This demonstration is well known and accepted internationally. It is summarized here for convenience. The curvature and torsion tensors are generated by the commutator of covariant derivatives as in eqs. (1) and (2). The six terms on the right hand side of eq. (2) must each be antisymmetric in mu and nu, because each is generated by the same antisymmetric commutator. This gives the correct antisymmetry law (3) to (5), showing in a simple way that the connection is antisymmetric. Gravitational theory goes wrong as described in points (1) and (2). In Cartan’s geometry the connection is defined by the tetrad postulate as in eq. (16). This gives the antisymmetry law used in notes 133(11). Next I will show that standard U(1) electrodynamics is trivially incorrect by using the commutator method again. This finding has already been reported and accepted for publication in a forthcoming international conference and accepted for its book of abstracts. So we can look forward to a new and interesting era of physics, with the possibility of new energy and counter gravitation through Euler Bernoulli resonance in the spin connection. There is no purpose in continuing to work with a theory that is so easily shown to be completely obsolete. This demonstration requires knowledge only of linear algebra, i.e. A level mathematics, or advanced O level mathematics. Eq. (16) gives a choice of antisymmetry constraints. The antisymmetry law is obvious, every term generated by an antisymmetric commutator is antisymmetric. One of these is the gamma connection, which in Cartan geometry is expanded as the sum of two terms, as in eq. (16). Any attempted misrepresentation of such simple results (e.g. wikipedia) immediately raises suspicion. Why has this incorrectness been overlooked for so long? There are motives to so with money, not with science. cc PM’s Office, and RSC

## 133(12): Simple Demonstration of the Incorrectness of Gravitational Theory

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