Failure of psychophysical supervenience in Everett's theory
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Psychophysical supervenience requires that the mental properties of a system cannot change without the change of its physical properties. For a system with many minds, the principle requires that the mental properties of each mind of the system cannot change without the change of the physical properties of the system. In this paper, I argue that Everett's theory seems to violate this principle of psychophysical supervenience. The violation results from the three key assumptions of the theory: (1) the completeness of the physical description by the wave function, (2) the linearity of the dynamics for the wave function, and (3) multiplicity. For a post-measurement state with two decoherent result branches, multiplicity means that each result branch corresponds to a mindful observer, whose mental properties supervene on the branch, and in particular, whose mental content contains a definite record corresponding to the result branch. Under certain unitary evolution which swaps the two result branches, the post-measurement state does not change, and the completeness of the physical description by the wave function then means that the physical state of the composite system does not change. While the linearity of the dynamics for the wave function requires that each result branch changes, and correspondingly the mental properties of the observer which supervene on the branch also change. Thus the principle of psychophysical supervenience as defined above is violated by Everett's theory.