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Questionable and Unquestionable in Quantum Mechanics

Szabó, László E. and Gömöri, Márton and Gyenis, Zalán (2023) Questionable and Unquestionable in Quantum Mechanics. [Preprint]

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Abstract

We derive the basic postulates of quantum physics from a few very simple and easily testable operational assumptions based exclusively on the relative frequencies of observable events (measurement operations and measurement outcomes). We isolate a notion which can be identified with the system's own state, in the sense that it characterizes the system's probabilistic behavior against all possible measurement operations. We investigate some important features of the possible states of the system. All those investigations remain within the framework of classical Kolmogorovian probability theory, meaning that any physical system (traditionally categorized as classical or quantum) that can be described in operational terms can be described within classical Kolmogorovian probability theory.
In the second part of the paper we show that anything that can be described in operational terms can, if we wish, be represented in the Hilbert space quantum mechanical formalism. The outcomes of each measurement can be represented by a system of pairwise orthogonal closed subspaces spanning the entire Hilbert space; the states of the system can be represented by pure state operators, and the probabilities of the outcomes can be reproduced by the usual trace formula. Each real valued quantity can be associated with a suitable self-adjoint operator, such that the possible measurement results are the eigenvalues and the outcome events are represented by the eigenspaces, according to the spectral decomposition of the operator in question.
This suggests that the basic postulates of quantum theory are in fact analytic statements: they do not tell us anything about a physical system beyond the fact that the system can be described in operational terms. This is almost true. At the end of the paper we discuss a few subtle points where the representation we obtained is not completely identical with standard quantum mechanics.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Szabó, László E.laszlo.e.szabo@gmail.com0000-0001-7454-8421
Gömöri, Mártongomorim@gmail.com0000-0003-2242-8107
Gyenis, Zalánzalan.gyenis@gmail.com0000-0003-2058-1255
Keywords: probabilistic–operational model prepare-and-measure experiment simultaneous measurability notion of state contextuality Kolmogorovian censorship postulates of quantum mechanics operator-observable correspondence
Subjects: General Issues > Operationalism/Instrumentalism
General Issues > Philosophers of Science
Specific Sciences > Probability/Statistics
Specific Sciences > Physics > Quantum Mechanics
General Issues > Theory/Observation
Depositing User: Prof. Laszlo E. Szabo
Date Deposited: 08 Sep 2023 21:09
Last Modified: 08 Sep 2023 21:09
Item ID: 22504
Subjects: General Issues > Operationalism/Instrumentalism
General Issues > Philosophers of Science
Specific Sciences > Probability/Statistics
Specific Sciences > Physics > Quantum Mechanics
General Issues > Theory/Observation
Date: 7 September 2023
URI: https://philsci-archive.pitt.edu/id/eprint/22504

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