110
DOC.
22
ADDENDUM TO DOC.
21
Based
upon
this
system
one
can-by
retroactive choice of
coordinates-return
to
those laws which I established
in
my
recent
paper,
and without
any
actual
change
in these
laws,
because it is clear that
we
can
introduce
a new
coordinate
system
such
that relative to
it
V-g
=
1
holds
everywhere.
Sim
then vanishes and
one
returns
to
the
system
of
field
equations
Ruv
=
-KTuv
(16)
of the
recent
paper.
The formulas of absolute differential calculus
degenerate exactly
in the
manner
shown in said
paper.
And
our
choice
of coordinates still allows
only
transformations of determinant
1.
The
only
difference in content between the field
equations
derived
from
general
covariance and those
of
the recent
paper
is that the value
of
L-g
could not be
prescribed
in the latter. This value
was
rather determined
by
the
equation
{1}
a
_____
=
-KET:.
Xa
Xp
U
(21a)
This
equation
shows that
here
yf-g can
only
be
constant
if
the scalar of the
energy
tensor
vanishes.
Under
our
present
derivation
yf-g
=
1
due
to
our arbitrary
choice of
coordinates.
The
vanishing
of the scalar of the
energy
tensor
of
"matter" follows
now
from
our
field
equations
instead
of
from
equation (21a).
The
generally
covariant
field
equations
(16b),
which
form
our
starting point,
do
not
lead
to
a
contradiction
only
when the
hypothesis,
which
we
explained
in
the
introduction,
applies.
Then, however,
we are
also entitled
to
add to
our previous
field
equation
the
limiting
condition:
v/-g
=
1.
(21b)
Additional
note
by
translator
{1}
The
"dxa"
inside of the
parentheses
has been corrected to
"dxß."