The antisymmetry laws discovered for gravitation in paper 122 and extended to electrodynamics in paper 131 can also be extended straightforwardly to mathematics, because they apply to Cartan geometry itself, and also to other areas such as hydrodynamics, aerodynamics, magnetohydrodynamics and thermodynamics. They will probably assume the importance of something like Maxwell’s symmetry relations. The commutator method on which they are based is very fundamental, as in the definitive proofs on www.aias.us it produces the Riemannian curvature and torsion without any other assumption and in any spacetime. It shows that the Riemannian connection is always antisymmetric, and so the Riemannian torsion is identically non-zero in any spacetime and in any dimension, regardless of any other assumption. The antisymmetry laws are very powerful, for example they show immediately that U(1) sector symmetry is incorrect, and that classical electrodynamics must be a theory of general relativity. It shows that teh electric and magnetic fields must be spin connections of spacetime itself, yielding a new source of electric power and counter gravitation. ECE is one theory that obeys the antisymmetry laws correctly, and there are probably others still to be discovered. The Cartan torsion is well known to be the product of the Cartan tetrad and the Riemann torsion, so the Cartan torsion is also subject to the antisymmetry laws. This inference works its way throughout the subject of Cartan geometry and all the mathematical variations on that theme, of which there are many. So there is plenty of scope for much further work in several subject areas. I intend to divide my time between writing further GCUFT volumes for the pioneering, high quality, publisher Abramis, and poetry. Also I intend to help Ken Russell with his biographical film for which Kerry Penderhast has written a filmscript. bcc Sometime Oxford colleagues, RSC and PM’s Office

## Antisymmetry Laws in Mathematics, Hydrodynamics and Aerodynamics

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