This note develops a new theory of the internal structures of the electron, proton and neutron on the basis of a Beltrami equation for the tetrad. Each property is the expectation value using wavefunctions that are solutions of the Helmholtz wave equation, products of Bessel functions and spherical harmonics. For example the recent ten year experiment at Imperial College London has shown that the electron has no electric dipole moment, and is a sphere of unmeasurably small radius. In the ECE theory this result is described by Eq. (32), by choice of the wavefunction. The magnetic dipole moment of the electron is described by Eq. (35), and is well known to be proportional to the intrinsic spin angular momentum of quantum mechanics. The homogeneous internal structure of the electron is again described by a choice of wavefunction, analogous to the S orbitals in hydrogenic wavefunctions but using Helmholtz / Beltrami wavefunctions. The wavefunctions being used here are not hydrogenic, atomic or molecular they come from a Beltrami structure. The results of the Imperial College experiment have refuted all supersymmetry theories of the standard model, and there is no actual experimental evidence for quarks inside the electron. The particles predicted by supersymmetry have not been detected at CERN in electron positron collisions, and UFT225 shows that the GWS theory is wildly incorrect. No one has challenged UFT225 in almost three years and it has been sent to CERN. All that is observed experimentally for the electron is a perfect sphere without an electric dipole moment but with a magnetic dipole moment coming from intrinsic spin angular momentum. The next note will deal with the internal structures of the proton and neutron using the same Beltrami sub geometry of Cartan geometry in the context of ECE theory. The experimental data here come from deep inelastic electron proton and electron neutron scattering, and again give no evidence at all for quarks. The latter are just figments of imagination produced by a curve fitting exercise with over a hundred adjustables in supersymmetry theories that have just collapsed entirely, along with superstring theories and so on. The ECE / Beltrami theory has no adjustables except for kappa of the Beltrami tetrad equation.

a260thpapernotes5.pdf

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