**Subject:** 131(5) : Consequencies of Antisymmetry on the U(1) Level

**Date:** Tue, 28 Apr 2009 10:20:03 EDT

Attachment: a131stpapernotes5.pdf

This note develops a note written about three weeks ago. The general antisymmetry law is that when ANY tensor quantity with mu and nu lower indices is generated by a commutator with mu and nu indices, it vanishes unless it is antisymmetric. If it were symmetric it could not have been generated by a commutator. This is as elucidated in the flow charts of proof one on _www.aias.us_ (http://www.aias.us) . No serious scholar has objected to this proof. In this note I give three examples of the power of the antisymmetry law on the U(1) level. There is a relation or constraint between the scalar and vector potentials in the static electric field. The vector potential of the magnetic field must also obey antisymmetry constraints such as eq. (29) (also given by Atkins in “Molecular Quantum Mechanics” (many editions, Oxford University Press)). Finally, in the third example, the antisymmetry law removes gauge freedom, (U(1) Lorenz gauge freedom) a finding that makes gauge theory obsolete in another way. Gauge theory was in fact wrong from the very beginning because it was incompatible with photon mass, (the Proca equation is not gauge invariant). Photon mass is a fundamental necessity introduced by Einstein in 1906 and advocated by Vigier and de Broglie. Gauge theory is mainly due to Weyl. The B(3) field is also antisymmetric in mu and nu on the O(3) and ECE levels of electromagnetism. Gauge freedom so called was simply due to a problem being underdetermined mathematically in Heaviside’s formalism, it needed a constraint, and that constraint is antisymmetry of the commutator acting on the gauge field. On the ECE level the commutator acts on the vector in any spacetime and of any dimension. The connection takes the antisymmetry of the commutator, otherwise it would not have been generated by the commutator, QED.

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