Non-Boolean probabilities and quantum measurement

TL;DR

This paper introduces a non-Boolean probability model that captures quantum phenomena, offering a more general and interpretable framework than traditional Hilbert space quantum mechanics, with potential insights into quantum measurement.

Contribution

It proposes a novel non-Boolean probability framework that reproduces quantum effects and introduces state-independent conditional probabilities, enhancing understanding of quantum measurement.

Findings

Reproduces typical quantum phenomena using non-Boolean probabilities

Introduces state-independent conditional probabilities in the model

Uses Jordan operator algebras for concrete examples

Abstract

A non-Boolean extension of the classical probability model is proposed. The non-Boolean probabilities reproduce typical quantum phenomena. The proposed model is more general and more abstract, but easier to interpret, than the quantum mechanical Hilbert space formalism and exhibits a particular phenomenon (state-independent conditional probabilities) which may provide new opportunities for an understanding of the quantum measurement process. Examples of the proposed model are provided, using Jordan operator algebras.