision.
This
seems
to
me
to
be
a
very
important
difference of
fundamental
principle
between
the
theory of
flat and of curved
space.
With best
regards, yours truly,
Gustav
Mie.
[7]Deleted
line in
draft:
“the
same
body
cannot
be
simultaneously
at rest
and
in
motion.”
[14]Deleted
text in
draft:
“I
hope
...
I
can
win
you
over
to
this
interpretation
as
well.”
[15]Draft
passage:
“I
am
quite
shocked
to note
now
that
in
the
new
theory absolutely
none
of the
principles
that
I
had
seen as
the
nicest in
your
theory
of
gravitation
are
valid
anymore.
The
principle
of
the
relativity
of motion
certainly is
no
longer
valid,
because
within the
universe
itself the time
axis
plays
a
different role from
the three
spatial
axes;
hence
there
must
be
experiments
that
do not
produce
a
negative
result
like Michelson’s