HALIM, UMAIR (2025) The Real-Alignment Interpretation: A Single Postulate for Discreteness and the Born Rule. [Preprint]

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Abstract

We introduce the Real Alignment Interpretation (RAI), a new structural framework for quantum mechanics in which discreteness, Born-type probabilities, and contextuality follow from a single postulate. Alongside the system state f(t), a contextual state g(t) represents the measurement setting or environment. A discrete event occurs whenever the overlap ⟨f, g⟩ is real, with the recorded eigenvalue selected by a dominance rule. This real alignment criterion predicts null outcomes, intervals in which no event occurs, as an intrinsic feature rather than a detector imperfection. Under ergodic exploration of the event hypersurface, the long run frequencies of outcomes reproduce the Born rule; systematic deviations would arise if ergodicity fails, providing a clear avenue for experimental tests. In this first paper we establish the postulate, illustrate it with a two-state model, and present a geometric reformulation on projective Hilbert space. RAI thus offers a unified, empirically testable starting point for a new approach to quantum foundations.

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Item Type:	Preprint
Creators:	Creators Email ORCID HALIM, UMAIR umair@upm.edu.my
Keywords:	Quantum foundations; Real-alignment interpretation; Born rule; Contextuality; Ergodicity
Subjects:	General Issues > Philosophers of Science Specific Sciences > Physics > Quantum Mechanics General Issues > Structure of Theories
Depositing User:	Dr. Umair Abdul Halim
Date Deposited:	22 Sep 2025 10:50
Last Modified:	22 Sep 2025 10:50
Item ID:	26713
Subjects:	General Issues > Philosophers of Science Specific Sciences > Physics > Quantum Mechanics General Issues > Structure of Theories
Date:	21 September 2025
URI:	https://philsci-archive.pitt.edu/id/eprint/26713

Available Versions of this Item

• The Real-Alignment Interpretation: A Single Postulate for Discreteness and the Born Rule. (deposited 22 Sep 2025 10:50) [Currently Displayed]
  • The Real-Alignment Interpretation: A Single Postulate for Discreteness and the Born Rule. (deposited 01 Oct 2025 18:21)

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