Recovering the quantum formalism from physically realist axioms

TL;DR

This paper derives the core mathematical structure of quantum mechanics, including Born's rule and unitary transformations, from physically motivated axioms based on quantized modalities and contexts, offering a realist interpretation.

Contribution

It introduces a new realist framework that derives quantum formalism from simple axioms related to quantization and contextuality, connecting physical phenomenology with mathematical structure.

Findings

Derivation of Born's rule from axioms

Quantum formalism as a consequence of modality-context interplay

Hilbert space structure linked to extra-contextuality and Gleason's theorem

Abstract

We present a heuristic derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. This approach naturally leads to the usual quantum formalism, within a new realistic conceptual framework that is discussed in details. Physically, the structure of Quantum Mechanics appears as a result of the interplay between the quantized number of "modalities" accessible to a quantum system, and the continuum of "contexts" that are required to define these modalities. Mathematically, the Hilbert space structure appears as a consequence of a specific "extra-contextuality" of modalities, closely related to the hypothesis of Gleason's theorem, and consistent with its conclusions.