Summary of Progress in the Past Few Months


Major progress has been made in the past few months since the discovery of the antisymmetry law in paper 122. This paper was kindly typeset and translated into Spanish by Alex Hill and subsequently expanded in proof one. By elementary arguments it made a basic discovery in Riemannian geometry, that the connection is always antisymmetric. This discovery ended the Einsteinian era of gravitational theory because in that era (twentieth century) the connection was wrongly assumed to be symmetric. The reason for this is that the Riemannian torsion was wrongly assumed to be zero. The simple logic of paper 122 shows that the Riemannian torsion is identically non zero and that the Riemannian connection is identically antisymmetric. This is simply because the commutator of covariant derivatives is identically antisymmetric by definition. There is no symmetric part to the commutator. In consequence, the symmetry law states that any object in which appears the commutator subscipts takes the antisymmetry of the commutator by definition. This discovery led to the major discovery of papers 131 and 132 (accepted for a forthcoming conference), in which new antisymmetry relations between electromagnetic and gravitational potentials were inferred. Similarly there will be antisymmetry relations in electroweak theory and in strong field theory. In the notes for paper 133, the consequencies of the antisymmetry law have been worked out in Cartan’s geometry itself, and in continuation of this work, the consequencies for Riemann geometry will bw further explored. In the series of papers 122 onwards major progress has also been made in torsion based cosmology and in the Dirac equation, which has been written for the first time in terms of 2 x 2 matrices.


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