Problem operacjonizmu z definicją czasu w mechanice kwantowej

Autor

DOI:

https://doi.org/10.14394/filnau.2023.0006

Słowa kluczowe:

operationalism, Percy Bridgman, operational definition, time, problem of time, quantum mechanics

Abstrakt

Bridgman’s operationalism imposes a set of methodological requirements on its proponents, which become untenable when applied to the definition of time within the formalism of non-relativistic quantum mechanics. This paper explores the operational definition of time and investigates how far it can be aligned with the core principles of operationalism. To this end, Busch’s (2008) framework, which distinguishes three roles of time in the quantum mechanical formalism, is employed. One of these roles introduces demands that operationalism cannot meet without compromising its essential principles. As a result, it seems reasonable to conclude that operationalism and quantum mechanics are incompatible (at least in the context of the problem of time in quantum mechanics).

Bibliografia

Aharonov Y., Bohm D. (1961), Time in the Quantum Theory and the Uncertainty Relation for Time and Energy, „Physical Review D” 122(1), 1649–1658. https://doi.org/10.1103/PhysRev.122.1649

Aharonov Y., Oppenheim J., Popescu S., Reznik B., Unruh W. (1998), Measurement of Time of Arrival in Quantum Mechanics, „Physical Review A” 57(6), 4130–4139. https://doi.org/10.1103/PhysRevA.57.4130

Anderson E. (2017), The Problem of Time: Quantum Mechanics Versus General Relativity, Cham: Springer. https://doi.org/10.1007/978-3-319-58848-3

Bauer M. (1983), A Time Operator in Quantum Mechanics, „Annals of Physics” 150(1), 1–21. https://doi.org/0003-4916(83)90002-7

Bridgman P. W. (1954), Remarks on the Present State of Operationalism, „The Scientific Monthly” 79(4), 224–226.

Bridgman P. W. (1958), The Logic of Modern Physics, New York: The Macmillan Company.

Bridgman P. W. (1959a), P. W. Bridgman’s „The Logic of Modern Physics” after Thirty Years, „Daedalus” 88(3), 518–526.

Bridgman P. W. (1959b), The Way Things Are, Cambridge, Mass.: Harvard University Press.

Busch P. (2008), The Time–Energy Uncertainty Relation, [w:] Time in Quantum Mechanics, J. G. Muga, R. Sala Mayato, Í. Egusquiza (red.), Berlin–Heidelberg: Springer, 73–105. https://doi.org/10.1007/978-3-540-73473-4_3

Busch P., Grabowski M., Lahti P. J. (2009), Operational Quantum Physics, Berlin–Heidelberg: Springer. https://doi.org/10.1007/978-3-540-49239-9

Das S., Struyve W. (2021), Questioning the Adequacy of Certain Quantum Arrival-Time Distributions, „Physical Review A” 104(042214), 1–7. https://doi.org/10.1103/PhysRevA.104.042214

Delgado V., Muga J. G. (1997), Arrival Time in Quantum Mechanics, „Physical Review A – Atomic, Molecular, and Optical Physics” 56(5), 3425–3435. https://doi.org/10.1103/PhysRevA.56.3425

Egusquiza Í. L., Muga J. G., Baute A. D. (2008), „Standard Quantum-Mechanical Approach to Times of Arrival”, [w:] Time in Quantum Mechanics, J. G. Muga, R. S. Mayato, Í. Egusquiza (red.), Berlin–Heidelberg: Springer, 305–332. https://doi.org/10.1007/978-3-540-73473-4_10

Field G. E. (2022), On the Status of Quantum Tunnelling Time, „European Journal for Philosophy of Science” 12(4), 1–30. https://doi.org/10.1007/s13194-022-00483-9

Galapon E. A. (2002a), Pauli’s Theorem and Quantum Canonical Pairs: The Consistency of a Bounded, Self-adjoint Time Operator Canonically Conjugate to a Hamiltonian with Non-empty Point Spectrum, „Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences” 458(2018), 451–472. https://doi.org/10.1098/rspa.2001.0874

Galapon E. A. (2002b), Self-adjoint Time Operator is the Rule for DiscreteSemi-bounded Hamiltonians, „Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences” 458(2027), 2671–2689. https://doi.org/10.1098/rspa.2002.0992

Giannitrapani R. (1997), Positive-Operator-Valued Time Observable in Quantum Mechanics, „International Journal of Theoretical Physics” 36, 1575–1584. https://doi.org/10.1007/BF02435757

Gillies D. A. (1972), Operationalism, „Synthese” 25, 1–24. https://doi.org/10.1007/BF00484997

Gisin N., Cruzeiro E. Z. (2018), Quantum Measurements, Energy Conservation and Quantum Clocks, „Annalen der Physik” 530(6), 1–10. https://doi.org/10.1002/andp.201700388

Gnanapragasam B., Srinivas M. (1979), Uncertainty Relation for Successive Measurements, „Pramana” 12, 699–705. https://doi.org/10.1007/BF02846858

Góźdź A., Góźdź M., Pędrak A. (2023), Quantum Time and Quantum Evolution, „Universe” 9(6), 1–31. https://doi.org/10.3390/universe9060256

Grace R. C. (2001), On the Failure of Operationism, „Theory & Psychology” 11(1), 5–33.

