Carroll’s Online Notes

The commutator method of generating curvature and torsion is given by Carroll in his Eq. (3.66) of his online notes. ECE theory uses exactly the same method, which is explained in full in UFT99 and in many of the 272 UFT papers now available, and in the five definitive proofs. Carroll writes in his notes that the antisymmetry of the curvature in its last two indices is immediate from the commutator. Therefore so is the antisymmetry of the torsion and of the connection. The Einstein field equation relies on the assumption that torsion is zero. If so, the connection is symmetric. A symmetric connection leads however to a symmetric commutator, a null operator, so the curvature vanishes if torsion vanishes because both are always generated by the commutator. The entire Einsteinian general relativity collapses. In ECE theory the torsion and curvature are both non zero. The Christoffel connection is not assumed in ECE theory, and the second Bianchi identity is replaced by an identity derivable from the Cartan identity (UFT88, UFT255). It is clear that any metric based on the Einstein field equation is meaningless, these metrics include those of Big Bang, black holes and so on. Recently ECE has replaced all of the claims of the Einstein theory by x theory. Few of the dogmatists are even aware of the existence of torsion. Those few who have studied it deliberately set it to zero by choice of a symmetric connection. They do not realize that this choice leads to zero curvature and no gravitation. So the funding of Einsteinian general relativity must be discontinued, it is entirely wrong. The dogmatists have completely failed to address the commutator proof that they are wildly incorrect. Nature shows experimentally that they are wildly wrong in whirlpool galaxies. This complete experimental refutation of Einsteinian general relativity appeared in 1958, and was quickly covered up by “dark matter”, now known experimentally not to exist. Meanwhile the irrefutable and simple logic of ECE theory goes from strength to strength. The general public now knows that black holes and Big Bang are propagandist, so they will begin to press for the abandonment of public funding for ideas that are matheamtically incorrect, and also refuted experimentally.

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