Phenomenological quantum mechanics I: phenomenology of quantum observables

• URL: http://arxiv.org/abs/2410.14410v3
• Date: Tue, 08 Jul 2025 07:03:08 GMT
• Title: Phenomenological quantum mechanics I: phenomenology of quantum observables
• Authors: Piotr Szańkowski, Davide Lonigro, Fattah Sakuldee, Łukasz Cywiński, Dariusz Chruściński,
• Abstract summary: We show that it is possible to derive a complete and fully functional formalism rooted in the structures of Hilbert spaces.<n>The resulting formalism--the bi-trajectory formalism--differs significantly from the standard state-focused formulation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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