Quantum mechanics as a deterministic theory of a continuum of worlds

Abstract

A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions about objects in a multiplicity of worlds. In this logical framework, the continuum of worlds is treated in analogy to the continuum of time points, both "time" and "world" are considered as mutually independent modes of existence. The theory combines elements of Bohmian mechanics and of Everett's many-worlds interpretation, it has a clear ontology and a set of precisely defined postulates from where the predictions of standard quantum mechanics can be derived. Probability as given by the Born rule emerges as a consequence of insufficient knowledge of observers about which world it is that they live in. The theory describes a continuum of worlds rather than a single world or a discrete set of worlds, so it is similar in spirit to many-worlds interpretations based on Everett's approach, without being actually reducible to these. In particular, there is no splitting of worlds, which is a typical feature of Everett-type theories. Altogether, the theory explains (1) the subjective occurrence of probabilities, (2) their quantitative value as given by the Born rule, and (3) the apparently random "collapse of the wavefunction" caused by the measurement, while still being an objectively deterministic theory.

arXiv commentfourth and final revision, this paper is a thoroughly reworked and enhanced formulation of ideas originally published in 2012 as a preprint in arXiv1208.5632, it has been published as a regular article in 2015 in Quantum Studies: Mathematics and Foundations

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• Multiplicity in Everett's interpretation of quantum mechanics
• Born rule: quantum probability as classical probability
• Making sense of Born's rule $p_{\alpha }=\Vert {\Psi }_{\alpha }{\Vert }^2$ with the many-minds interpretation
• An Elementary Proof That Everett's Quantum Multiverse Is Nonlocal: Bell-Locality and Branch-Symmetry in the Many-Worlds Interpretation
• Constructing and Constraining Wave Functions for Identical Quantum Particles
• Epistemic uncertainty from an averaged Hamilton-Jacobi formalism