462 DOC.
456
FEBRUARY
1918
matter to
me
at
all,[4]
and
although I
see
from
your
writing
that this
is not
so
for
all
scientists, I
do know
that there
are some
other
people
of
my persuasion.
As
your paper
demonstrates,
pondering
about
these
things
can
certainly
provide
an
impetus
for
very
interesting
reflections,
but
one
will
probably
not be able to
arrive at
the
definitive conclusions
on
the
basis of
them.[5]
Now I
would
like to
venture
a
remark
on
the
statement
expressed
in
eq. (15)
of
this
paper:
p
=
2/k.R2.[6]
This
relation
seems
to
state
that the radius
of
curvature
R
of the
space
is
determined
by
the
density
of the
total
mass
distributed
approximately
evenly
within it. This claim would be
wrong, though.[7]
If, as
is
commonly done,
we
define
the
unit
of
mass
as
the
mass
of
a
specific
atom
(1
gr
=
N/16
oxygen atoms,
where
N
is
Avogadro’s number)
and define
the units
of
length
and
time
through
a
particular
atomic
process
(1
cm
=
15
531.6403
x
wavelengths
of
the
red Cd
line;
1
sec
=
3.1010/15531.6403
x
period
of
this
light),
it
is
then
easy
to
see
that, for
any
given
value
of R
cm
for
the
radius of curvature of
the
space,
the
density
of the world’s
mass
distributed
evenly throughout
the
space
can
have
an
entirely
arbitrary
value
pgT/cm3.
If
I call
the
value
that
would
result
from
equation
(15)
specifically
for
the
density,
p1,
hence
p1 = 2/k.R2gr/cm3
then,
for
p
=
p1,
the
gravitational
potential
in
the
regions
without
matter between
the
uniformly
distributed individual celestial bodies in
the
space
would be
equal
to
-1, g11
=
g22
=
g33
=
-g44
=
-1;
but
if
p
were
to
have
some
other
constant
value,
the result
would
then
simply
be:
g11 = g22 = g33 =
-g44 =-p/p1;
this
would be
the
only
difference.[8]
The
gravitational potential
in free
space depends
on
the
average density
of
the
celestial bodies
filling
the
space,
otherwise
this
density
has
no
influence
on
the
events
in
the
world. If
desired,
the
units of
mass,
length,
and time
can,
of
course,
be selected for
any
contents of
matter
in
the
world such
that
g°°
=
-1
results
exactly;
in this
mass system,
eq. (15)
then
also
applies
unchanged.-
I did
want
to
write
this,
at
the
risk
of imparting
things long
since familiar
to
you,
to
make
you
aware
that
eq. (15) can
possibly
be misunderstood.
But
I
was
naturally particularly
interested in
what
you say on p.
148
about the
approxi-
mation
of
the
“real” spatio-temporal
continuum with
a
mathematically
simple
space-time
of constant
curvature,
because
there
you express
the
same
idea I
had
presented-for
a
flat
space-time,
of
course-in
my
third
lecture.[9]
I
find
your
comparison
to
the
geodesists’
method
of
approximating
the Earth’s
surface
with
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