DOC. 22 ADDENDUM TO DOC.
21 109
Whoever
does
not
categorically
reject
the
possibility
that
gravitational
fields
could constitute
an
essential
part
of
matter
will find
powerful support
for this
conception
in
the
following.2
Derivation
of
the Field
Equations
Our
hypothesis
allows
us
to take the last
step
that the idea of
general relativity may
consider
as
desirable. It allows
us,
namely,
also to write the field
equations
of
gravitation
in
a
general
covariant form. I have shown in the
previous paper (equation
(13))
that
Gim
=
£
(il, lm)
= Rim
+
Sim
I
(13)
is
a
covariant tensor. And
we
had
im)
*»--E
a
«
p m
/
dX[
I
(13a)
S:im
(13b)
This tensor
Gim
is the
only
tensor available
for
the establishment of
generally
covariant
equations
of
gravitation.
We have
won
generally
covariant field
equations
if
we agree
that the field
equations
of
gravitation
should be
Guv = -KTuv.
(16b)
These,
together
with the
generally
covariant
laws,
provided
for
by
the absolute
differential
calculus, express
the causal
nexus
for "material"
processes
in
nature;
and
they express
it in
a
form that
emphasizes
the fact that
any special
choice of
coordinate
system-which
logically
has
nothing
to do with nature's law anyway-is
[p. 801]
not
used in the formulation
of
these laws.
2In
writing
this
paper
I
was
not
yet
aware
that
the
hypothesis
^
T*
=
0
is,
in
principle,
admissible.