Recovering the quantum formalism from physically realist axioms

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.

This is an improved version of arXiv:1505.01369 [quant-ph]. In v2 clarifications on the link between axioms and mathematics

References in corpus (5)

• Significant-loophole-free test of Bell's theorem with entangled photons
• No extension of quantum theory can have improved predictive power
• Quantum Darwinism, Classical Reality, and the Randomness of Quantum Jumps
• Information Invariance and Quantum Probabilities
• Violation of Bell's inequalities in a quantum realistic framework

Cited by in corpus (4)

• Deriving Born's rule from an Inference to the Best Explanation
• Relational Quantum Mechanics and Probability
• The Stochastic-Quantum Correspondence
• Roots and (re)sources of value (in)definiteness versus contextuality. A contribution to the Pitowsky Volume in memory of Itamar Pitowsky (1950--2010)