The Commutator Method of Generating Torsion and Curvature

Feed: Dr. Myron Evans
Posted on: Thursday, March 22, 2012 2:53 AM
Author: metric345
Subject: The Commutator Method of Generating Torsion and Curvature

For interested scholars this method is described in the online notes by Sean Carroll, freely available to all. I give all the details left out by Carroll in the UFT series and my proofs are now routine study at the best universities and so forth. The UFT series on represents some of the most detailed scholarship available in differential geometry. Nothing is “left to the student”, who is usually terminally reluctant to accept the gift. I suspect that the instructor leaves things to the student because he can’t do the proofs himself. The mathematical definition of commutator includes the null commutator:

[A, A] = 0

The only possible argument for a symmetric connection has therefore evaporated, because that argument rests on the idea that a null commutator cannot exist or is somehow meaningless. The delightful Gerard Bruhn tried that one in one of his many unwanted missives. These seemingly small but very important points of mathematics were overlooked by the EGR crowd. All but a few top cats and their dustbins have accepted my proofs. To reject them invites some satire at school. Another false argument that was used in the past is that the commutator method produces only the antisymmetric part of fundamental quantities in Riemann Christoffel geometry: connection, torsion and curvature. That was another unfortunate scarecrow put up to be howled down in the ravens and blizzards of time. These quantities have no symmetric component by definition. Their properties are exactly the same as those of the commutator. The null commutator is zero because it is the only commutator that must be symmetric. This is all perfectly clear now to entire professions, showing very clearly that the dogmatists are either ignorant or deliberately obstructing new science. They are being told by their own colleagues worldwide that they are not as clever as the concrete in which they are embedded. This is another ineluctable consequence of objectivity – feedback software representing continuous refereeing by many tens of thousands of professionals all the time.

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