Phenomenological quantum mechanics: I. Phenomenology of quantum observables

[2410.14410] Phenomenological quantum mechanics: I. Phenomenology of quantum observables Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Quantum Physics arXiv:2410.14410 (quant-ph) [Submitted on 18 Oct 2024 ( v1 ), last revised 16 Aug 2026 (this version, v4)] Title: Phenomenological quantum mechanics: I. Phenomenology of quantum observables Authors: Piotr Szańkowski , Davide Lonigro , Fattah Sakuldee , Łukasz Cywiński , Dariusz Chruściński View a PDF of the paper titled Phenomenological quantum mechanics: I. Phenomenology of quantum observables, by Piotr Sza\'nkowski and Davide Lonigro and Fattah Sakuldee and {\L}ukasz Cywi\'nski and Dariusz Chru\'sci\'nski View PDF HTML (experimental) Abstract: We propose an exercise in which one attempts to deduce the formalism of quantum mechanics solely from phenomenological observations. The only assumed inputs are obtained through sequential probing of quantum systems; no presuppositions about the underlying mathematical structures are permitted. We demonstrate that it is indeed possible to derive, on this basis, a complete and fully functional formalism rooted in the structures of Hilbert spaces. However, the resulting formalism--the bi-trajectory formalism--differs significantly from the standard state-focused formulation. In Part I of the paper, we analyze the outcomes of various experiments involving sequential measurements of quantum observables. These outcomes are quantitatively described by phenomenological multi-time probability distributions, estimated from experimental data. Our first conclusion is that the theory describing these experiments must be non-classical: the measured sequences cannot be interpreted as sampling of a uni-trajectory representing the system's observable. The non-classical nature of the investigated systems manifests in a range of observed phenomena, including quantum interference, the quantum Zeno effect, and uncertainty relations between the measured observables. Comments: Part I of a two-part series; Part II arXiv:2507.04812 . Note that the original submission arXiv:2410.14410v1 has been now split into two parts. Published in J. Phys. A: Math. Theor Subjects: Quantum Physics (quant-ph) ; Mathematical Physics (math-ph); History and Philosophy of Physics (physics.hist-ph) Cite as: arXiv:2410.14410 [quant-ph] (or arXiv:2410.14410v4 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2410.14410 Focus to learn more arXiv-issued DOI via DataCite Journal reference: J. Phys. A: Math. Theor. 59, 355303 (2026) Related DOI : https://doi.org/10.1088/1751-8121/ae97a0 Focus to learn more DOI(s) linking to related resources Submission history From: Piotr Szańkowski [ view email ] [v1] Fri, 18 Oct 2024 12:17:30 UTC (54 KB) [v2] Mon, 7 Jul 2025 09:51:58 UTC (36 KB) [v3] Tue, 8 Jul 2025 07:03:08 UTC (36 KB) [v4] Sun, 16 Aug 2026 07:44:38 UTC (38 KB) Full-text links: Access Paper: View a PDF of the paper titled Phenomenological quantum mechanics: I. Phenomenology of quantum observables, by Piotr Sza\'nkowski and Davide Lonigro and Fattah Sakuldee and {\L}ukasz Cywi\'nski and Dariusz Chru\'sci\'nski View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2024-10 Change to browse by: math math-ph math.MP physics physics.hist-ph References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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