DOC.
487
MARCH
1918 505
10)
Therefore, by
no means am
I
capable
of
seeing
how
any physical
statements
about the
nature of
the
field
(K,
aQ)
can
be obtained from
(9).-
So
much for criticism.
However,
I
have
long
since
given
a
positive
turn to
the
matter
by presenting
to
our
Soc. of Sci.
on
22
February
the
closely
related
proposal[10]
of
avoiding
all identities
by
not
attributing
to
the
gravitational
field
any special energy
at
all,
rather
simply choosing
Q,u
=
-K"
as
components
of
the
“energy
tensor.”[11] As
a
test, I
applied
Schwarzschild’s
formulas for
the
gravitational field of
a
homogeneous, incompressible
fluid
sphere
at rest
(Sitzungsberichte
1916).[12]
To
simplify
the
comparison
to
the
statements
of classical
mechanics,
I
immediately placed,
instead
of
the
energy tensor,
its
simplest
scalar:[13]
E
K^çr
^
T.KZ
a
*\f9
(which,
by
the
way,
converts into
+K/a
according
to Hilbert’s first
note,[14]
p.
8)
into the
foreground
and
regarded
it
as
analogous
to
the
“Lagrangian” (T
-
U).
This
means
that
I regard
K
•
aw,
J
a
integrated
over
any segment
of
the
world,
as
analogous
to Hamilton’s
integral
(and
not,
for
instance,
as
Lorentz does in his lectures of
1916,[15] ƒ
K/adw
+
ƒ
Qdw ).
In
Schwarzschild’s
case,
the
mentioned
scalar,
in conformance with
your
for-
mula of
1914[16]
from which Schwarzschild starts,
is equal
to
p0
-
3p-or,
how
I
still
always
prefer
to
write it in
the
cm.gr.sec. system
=
c2p0
-
3p.
For
p,
Schwarzschild indicates here in formula
(30)
of his
paper,
if
I also add
the factor
c2,
2
COSX-COSXa
V
=
Poc
^-•
3
COS Xa
-
COS
X
Here,
to make
the transition
to
classical
mechanics,
I
replace
the
cos.
with their
series
expansion
and
have
as
the
lowest
term[17]
.2
xl
X
Poc
u
or,
with
k as
the
normal
gravitation
constant:
2TTKp20(rl
-
r2)
3