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Compatibility between Environment-Induced Decoherence and the Modal-Hamiltonian Interpretation of Quantum Mechanics

Published online by Cambridge University Press:  01 January 2022

Olimpia Lombardi ,
Juan Sebastián Ardenghi ,
Sebastian Fortin  and
Mario Castagnino
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Abstract

Given the impressive success of environment-induced decoherence (EID), nowadays no interpretation of quantum mechanics can ignore its results. The modal-Hamiltonian interpretation (MHI) has proved to be effective for solving several interpretative problems, but since its actualization rule applies to closed systems, it seems to stand at odds with EID. The purpose of this article is to show that this is not the case: the states einselected by the interaction with the environment according to EID (the elements of the “pointer basis”) are the eigenvectors of an actual-valued observable belonging to the preferred context selected by the MHI.

Type
Research Article
Information
Philosophy of Science , Volume 78 , Issue 5 , December 2011 , pp. 1024 - 1036
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

‡

We want to thank Roberto Torretti and Rodolfo Gambini for their interesting and stimulating comments. This article was supported by grants from CONICET (Consejo Nacional de Investigaciones Científicas y Técnicas), ANPCyT (Agencia Nacional de Promoción Científica y Tecnológica), UBA (Unversidad de Buenos Aires), and SADAF (Sociedad Argentina de Análisis Filosófico).

