Some Remarks on Note 134(1)


The key point is that all terms on the right hand side of eq. (8) are antisymmetric in mu and nu, because interchanging mu and nu means traversing the loop in the opposite direction. The loop transformation vanishes if mu = nu. So the reduction to absurdity proofs on page (5) onwards prove this point. Each term is either zero or antisymmetric in mu and nu. In eq. (20) there are six terms on the right hand side, each of which is antisymmetric. In the now obsolete standard model, it was asserted incorrectly that only two sums of terms are antisymmetric. The first is the curvature tensor, the sum of four terms, and the second the sum of two terms, the torsion tensor. Even worse, the torsion tensor is usually omitted altogether, because the connection is incorrectly asserted to be symmetric. There can be no symmetric connection, it is antisymmetric or zero. Although obvious and simple, this is a major discovery in Riemann geometry, so paper 134 will develop the discovery.


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