Fundamental Role of the Commutator of Covariant Derivatives

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The commutator is fundamental to geometry and has antisymmetry properties which work their way into all aspects of gravitation and electromagnetism. In papers 122 onwards these antisymmetry properties are developed comprehensively. The commutator acts on a vector in any spacetime of any dimension to produce the spacetime torsion and curvature simultaneously. The commutator shows that the connection in Riemann geometry is antisymmetric. These fundamental properties have a profound effect on physics and technology, for example the formation of new companies as detailed in following blog messages. In the area of quantum computers for example the ECE vacuum structure is important, and is defined by the presence of potentials in the absence of fields. This definition holds for the unified field, the ECE field. Physics is no longer compartmentalized into separate subjects such as electrodynamics, gravitation and particle / field theory.

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