Grot N., Rovelli C., Tate R. S. (1996), Time-of-Arrival in Quantum Mechanics, „Physical Review A – Atomic, Molecular, and Optical Physics” 54(6), 4676–4690. https://doi.org/10.1103/PhysRevA.54.4676

Halvorson H. (2010), Does Quantum Theory Kill Time?, https://philarchive.org/archive/HALDQT

Hauge E., Støvneng J. (1989), Tunneling Times: A Critical Review, „Reviews of Modern Physics” 61(4), 917–936. https://doi.org/10.1103/RevModPhys.61.917

Hilgevoord J. (2002), Time in Quantum Mechanics, „American Journal of Physics” 70(3), 301–306. https://doi.org/10.1119/1.1430697

Horwitz L. P. (2006), On the Significance of a Recent Experiment Demonstrating Quantum Interference in Time, „Physics Letters A” 355(1), 1–6. https://doi.org/10.1016/j.physleta.2006.01.097

Kijowski J. (1974), On the Time Operator in Quantum Mechanics and the Heisenberg Uncertainty Relation for Energy and Time, „Reports on Mathematical Physics” 6(3), 361–386. https://doi.org/10.1016/S0034-4877(74)80004-2

Koch S. (1992), Psychology’s Bridgman vs Bridgman’s Bridgman, „Theory & Psychology” 2(3), 261–290. https://doi.org/10.1007/978-3-663-11198-6_8

Kochański P., Wódkiewicz K. (1999), Operational Time of Arrival in Quantum Phase Space, „Physical Review A” 60(4), 2689–2699. https://doi.org/10.1103/PhysRevA.60.2689

Leavens C. R. (2002), On the “Standard” Quantum Mechanical Approach to Times of Arrival, „Physics Letters A” 303(2-3), 154–165. https://doi.org/10.1016/S0375-9601(02)01239-2

Lindsay R. B. (1937), A Critique of Operationalism in Physics, „Philosophy of Science” 4(4), 456–470. https://doi.org/10.1086/286477

Mandelstam L., Tamm I. (1991), The Uncertainty Relation Between Energy and Time in Non-relativistic Quantum Mechanics, [w:] Selected Papers, B. Bolotovskii, V. Frenkel, R. Peierls (red.), Berlin–Heidelberg: Springer, 115–123. https://doi.org/10.1007/978-3-642-74626-0_8

Muga J. G., Leavens C. R. (2000), Arrival Time in Quantum Mechanics, „Physics Report” 338(4), 353–438. https://doi.org/10.1016/S0370-1573(00)00047-8

Muga J. G., Leavens C. R., Palao J. (1998), Space-Time Properties of Free-Motion Time-of-Arrival Eigenfunctions, „Physical Review A” 58(6), 4336. https://doi.org/10.1103/physreva.58.4336

Pauli W. (1980), General Principles of Quantum Mechanics, Berlin–Heidelberg: Springer. https://doi.org/10.1007/978-3-642-61840-6

Peres A. (1980), Measurement of Time by Quantum Clocks, „American Journal of Physics” 48(7), 552–557. https://doi.org/10.1119/1.12061

Przełęcki M. (1955), O tzw. definicjach operacyjnych, „Studia Logica: An International Journal for Symbolic Logic” 3, 125–183.

Ramos R., Spierings D., Racicot I., Steinberg A. (2020), Measurement of the Time Spent by a Tunnelling Atom within the Barrier Region, „Nature” 583(7817), 529–532. https://doi.org/10.1038/s41586-020-2490-7

Razavy M. (1971), Time of Arrival Operator, „Canadian Journal of Physics” 49(24), 3075–3081. https://doi.org/10.1139/p71-367

Ribes-Iñesta E. (2003), What Is Defined in Operational Definitions? The Case of Operant Psychology, „Behavior and Philosophy” 31(2003), 111–126.

Robertson H. P. (1929), The Uncertainty Principle, „Physical Review” 34, 163–164. https://doi.org/10.1103/PhysRev.34.163

Róg J. (2023), Krytyka operacjonizmu z uwzględnieniem operacyjnej definicji czasu, „Roczniki Filozoficzne” 71(3), 231–250. https://doi.org/10.18290/rf23713.11

Stevens S. S. (1935), The Operational Definition of Psychological Concepts, „Psychological Review” 42(6), 517–527. https://doi.org/10.1037/h0056973

Vessonen E. (2021), Respectful Operationalism, „Theory & Psychology” 31(1), 84–105.

Wang Z.-Y., Chen B., Xiong C.-D. (2003), Time in Quantum Mechanics and Quantum Field Theory, „Journal of Physics A: Mathematical and General” 36(18), 5135–5148. https://doi.org/10.1088/0305-4470/36/18/317

Wang Z.-Y., Xiong C.-D. (2007), How to Introduce Time Operator, „Annals of Physics” 322(10), 2304–2314. https://doi.org/10.1016/j.aop.2006.10.007

Werner R. (1987), Arrival Time Observables in Quantum Mechanics, „Annales de l’Institut Henri Poincaré série A – physique théorique” 47(4), 429–449.

Pobrania

Opublikowane

2024-12-01

Jak cytować

Róg, J. (2024). Problem operacjonizmu z definicją czasu w mechanice kwantowej. Filozofia Nauki, 31(1), 1–21. https://doi.org/10.14394/filnau.2023.0006

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