Extended Representations of Observables and States for a Noncontextual Reinterpretation of QM

TL;DR

The paper presents an improved mathematical framework for the ESR model, which reinterprets quantum probabilities to restore objectivity and noncontextuality in quantum mechanics, and proposes an experiment to test its predictions against standard QM.

Contribution

It offers a more complete mathematical representation of the ESR model and extends it to mixtures, addressing interpretative issues in quantum mechanics.

Findings

Mathematical representation of proper mixtures differs from QM

Representation of improper mixtures aligns with QM

Proposes an experiment to distinguish ESR from QM predictions

Abstract

A crucial and problematical feature of quantum mechanics (QM) is nonobjectivity of properties. The ESR model restores objectivity reinterpreting quantum probabilities as conditional on detection and embodying the mathematical formalism of QM into a broader noncontextual (hence local) framework. We propose here an improved presentation of the ESR model containing a more complete mathematical representation of the basic entities of the model. We also extend the model to mixtures showing that the mathematical representations of proper mixtures does not coincide with the mathematical representation of mixtures provided by QM, while the representation of improper mixtures does. This feature of the ESR model entails that some interpretative problems raising in QM when dealing with mixtures are avoided. From an empirical point of view the predictions of the ESR model depend on some parameters which may be such that they are very close to the predictions of QM in most cases. But the nonstandard representation of proper mixtures allows us to propose the scheme of an experiment that could check whether the predictions of QM or the predictions of the ESR model are correct.