76 DOCS.
63,
64
MARCH
1915
dE41/dt
vanishes in
the
static
case.
If
I
multiply
the
equation
by
x
and
integrate
over
the
entire
body,
then
I
(&r~
&r~
&r~\
~ax
ôy
i9zj
dx
dy
dz
=
0
changes
through partial
integration
to
ƒ
%\dx
dy
dz
=
0,
as
Laue has
already
recognized.[3]
Thus it
is
proven
that
for
the
planetary
prob-
lem[4]
a
g11
field
cannot
come
into
consideration.[5]
With best
regards, yours,
Einstein.
64. To
Tullio Levi-Civita
[Berlin,
20
March
1915]
Dear
Colleague,
I
have received
your
letter with
the
counterargument
to
disprove
the tensorial
character
of
1/-g
Euv,
which bases itself
on
the
case
where
among
the
adapted
coordinate
systems
such exist whose
guv's are
constant.[1]
You
say
under
(2)
“This
tensor
is,
to
the
contrary,
not
identical
to
zero
for
all
adapted
coordinate
systems;
this
is especially
obvious in Newton’s
case.”[2]
I
do
not
consider
this
correct, however.
It should be noted that, in
general,
it
is not
possible
to
alter
through
transformation
of
the
coordinates
any given
guv
field
into
one
in
which
the
guv's
are
constant. This
will
always
be
impossible
for
parts
of
a
Newtonian
field
containing masses,
for
ex.;
this
is
also
generally
true
of mass-free
regions, incidentally.
I
believe
that
the
proof
or
disproof
of
the statement
quoted
from
your
letter
is just
as
problematic as
the
proof
or
disproof
of
the
general
statement of
the
tensor
character
of
/Euv-g.
With cordial
greetings
and
hoping
for
a
prompt
reply, yours,
A.
Einstein.
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