Theorems motivated by foundations of quantum mechanics and some of their applications

TL;DR

This paper introduces theorems that clarify foundational issues in quantum mechanics, enabling new interpretations and providing stronger equivalence proofs for pilot-wave theories, along with proposals for minimalistic ontologies and insights into Born's rule.

Contribution

The paper presents new theorems that strengthen the theoretical foundations of quantum mechanics, including a proof of equivalence for pilot-wave theories and a minimalistic ontology proposal.

Findings

Proof of fully equivalent pilot-wave theories

Proposal of a minimalistic ontology for non-collapse quantum mechanics

Identification of a close relationship between Born's rule and superposition

Abstract

This paper provides theorems aimed at shedding light on issues in the foundations of quantum mechanics. These theorems can be used to propose new interpretations to the theory, or to better understand, evaluate and improve current interpretations. Some of these applications include: (1) A proof of the existence of pilot-wave theories that are fully equivalent to standard quantum mechanics in a path-wise sense. This equivalence is stronger than what is entailed from the more traditional requirements of equivariance, or good mixing properties, and is necessary to assure proper correlations across time and proper records of the past. (2) A proposal for a minimalistic ontology for non-collapse quantum mechanics, in which Born's rule provides the proper predictions.(3) The observation of a close relationship between Born's rule and a version of the superposition principle.