518
DOC.
495 MARCH
1918
applies.[10] (In
my paper
GiK
=
kTik
appears
because
I had calculated
the inertial
forces
as negative.)
These
GiK’s
are
Hilbert’s[11]
-~[[\/~K]jK.
They
identically
fulfill
the
energy-momentum
conservation
law:[12]
^9(rs)Gir/s
=
0
*
=
1, 2,
3,
4;
they
are
therefore
the
complete
covariant
counterparts to
the
TiK's.
Their
adop-
tion
as
gravitational
tensors
are
thus
so
plain
that, under
the
influence of Hilbert’s
papers
and the
excellent
little
paper by Herglotz
in
the
Leipzig Berichte,[13]
I
as-
sumed
you
had
already
abandoned
your
tik's.[14]
But
now
I gather
that
you
still
are
retaining
them
and shall
therefore
point
out
this
difference,
which
is
lacking
in
my
paper,
later
in
the
correction
stage.[15]
I
suspect, incidentally,
that
the
tiK's
used
by
Lorentz and Levi-Civita
are
identical to
the
GiK’s.[16]
Since
I
cannot ob-
tain the
papers
of these
authors
here,
I
would be
grateful
for
your
confirmation
of
my suspicion.
Allow
me
to add
to
the
arguments against
the
tiK's
and for
the
GiK’s
(non-
covariance,
hence
physical insignificance!
sic!;
arbitrary
vanishing
upon
changes
in
coordinates,[17] etc.)
the
following
essential
points
to
my
interpretation:
The
gravitational
tensors
disappear
outside of matter
(with
regard
to
the
electromag-
netic
energy fields): Gik
=
0.
That
is, no
gravitational
energy
exists
detached
from matter,
therefore,
also
no (pure)
gravitational
waves,
in conformance with
experience,
which
demonstrates
a
complete
lack
of propagation
effects.
As
concerns
your argument re.
the
vanishing
of
the total
amount
of
energy
GiK
+
kTik
= 0,[18]
I
refer to
§6
of
my paper,
where
I
say:
there
is
no
interaction
between
material
and
gravitational
energy;
gravitation,
and
only
gravitation, is
purely
conservative.
This also
follows mathematically
from
the
fact
that the
Gik's
and
the
TiK’s
each
on
their
own
satisfy
the
energy-momentum
conservation
law;
thus the
Gik's
are
eliminated from
the
energy
law,
etc.
I
recall here
again my
emphasis
on
the
“force-free”
nature
of
gravitation;
I
said in
1916:
kinematic
versus
dynamic
conception,[19]
which comment
you
seem
to
have misunderstood.[20]
3)
Hence
here
we
already
see
that
arguing
from
an
analogy
between
electricity,
where free field
energy exists,
and
gravitation,
where this
energy
does not
exist,
is
inadmissible;
this
therefore
applies
all
the
more
to
your
third
objection,
which
seems
to
me
to have been
taken
over
directly
from
electricity.
For Maxwell’s theory treats
the
boundary
between
two
media
E1
and
E2
as
follows:
An
electromagnetic
field
exists
on
both
sides.
Hence, no
qualitative
differences, only
quantitative
ones.
It then
evidently
leads to
the
same
thing
if,