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Assuming the standard axioms for quaternionic quantum theory and a spatiallylocalized scattering interaction, the $S$-matrix in quaternionic quantum theoryis complex valued, not quaternionic. Using the standard connections between the$S$-matrix, the forward scattering amplitude for electromagnetic wavescattering, and the index of refraction, we show that the index of refractionis necessarily complex, not quaternionic. This implies that the recent opticalexperiment of Procopio et al. based on the Peres proposal does not test forhyper-complex or quaternionic quantum effects arising within the standardHilbert space framework. Such a test requires looking at near zone fields, notradiation zone fields.

Does the Peres experiment using photons test for hyper-complex (quaternionic) quantum theories?