D O C . 2 8 2 O N E D D I N G T O N ’ S T H E O R Y 2 7 5
(13)
According to the second of these equations there exists a potential vector of the
electromagnetic field according to the equation
(14)
Therefore we can also write the first field equation as
(15)
The existence of practically current-free fields requires, according to (14), that β be
in fact vanishingly small. Then the last term in (15) will also be vanishingly small
compared to Maxwell’s energy term. Then our consideration leads to the same field
equations as the ones originally set up by the general theory of relativity, which are
obtained without any generalization of the geometrical foundations beyond the
Riemannian system.
These field equations do not, in any case, yield the electron as a singularity-free
solution. Furthermore, there is no hint from experience so far that electromagnetic
fields determine current densities locally.[7] To me the final outcome of this consid-
eration is, unfortunately, the impression that Weyl’s and Eddington’s delving into
the geometrical foundations cannot yield any advance in our physical understand-
ing; it is to be hoped that future developments will show that this pessimistic opin-
ion has been unjustified.
Gμν β2αEμν –
1
6
--α2iμiν - – =
βfμν
1§
6©
--¨ -
∂xν
∂iμ
∂xμ¹
∂iν
–
¸
·
. =
fμ
fμν
∂xν
∂fμ
∂xμ
∂fν
–=
6βfμ iμ. =
Gμν βα2Eμν – 6β2α2fμfν. – =