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Our model of the universe is a scaled 4-sphere where the physical universe is an evolving hypersurface.  The fact that the normal geodesics from $M$ all have the same length suggests that this is the circle (of length $1/\hbar$) is confused with a circle bundle that defines electromagnetism in the standard account.  One possible answer is that electromagnetism is simply defined by a 1-form on the 4-sphere similarly to how the connection form is defined on the total space of the circle bundle.  Indeed, one can embed the one-form into the Clifford bundle and consider electromagnetism to be defined by a potential.  The fact that there exists a Dirac equation for the photon implies that it might be reasonable to consider electromagnetism to be defined by a single spinor field potential.