364
DOC.
368 AUGUST
1917
energy,
is certainly not
present
relative
to
the
original (Galilean) system
K.
As
absolutely
all
components
of
the
energy
“tensor” in
question
vanish
altogether
with reference to
K,
this
vanishing
of
all
components
must also take
place
relative
to K',
provided
the
gravitational
energy really
can
be
expressed
as a
tensor.
The
pendulum clocks
example speaks against
it.
Altogether,
it
seems
that the
energy components
for
the
gravitational field
should
just
be
dependent
on
the
1st
derivatives
of the
guv's,
because
this
is
also valid for
the
forces
exerted
by
the
fields.
There
are no
1st order tensors
(dependent
only
on
dguv/dxo
&
guv),
however.[7]
2)
You
think that
the
field
equations
Gou
+
5£
=
0,
where
G°u
depends only
on
guv
&
the
1st
and
2nd derivatives
and
Xou
on
the
mass, ought
to be
understood
as
energy equations,
hence
that
G°u
would be
the
energy components.
But
with this
approach
it
is
completely incomprehensible
why
such
a
thing
as an energy
law
even
exists in
spaces
in which
gravitation
can
be
disregarded. Why,
for
ex.,
should
a
body
not
be able to cool down
without
emitting
heat
outwards? The
equation
G44
+
X44
=
0
does allow
X44
to
diminish
throughout,
whereby
this
change
is compensated
by
a
reduction in
the
absolute
value
of
the
quantity
G44,
which does
not
fall
within
physical
observation.
That
is
why
I
contend
that what
you
call
an energy
law
has
nothing to
do with what is otherwise known
as
such in
physics.
3)
I set
up
a
law in
the
form
dTa
+
U!/*
~
_
Q
dxa
and
draw
consequences
from
it.[8]
These
consequences are
correct
independently
of
whether
one
concedes
that
the
tov’s
are
“real”
energy components
of
the
grav-
itation.
Since,
with
the
vanishing
of
the
Xov’s
and
tov’s
at
(spatial) infinity,
the
theorem
d/dx4{/z44+t44)dv}=0
is
always
valid, whereby
the
integral
is
extended
over
the
entire three-dimensional
space.
For
my deduction,
it
is
necessary only
that
X44
be
the
energy density
of
the
mass,
which
neither
of
us
doubt.
4)
Finally,
in
an
appeal to
your physical sense,
I
would
like to
call
your
attention
to
the
following
case.
Let
the
space
be Galilean
(field-free)
except
for
the
field