✍ Scribed by Evans, Myron W.
No coin nor oath required. For personal study only.
The topological approach of Ran ˜ada and Trueba, the general relativistic approach of Sachs, and the O(3) electrodynamics are interlinked and shown to be based on the concept of Faraday's lines of force.
In the review by Ran ˜ada and Trueba [1], electric and magnetic lines of force were discussed as real, physical entities, based on the original concepts of Faraday. These authors discussed Kelvin's suggestion of 1868 that atoms are knots of links of vortex lines of the ether, a topological concept, and that Kelvin found the concept of point particle to be extremely unsatisfactory. Point particles are eliminated from consideration in the Sachs [2] theory of electrodynamics, and are replaced by curvature of spacetime. The O(3) electrodynamics of Evans [3] has been demonstrated to be a subtheory of the Sachs theory. Ran ˜ada and Trueba discuss the fact that, in contemporary topology, invariant numbers characterize configurations that can deform, distort, or warp. These concepts are similar to the curving of spacetime in general relativity [2], of which O(3) electrodynamics [3] is a subtheory, and also a gauge theory. Topology shows that the variety of chemical elements is due to the way in which curves can be knotted and linked, transmutability of the elements
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