Derivation of the probability law in the many-worlds, one-MIND interpretation

Abstract

The basic mathematical structure, QM-A, of the many worlds interpretation consists solely of the linear mathematics plus the Hilbert space properties of the state vectors. There is no collapse and there are no particles or hidden variables. It is remarkable that QM-A alone can account for all our observations except probability. There is no need for particles, hidden variables or collapse to explain perception of only one classical version of reality, the photoelectric effect, localized effects from a spread-out wave function in scattering and interference experiments, wave-particle duality, and so on. But probability cannot be defined within QM-A. Nevertheless, because of its astonishing success, it seems reasonable to require (1) that the mathematics of an interpretation be limited to the highly successful QM-A and (2) that "matter" be composed of state vectors alone. But the probability law requires, in essence, that one version of the observer be singled out. The most straightforward way to accomplish this under (1) and (2) is to assume there is an aspect of the observer-the Mind-which is outside the laws of quantum mechanics and perceives just one version of reality. Under that assumption, the probability law can then be derived. Thus we have an interpretation, QM-A plus "outside" observer, which explains all our perceptions.