2 7 4 D O C . 2 8 2 O N E D D I N G T O N S T H E O R Y
or according to (4a)
These equations, together with (2), (3), and the equations (1c), determine the field
equations. is the electromagnetic energy tensor of Maxwell’s theory. Let it be
noted that a term of the form could be appended additively to the func-
tion H that would correspond to the “cosmological” term of the general theory of
By the calculation indicated one obtains field equations of the form
where means, as in (37, 2), the contracted Riemann tensor. As concerns the
physical interpretation of these equations, one does in any event have to interpret
as the tensor of the electromagnetic field. The first of equations (12) exactly
corresponds to the familiar field equations of the general theory of relativity in the
case being considered here, that apart from the metric field only an electromagnetic
one exists, but that to which another energetic term is added that is determined by
the current density. The second of equations (12) seems to directly contradict ex-
perience, for it requires that the electromagnetic field vanish wherever the charge
density vanishes.
This objection however does not hold, since in fact we do not know whether very
small densities of the electrically charged masses aren’t associated with electro-
magnetic fields. In order to be able to assess the permissibility of equations (12),
we must furthermore take into account that the unit of the electromagnetic field has
to be changed if length is supposed to be measured in centimeters, and mass, i.e.,
energy, in grams. We then have to write instead of (12)
dH* β
--gαβfστfστ - fασfβ¹

δgαβ fαβδfαβ + –=
--gαβfστfστ - fασfβ¹

–βEμν = =
ϕμν βfμν. –=
const –g
Gμν βEμν
--iμiν - –=

--¨ -

, =
[p. 371]
Previous Page Next Page