DOC. 17 GRAVITY AND MATTER 83
A.
EINSTEIN
193
we
obtain
for
(2), by
taking
the
divergence,
and
after
some
reduction,*
fß,y
=
o

(4)
where,
for
brevity, we
have set
d/dx(-g
duvgua)
=
ja

(5)
In
the
calculation
we
have
employed
the
second of
Maxwell’s
systems
of equations
typ-
+
^P
+
typp
=
Q
^Xp '¿Xp
iXp
.
(6)
We
see
from
(4)
that the
current-density Ja
must
everywhere
vanish.
Therefore,
by
equation
(1),
we
cannot arrive at
a
theory of
the electron
by
restricting
ourselves to
the
electro-
magnetic
components of
the Maxwell-Lorentz
theory,
as
has
long
been known. Thus if
we
hold to
(1)
we are
driven
on
[11]
to
the
path
of Mie’s
theory.f
Not
only
the
problem
of
matter,
but
the
cosmological
problem
as
well,
leads to doubt
as
to
equation
(1).
As I have
shown
in the
previous paper,
the
general
theory of relativity
[13]
requires
that
the universe be
spatially
finite.
But this
view
of
the
universe
necessitated
an
extension
of equations
(1),
with the introduction
of
a new
universal constant
A,
standing
in
a
fixed relation
to
the total
mass
of the
universe
(or,
re-
spectively,
to the
equilibrium
density
of
matter).
This
is
gravely
detrimental
to
the
formal
beauty of
the
theory.
d
2.
The Field
Equations
Freed
of
Scalars
The difficulties set
forth
above
are
removed
by setting
in
place
of
field
equations (1)
the
field equations
Guv
-
1/4guvG
=
-
kTuv
.
(la)
[14]
where
Tuv
denotes
the
energy-tensor
of
the
electromagnetic
field
given by (3).
The
formal
justification
for
the factor
-
1/4
in
the
second
*
Cf.
e.g.
A.
Einstein,
Sitzungsber.
d. Preuss. Akad. d.
Wiss.,
1916,
[10]
pp.
187,
188.
f
Cf. D. Hilbert,
Göttinger Nachr.,
20 Nov., 1915.
[12]
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