This note confirms the recent finding by Doug Lindstrom and in previous papers that the spin curvature has a Beltrami structure in the absence of a magnetic monopole. In this case we obtain the Helmholtz equation for spin curvature, Eq. (22), with a rich and intricate variety of solutions for spin curvature in terms of spherical harmonics, Bessel functions and so on, including the shell solutions discussed this morning. Therefore the electronic structure of an atom and the structure of the nucleus are described by these quantized spin curvatures. The internal structure of an electron, proton or neutron may also have these quantized spin curvature structures. So this is a route into a completely new theory of elementary particles without use of SU(3), quarks, approximate symmetry, Higgs boson and so on. It has only one adjustable, kappa, compared with over a hundred adjustables in some standard supersymmetry theories. The latter have all been refuted experimentally at CERN. The Higgs boson was refuted in UFT225 and cannot exist as predicted. The same quantized spin curvature equation can be used for galactic structure, flow dynamics, plasma dynamics, the free electromagnetic field, and so on, because ECE is a unified field theory that applies to all scales from sub atomic to galactic clusters.

a260thpapernotes2.pdf

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