The Separability Problem in Quantum Mechanics: Insights from Research on Axiomatics and Human Language

TL;DR

This paper explores the separability problem in quantum mechanics, revealing structural limitations in the formalism and drawing analogies with human language to understand the concept of separability.

Contribution

It identifies a structural limitation in the quantum formalism regarding the description of separate systems and proposes an analogy with human language to gain insights.

Findings

Quantum formalism lacks enough properties to describe separate systems.

Structural limitations are present at the level of properties, not states.

Analogies with human language provide new perspectives on separability.

Abstract

Einstein's article on the EPR paradox is the most cited of his works, but not many know that it was not fully representative of the way he thought about the incompleteness of the quantum formalism. Indeed, his main worry was not Heisenberg's uncertainty principle, which he accepted, but the experimental non-separability of spatially separate systems. The same problem was also recognized, years later, by one of us, as part of an axiomatic analysis of the quantum formalism, which revealed an unexpected structural limitation of the quantum formalism in Hilbert space, preventing the description of separate systems. As we will explain, this limitation does not manifest at the level of the states, but of the projectors describing the properties, in the sense that there are not enough properties in the formalism to describe separate systems. The question remains whether separability is a possibility at the fundamental level and if a formalism should integrate it into its mathematical structure, as a possibility. To aid our intuition, we offer a reflection based on a powerful analogy between physical systems and human conceptual entities, as the question of separability also arises for the latter.