Phenomenological quantum mechanics: I. Phenomenology of quantum observables

Szańkowski P, Lonigro D, Sakuldee F, Cywiński Ł, Chruściński D (2026)

Publication Type: Journal article

Publication year: 2026

Journal

Journal of Physics A: Mathematical and Theoretical Institute of Physics Publishing (IOP)

Original Authors: Piotr Szańkowski, Davide Lonigro, Fattah Sakuldee, Łukasz Cywiński, Dariusz Chruściński

Book Volume: 59

Issue: 35

Journal Issue: 35

DOI: 10.1088/1751-8121/ae97a0

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.

Authors with CRIS profile

Davide Lonigro Professur für Theoretische Physik

Involved external institutions

Shanghai Jiao Tong University / 上海交通大学 CN China (CN) Nicolaus Copernicus University (NCU) / Uniwersytet Mikołaja Kopernika w Toruniu (UMK) PL Poland (PL) Institute of Physics Polish Academy of Sciences / Instytut Fizyki Polskiej Akademii Nauk (IF PAN) PL Poland (PL)

How to cite

APA:

Szańkowski, P., Lonigro, D., Sakuldee, F., Cywiński, Ł., & Chruściński, D. (2026). Phenomenological quantum mechanics: I. Phenomenology of quantum observables. Journal of Physics A: Mathematical and Theoretical, 59(35). https://doi.org/10.1088/1751-8121/ae97a0

MLA:

Szańkowski, Piotr, et al. "Phenomenological quantum mechanics: I. Phenomenology of quantum observables." Journal of Physics A: Mathematical and Theoretical 59.35 (2026).

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