Why the Many-Worlds Interpretation of quantum mechanics needs more than Hilbert space structure

Abstract

McQueen and Vaidman argue that the Many Worlds Interpretation (MWI) of quantum mechanics provides local causal explanations of the outcomes of experiments in our experience that is due to the total effect of all the worlds together. We show that although the explanation is local in one world, it requires a causal influence that travels across different worlds. We further argue that in the MWI the local nature of our experience is not derivable from the Hilbert space structure, but has to be added to it as an independent postulate. This is due to what we call the factorisation-symmetry and basis-symmetry of Hilbert space