The Modal-Hamiltonian Interpretation of Quantum Mechanics and the Measurement Problem
DOI:
https://doi.org/10.35588/cc.v6d7879Keywords:
Modal-Hamiltonian Interpretation, Quantum Measurement Problem, Quantum Ontology, Symmetry, Non-Ideal MeasurementsAbstract
This paper presents the Modal-Hamiltonian Interpretation (MHI) of quantum mechanics and shows how it provides a conceptually consistent and physically plausible solution to the measurement problem.
By assigning a central role to the system's Hamiltonian and its symmetries in determining the observables that acquire definite values, the MHI avoids the difficulties faced by other interpretations when dealing with non-ideal measurements.
Its update rule ensures that the measurement pointer always acquires a definite value and allows one to distinguish between reliable and unreliable frequency measurements.
Furthermore, the MHI proposes a physical model that complements von Neumann's formal approach, conceiving measurement as a symmetry-breaking process through which previously inaccessible generators of the Hamiltonian become empirically accessible.
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References
Albert, D. y B. Loewer (1990). “Wanted dead or alive: two attempts to solve Schrödinger’s paradox.” Pp. 277-285 en A. Fine, M. Forbes y L. Wessels (eds.), Proceedings of the PSA 1990, Vol. 1. A. East Lansing, Michigan: Philosophy of Science Association.
Albert, D. y B. Loewer (1991). “Some alleged solutions to the measurement problem.” Synthese, 88: 87-98.
Albert, D. y B. Loewer (1993). “Non-ideal measurements.” Foundations of Physics Letters, 6: 297-305.
Ardenghi, J. S., M. Castagnino y O. Lombardi (2009). “Quantum mechanics: Modal interpretation and Galilean transformations.” Foundations of Physics, 39: 1023-1045.
Ardenghi, J. S., M. Castagnino y O. Lombardi (2011). “Modal-Hamiltonian interpretation of quantum mechanics and Casimir operators: the road to quantum field theory.” International Journal of Theoretical Physics, 50: 774-791.
Ardenghi, J. S., O. Lombardi y M. Narvaja (2013). “Modal interpretations and consecutive measurements.” Pp. 207-217 en V. Karakostas y D. Dieks (eds.), EPSA 2011: Perspectives and Foundational Problems in Philosophy of Science. Berlin: Springer.
Bacciagaluppi, G. and M. Hemmo (1996). “Modal interpretations, decoherence and measurements.” Studies in History and Philosophy of Modern Physics, 27: 239-277.
da Costa, N. y O. Lombardi (2014). “Quantum mechanics: ontology without individuals.” Foundations of Physics, 44: 1246-1257.
da Costa, N., O. Lombardi y M. Lastiri (2013). “A modal ontology of properties for quantum mechanics.” Synthese, 190: 3671-3693.
Dieks, D. y P. Vermaas (eds.) (1998). The Modal Interpretation of Quantum Mechanics. Dordrecht: Kluwer Academic Publishers.
Fortin, S. and O. Lombardi (2022). “Entanglement and indistinguishability in a quantum ontology of properties.” Studies in History and Philosophy of Science, 91: 234-243.
Fortin, S., O. Lombardi y J. C. Martínez González (2018). “A new application of the modal-Hamiltonian interpretation of quantum mechanics: the problem of optical isomerism.” Studies in History and Philosophy of Modern Physics, 62: 123-135.
Kochen, S. y E. Specker (1967). “The problem of hidden variables in quantum mechanics.” Journal of Mathematics and Mechanics, 17: 59-87.
Lombardi, O. (2023a). “Not individuals, nor even objects: On the ontological nature of quantum systems.” Pp. 45-77 en J. Arenhart y R. Arroyo (eds.), Non-Reflexive Logics, Non-Individuals, and the Philosophy of Quantum Mechanics. Essays in Honour of the Philosophy of Décio Krause. Dordrecht: Springer-Synthese Library.
Lombardi, O. (2023b). “Entanglement and indistinguishability: facing some challenges from a new perspective.” Philosophical Transactions of the Royal Society A, 381: #20220101.
Lombardi, O. (2025). The Modal-Hamiltonian Interpretation of Quantum Mechanics. Oxford: Oxford University Press, en prensa.
Lombardi, O., M. Castagnino y J. S. Ardenghi (2010). “The modal-Hamiltonian interpretation and the Galilean covariance of quantum mechanics.” Studies in History and Philosophy of Modern Physics, 41: 93-103.
Lombardi, O. y D. Dieks (2016). “Particles in a quantum ontology of properties.” Pp. 123-143 en T. Bigaj y C. Wüthrich (eds.), Metaphysics in Contemporary Physics (Poznan Studies in the Philosophy of the Sciences and the Humanities). Leiden: Brill-Rodopi
Lombardi, O. y D. Dieks (2024). “Modal interpretations of quantum mechanics.” En E. N. Zalta y U. Nodelman (eds.), The Stanford Encyclopedia of Philosophy (Summer 2024 Edition). URL = https:// plato.stanford.edu/archives/sum2024/entries/qm-modal/.
Lombardi, O. y M. Castagnino (2008). “A modal-Hamiltonian interpretation of quantum mechanics.” Studies in History and Philosophy of Modern Physics, 39: 380-443.
Lombardi, O. y S. Fortin (2015). “The role of symmetry in the interpretation of quantum mechanics.” Electronic Journal of Theoretical Physics, 12: 255-272.
Maudlin, T. (1995). “Three measurement problems.” Topoi, 14: 7-15.
Omnès, R. (1994). The Interpretation of Quantum Mechanics. Princeton: Princeton University Press.
Omnès, R. (1999). Understanding Quantum Mechanics. Princeton: Princeton University Press.
Ruetsche, L. (1995). “Measurement error and the Albert-Loewer problem.” Foundations of Physics Letters, 8: 327-344.
Ruetsche, L. (2003). “Modal semantics, modal dynamics and the problem of state preparation.” International Studies in the Philosophy of Science, 17: 25-41.
van Fraassen, B. (1972). “A formal approach to the philosophy of science.” Pp. 303-366 en R. Colodny (ed.), Paradigms and Paradoxes: The Philosophical Challenge of the Quantum Domain. Pittsburgh: University of Pittsburgh Press.
van Fraassen, B. (1974). “The Einstein-Podolsky-Rosen paradox.” Synthese, 29: 291–309.
van Fraassen, B. (1991), Quantum Mechanics. Oxford: Clarendon Press.
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