**Subject:** Next Note on Paper 131

**Date:** Tue, 5 May 2009 06:33:28 EDT

This will illustrate the new potential antisymmetry relations with plane waves, showing on the U(1) level of electrodynamics that whenever there is a vector potential plane wave accompanying the electric field plane wave, there must also be a scalar wave. On the ECE level a spin connection vector is always accompanied by a spin connection scalar. These new ideas of antisymmetry can also be applied to the ECE engineering model. The new commutator generated antisymmetry relations are:

partial sub mu A sub nu = – partial sub nu A sub mu

On the U(1) level for the electric field for example:

E = – del phi – partial A / partial t

with

del phi = partial A / partial t

This makes the fundamental discovery that an electric field is both the gradient of a scalar potential and the time derivative of a vector potential. This fundamental property has been overlooked ever since Heaviside’s time, yet is a straightforward result of using the antisymmetric commutator. Similarly, the commutator produces the antisymmetric connection of Riemann geometry, another major discovery of ECE theory. This result has been overlooked since tensors were inferred, in about 1900, but again is straightforward in retrospect. Looking forward, research is anything but straightforward. The theory of the Aharonov Bohm effects is also affected by this new discovery. The standard theory is based on a non Baconian unobservable, a non-simply connected vacuum, and makes erroneous use of the Stokes Theorem, as was shown in GCUFT1. The ECE theory of the AB effects explains them straightforwardly with the connection of spacetime in four dimensions (see AB papers of the UFT series).

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