Phenomenological quantum mechanics: deducing the formalism from experimental observations

• URL: http://arxiv.org/abs/2410.14410v1
• Date: Fri, 18 Oct 2024 12:17:30 GMT
• Title: Phenomenological quantum mechanics: deducing the formalism from experimental observations
• Authors: Piotr Szańkowski, Davide Lonigro, Fattah Sakuldee, Łukasz Cywiński, Dariusz Chruściński,
• Abstract summary: We show that it is possible to derive in such a way a complete and fully functional formalism based on the structures of Hilbert spaces. The obtained formal description -- the bi-trajectory formalism -- turns out to be quite different from the standard state-focused formalism.
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• Abstract: We propose an exercise in which one attempts to deduce the formalism of quantum mechanics from phenomenological observations only. Thus, the only assumed inputs are the multi-time probability distributions estimated from the results of sequential measurements of quantum observables; no presuppositions about the underlying mathematical structures are allowed. We show that it is indeed possible to derive in such a way a complete and fully functional formalism based on the structures of Hilbert spaces. However, the obtained formal description -- the bi-trajectory formalism -- turns out to be quite different from the standard state-focused formalism.

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