82 DOC. 17 GRAVITY AND MATTER
192
ATOMIC
STRUCTURE
So
far the
general theory of relativity
has
made
no
change
in this
state
of
the
question.
If
we
for
the
moment
disregard
the additional
cosmological
term,
the
field
equations
take
the
form
- = -
KT~~
•
(1)
where
Guv
denotes
the
contracted Eiemann
tensor of
curva-
ture,
G the scalar
of
curvature formed
by
repeated
contraction,
and
Tuv
the
energy-tensor
of
“matter.”
The
assumption
that
the
Tuv
do not
depend
on
the
derivatives
of
the
guv
is
in
keeping
with the historical
development
of
these
equations.
For these
quantities are, of course,
the
energy-components
in
the
sense
of
the
special
theory
of
relativity,
in which
variable
[7]
do
not
occur.
The
second term
on
the
left-hand side
of
the
equation
is
so
chosen that the
divergence
of
the left-
[8]
hand
side
of
(1)
vanishes
identically,
so
that
taking
the
divergence
of
(1), we
obtain
the
equation
^
rr
=
0
•
(2)
which in
the
limiting
case
of
the
special
theory of relativity
gives
the
complete
equations
of conservation
~xv
Therein
lies
the
physical
foundation
for
the
second term
of
the left-hand
side
of
(1).
It
is
by
no means
settled
a
priori
that
a
limiting
transition
of
this
kind
has
any possible mean-
ing.
For
if
gravitational
fields
do
play
an
essential
part
in
the
structure of the
particles
of
matter,
the
transition to
the
limiting
case
of
constant
guv
would,
for
them,
lose its
justifi-
cation,
for
indeed,
with
constant
guv
there
could not be
any
particles
of
matter.
So if
we
wish
to
contemplate
the
possi-
bility
that
gravitation may
take
part
in the
structure
of
the
fields
which constitute the
corpuscles,
we
cannot
regard
equation
(1)
as
confirmed.
Placing
in
(1)
the
Maxwell-Lorentz energy-components
of
the
electromagnetic
field
Cuv,
[6]
[9]
Tm,
=
-
P^gVT,
.(3)