The BohmAharanov effect can be simply understood to mean that electromagnetic potential has physical meaning. It is wellknown that Maxwell’s equations are invariant under phase translations. Now in S4(1/h) universe, take a small neighborhood of the physical universe (a hypersurface). You have approximately a trivial circle bundle if the neighborhood is sufficiently small and close enough to flat; the fibers are circles of radius . One possible explanation of BohmAharanov is that electromagnetism is not in fact described by Maxwell’s equations which are gauge invariant but described by some variation of it which are gauge invariant only when the hypersurface is sufficiently nice. This is an interesting technical question. In any case, there is no reason to exclude the possibility of a macroscopic fourth space dimension that is ‘purely electromagnetic’ in the same sense that electromagnetic potentials are real in BohmAharanov effects. It is claimed that KaluzaKlein type theories must have very tiny extra dimension by experiments in particle accerators but this is not quite right. A purely electromagnetic extra dimension can describe the phases of electromagnetism while not being reduced to the type of extra physical dimension that was tested.
ELECTROMAGNETISM IS PROBABLY NOT A U(1) GAUGE THEORY
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8:01 AM (4 hours ago)


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