Quantum mechanics as a deterministic theory of a continuum of worlds

TL;DR

This paper proposes a deterministic quantum theory describing the universe as a continuum of worlds, explaining quantum phenomena, probabilities, and wavefunction collapse without world splitting, combining elements of Bohmian and Everett interpretations.

Contribution

It introduces a novel continuum-of-worlds framework that derives quantum probabilities and phenomena without world splitting, unifying Bohmian and Everett interpretations.

Findings

Derives Born rule probabilities from observer ignorance.

Explains wavefunction collapse as an objective, deterministic process.

Describes a continuum of worlds without splitting, avoiding typical Everett features.

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.