References

Albert, David. 1992. Quantum Mechanics and Experience. Cambridge, MA: Harvard University Press.Google Scholar
Albert, David, and Loewer, Barry. 1990. “Wanted Dead or Alive: Two Attempts to Solve Schrödinger's Paradox.” In PSA 1990: Proceedings of the 1990 Biennial Meeting of the Philosophy of Science Association, Vol. 1, ed. Fine, Arthur and Forbes, Micky, 277–85. East Lansing, MI: Philosophy of Science Association.Google Scholar
Albert, David, and Loewer, Barry. 1993. “Non-ideal Measurements.” Foundations of Physics Letters 6:297–305.CrossRefGoogle Scholar
Ardenghi, Juan Sebastián, Castagnino, Mario, and Lombardi, Olimpia. 2009. “Quantum Mechanics: Modal Interpretation and Galilean Transformations.” Foundations of Physics 39:1023–45.CrossRefGoogle Scholar
Bacciagaluppi, Guido. 2000. “Delocalized Properties in the Modal Interpretation of a Continuous Model of Decoherence.” Foundations of Physics 30:1431–44.CrossRefGoogle Scholar
Bacciagaluppi, Guido, and Hemmo, Meir. 1996. “Modal Interpretations, Decoherence and Measurements.” Studies in History and Philosophy of Modern Physics 27:239–77.CrossRefGoogle Scholar
Castagnino, Mario, Laura, Roberto, and Lombardi, Olimpia. 2007. “A General Conceptual Framework for Decoherence in Closed and Open Systems.” Philosophy of Science 74:968–80.CrossRefGoogle Scholar
Castagnino, Mario, and Lombardi, Olimpia. 2008. “The Role of the Hamiltonian in the Interpretation of Quantum Mechanics.” Journal of Physics, conferences series, 28:012014.Google Scholar
Dieks, Dennis. 1988. “The Formalism of Quantum Theory: An Objective Description of Reality?” Annalen der Physik 7:174–90.Google Scholar
Dieks, Dennis. 1994a. “The Modal Interpretation of Quantum Mechanics, Measurement and Macroscopic Behavior.” Physical Review D 49:2290–2300.CrossRefGoogle Scholar
Dieks, Dennis. 1994b. “Objectification, Measurement and Classical Limit according to the Modal Interpretation of Quantum Mechanics.” In Proceedings of the Symposium on the Foundations of Modern Physics, ed. Busch, Paul, Lathi, Pekka, and Mittelstaedt, Peter, 160–67. Singapore: World Scientific.Google Scholar
Dieks, Dennis, and Vermaas, Pieter. 1998. The Modal Interpretation of Quantum Mechanics. Dordrecht: Kluwer.CrossRefGoogle Scholar
Elby, Andrew. 1993. “Why ‘Modal’ Interpretations Don’t Solve the Measurement Problem.” Foundations of Physics Letters 6:5–19.CrossRefGoogle Scholar
Elby, Andrew. 1994. “The ‘Decoherence’ Approach to the Measurement Problem in Quantum Mechanics.” In PSA 1994: Proceedings of the 1994 Biennial Meeting of the Philosophy of Science Association, Vol. 1, ed. Hull, David and Forbes, Micky, 355–65. East Lansing, MI: Philosophy of Science Association.Google Scholar
Harshman, Nathan, and Wickramasekara, Sujeeva. 2007a. “Galilean and Dynamical Invariance of Entanglement in Particle Scattering.” Physical Review Letters 98:080406.CrossRefGoogle Scholar
Harshman, Nathan, and Wickramasekara, Sujeeva. 2007b. “Tensor Product Structures, Entanglement, and Particle Scattering.” Open Systems and Information Dynamics 14:341–51.CrossRefGoogle Scholar
Healey, Richard. 1989. The Philosophy of Quantum Mechanics: An Interactive Interpretation. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Healey, Richard. 1995. “Dissipating the Quantum Measurement Problem.” Topoi 14:55–65.CrossRefGoogle Scholar
Kochen, Simon. 1985. “A New Interpretation of Quantum Mechanics.” In Symposium on the Foundations of Modern Physics, ed. Lahti, Pekka and Mittelsteadt, Peter, 151–69. Singapore: World Scientific.Google Scholar
Lombardi, Olimpia, and Castagnino, Mario. 2008. “A Modal-Hamiltonian Interpretation of Quantum Mechanics.” Studies in History and Philosophy of Modern Physics 39:380–443.CrossRefGoogle Scholar
Lombardi, Olimpia, Castagnino, Mario, and Ardenghi, Juan Sebastián. 2010. “The Modal-Hamiltonian Interpretation and the Galilean Covariance of Quantum Mechanics.” Studies in History and Philosophy of Modern Physics 41 (2): 93–103.CrossRefGoogle Scholar
Mittelstaedt, Peter. 1998. The Interpretation of Quantum Mechanics and the Measurement Process. Cambridge: Cambridge University Press.Google Scholar
Monton, Bradley. 1999. “Van Fraassen and Ruetsche on Preparation and Measurement.” Philosophy of Science 66 (Proceedings): S82–S91.CrossRefGoogle Scholar
Omnès, Roland. 1994. The Interpretation of Quantum Mechanics. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Omnès, Roland. 1999. Understanding Quantum Mechanics. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Paz, Juan Pablo. 1994. “Decoherence in Quantum Brownian Motion.” In Physical Origins of Time Asymmetry, ed. Halliwell, Jonathan, Pérez-Mercader, Juan, and Zurek, Wojciech, 213–20. Cambridge: Cambridge University Press.Google Scholar
Paz, Juan Pablo, and Zurek, Wojciech. 1999. “Quantum Limit of Decoherence: Environment Induced Superselection of Energy Eigenstates.” Physical Review Letters 82:5181–85.CrossRefGoogle Scholar
Paz, Juan Pablo, and Zurek, Wojciech. 2002. “Environment-Induced Decoherence and the Transition from Quantum to Classical.” In Fundamentals of Quantum Information: Quantum Computation, Communication, Decoherence and All That, ed. Heiss, Dieter, 77–148. Heidelberg: Springer.CrossRefGoogle Scholar
Ruetsche, Laura. 1996. “Van Fraassen on Preparation and Measurement.” Philosophy of Science 63 (Proceedings): S338–S346.CrossRefGoogle Scholar
Schlosshauer, Maximilian. 2004. “Decoherence, the Measurement Problem, and Interpretations of Quantum Mechanics.” Reviews of Modern Physics 76:1267–1305.CrossRefGoogle Scholar
Schlosshauer, Maximilian. 2007. Decoherence and the Quantum-to-Classical Transition. Heidelberg: Springer.Google Scholar
van Fraassen, Bas. 1991. Quantum Mechanics: An Empiricist View. Oxford: Oxford University Press.CrossRefGoogle Scholar
Vermaas, Pieter, and Dieks, Dennis. 1995. “The Modal Interpretation of Quantum Mechanics and Its Generalization to Density Operators.” Foundations of Physics 25:145–58.CrossRefGoogle Scholar
Zurek, Wojciech. 1981. “Pointer Basis of Quantum Apparatus: Into What Mixtures Does the Wave Packet Collapse?” Physical Review D 24:1516–25.Google Scholar
Zurek, Wojciech. 1982. “Environment-Induced Superselection Rules.” Physical Review D 26:1862–80.Google Scholar
Zurek, Wojciech. 1993. “Preferred States, Predictability, Classicality and the Environment-Induced Decoherence.” Progress of Theoretical Physics 89:281–312.CrossRefGoogle Scholar
Zurek, Wojciech. 2003. “Decoherence, Einselection, and the Quantum Origins of the Classical.” Reviews of Modern Physics 75:715–76.CrossRefGoogle Scholar
Zurek, Wojciech, Habib, Salman, and Paz, Juan Pablo. 1993. “Coherent States via Decoherence.” Physical Review Letters 70:1187–90.CrossRefGoogle ScholarPubMed