Combining Bohm and Everett: Axiomatics for a Standalone Quantum Mechanics

TL;DR

This paper introduces a new non-relativistic quantum theory combining Bohmian mechanics and Everett's interpretation, resolving issues of both and deriving the Born rule without additional hypotheses.

Contribution

It presents a novel quantum framework with a clear ontology, a continuum of worlds, and a derivation of the Born rule without reliance on quantum equilibrium or branch weights.

Findings

Derives the Born rule without quantum equilibrium hypothesis.

Explains subjective probabilities and wavefunction collapse objectively.

Describes a continuum of worlds without world splitting.

Abstract

A non-relativistic quantum mechanical theory is proposed that combines elements of Bohmian mechanics and of Everett's "many-worlds" interpretation. The resulting theory has the advantage of resolving known issues of both theories, as well as those of standard quantum mechanics. It has a clear ontology and a set of precisely defined postulates from where the predictions of standard quantum mechanics can be derived. Most importantly, the Born rule can be derived by straightforward application of the Laplacian rule, without reliance on a "quantum equilibrium hypothesis" that is crucial for Bohmian mechanics, and without reliance on a "branch weight" that is crucial for Everett-type theories. 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, 3) the identification of observables as self-adjoint operators on Hilbert space, and 4) the apparently random "collapse of the wavefunction" caused by the measurement, while still being an objectively deterministic theory.