Recovering the quantum formalism from physically realist axioms

Area of Science:

• Theoretical Physics
• Quantum Mechanics
• Foundations of Physics

Background:

• The standard formulation of Quantum Mechanics lacks a clear conceptual basis for Born's rule and Hilbert space structure.
• Existing interpretations often struggle to reconcile quantum formalism with a realistic worldview.

Purpose of the Study:

• To provide a heuristic derivation of Born's rule and unitary transforms in Quantum Mechanics.
• To establish a new realistic conceptual framework for Quantum Mechanics.
• To elucidate the physical origins of Hilbert space structure.

Main Methods:

• Development of a simple set of axioms based on physical phenomenology of quantization.
• Analysis of the interplay between quantized 'modalities' and continuous 'contexts'.
• Investigation of 'extra-contextuality' of modalities and its relation to Gleason's theorem.

Main Results:

• A novel, realistic conceptual framework for Quantum Mechanics is presented.
• Born's rule and unitary transforms are derived from the proposed axioms.
• The Hilbert space structure is shown to arise from 'extra-contextuality' and is consistent with Gleason's theorem.

Conclusions:

• The proposed framework offers a new perspective on the fundamental structure of Quantum Mechanics.
• The interplay of modalities and contexts provides a physical explanation for quantum formalism.
• The derivation supports a realistic interpretation of quantum theory.