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arXiv · 2507.00098

Observable and Unobservable in Quantum Mechanics

Marcello Poletti
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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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Marcello Poletti. 2025-06-30. Observable and Unobservable in Quantum Mechanics. https://doi.org/10.1007/s10701-025-00868-9

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