Let us accept that the universe is a scaled 4-sphere, and since this is unorthodox, recall that observed crystal rotational symmetries of orders 5, 8, 10 and 12 imply at least four spatial dimensions. I have produced heat equation arguments for compactness — briefly the cosmic background radiation has a uniform lower bound of 2.7 K > 0 which is impossible in a noncompact manifold with lower bound on the Ricci curvature because there the heat kernel has a Gaussian upper bound. But more precisely a scaled 4-sphere of appropriate radius produces a sharp explanation of the redshift slope. So the physical universe is a compact three dimensional hypersurface. Now there is a natural circle-bundle like structure on a 4-sphere, which is that normal geodesics along the hypersurface are all perfect circles. The orthodox theories suggest from the Lagrangian of the electromagnetic field that there -invariance. But the natural geometric expectation is that the electromagnetic potential be a 1-form on S4(1/h) that is normal along the manifold in the sense that the 1-form produces a nonzero value evaluated at the normal vector field. This is similar to a connection but S4(1/h) is not the total space of an actual -bundle. The similarity is that the kernel of the 1-form at each point on the manifold is a choice of a ‘horizontal subspace’. Let be the one-form. Then the analogue of the curvature form is simply . This electromagnetism is not -invariant because one is not free to translate around the circle at will. I will make more precise this version of electromagnetism which should give some testable hypotheses.

## Electromagnetism is not quite a U(1) gauge theory

March 18, 2014 by zulfahmed

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