Observable and Unobservable in Quantum Mechanics

• URL: http://arxiv.org/abs/2507.00098v1
• Date: Mon, 30 Jun 2025 12:23:50 GMT
• Title: Observable and Unobservable in Quantum Mechanics
• Authors: Marcello Poletti,
• Abstract summary: It introduces the notion of textitonto-epistemic ignorance: situations in which the truth of a proposition is not deducible due to an objective breakdown in the phenomenal chain.<n>It is shown that, under such conditions, the probabilities accessible to a real observer are necessarily conditioned by decidability and obey a non-commutative algebra.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This work explores the connection between logical independence and the algebraic structure of quantum mechanics. Building on results by Brukner et al., it introduces the notion of \textit{onto-epistemic ignorance}: situations in which the truth of a proposition is not deducible due to an objective breakdown in the phenomenal chain that transmits information from a system A to a system B, rather than to any subjective lack of knowledge. It is shown that, under such conditions, the probabilities accessible to a real observer are necessarily conditioned by decidability and obey a non-commutative algebra, formally equivalent to the fundamental postulates of quantum mechanics.

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