Synthese

, Volume 190, Issue 17, pp 3671–3693

A modal ontology of properties for quantum mechanics

  • Newton da Costa
  • Olimpia Lombardi
  • Mariano Lastiri
Article

Abstract

Our purpose in this paper is to delineate an ontology for quantum mechanics that results adequate to the formalism of the theory. We will restrict our aim to the search of an ontology that expresses the conceptual content of the recently proposed modal-Hamiltonian interpretation, according to which the domain referred to by non-relativistic quantum mechanics is an ontology of properties. The usual strategy in the literature has been to focus on only one of the interpretive problems of the theory and to design an interpretation to solve it, leaving aside the remaining difficulties. On the contrary, our aim in the present work is to formulate a “global” solution, according to which different problems can be adequately tackled in terms of a single ontology populated of properties, in which systems are bundles of properties. In particular, we will conceive indistinguishability between bundles as a relation derived from indistinguishability between properties, and we will show that states, when operating on combinations of indistinguishable bundles, act as if they were symmetric with no need of a symmetrization postulate.

Keywords

Quantum Mechanics Modal-Hamiltonian interpretation Bundles of properties Contextuality Indistinguishability 

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References

  1. Ardenghi J. S., Lombardi O. (2011) The modal-Hamiltonian interpretation of quantum mechanics as a kind of “atomic” interpretation. Physics Research International 2011: 379–604CrossRefGoogle Scholar
  2. Ardenghi J. S., Castagnino M., Lombardi O. (2009) Quantum mechanics: Modal interpretation and Galilean transformations. Foundations of Physics 39: 1023–1045CrossRefGoogle Scholar
  3. Ballentine L. (1998) Quantum mechanics: A modern development. World Scientific, SingaporeCrossRefGoogle Scholar
  4. Brading K., Castellani E. (2007) Symmetries and invariances in classical physics. In: Butterfield J., Earman J. (Eds.), Philosophy of physics, part B. Elsevier, Amsterdam, pp 1331–1367CrossRefGoogle Scholar
  5. Brown H., Holland P. (1999) The Galilean covariance of quantum mechanics in the case of external fields. American Journal of Physics 67: 204–214CrossRefGoogle Scholar
  6. Bunge M. (1977) Treatise on basic philosophy, Vol. 3: Ontology I. Reidel, DordrechtCrossRefGoogle Scholar
  7. Butterfield J. (1993) Interpretation and identity in quantum theory. Studies in History and Philosophy of Science 24: 443–476CrossRefGoogle Scholar
  8. da Costa N., French S., Krause D. (1992) The Schrödinger problem. In: Bitbol M., Darrigol O. (Eds.) Erwin Schrödinger: Philosophy and the birth of quantum mechanics. Editions Frontières, ParisGoogle Scholar
  9. da Costa N., Krause D. (1994) Schrödinger logics. Studia Logica 53: 533–550CrossRefGoogle Scholar
  10. da Costa N., Krause D. (1997) An intensional Schrödinger logic. Notre Dame Journal of Formal Logic 38: 179–194CrossRefGoogle Scholar
  11. da Costa N., Krause D. (1999) Set-theoretical models for quantum systems. In: dalla Chiara M. L., Giuntini R., Laudisa F. (Eds.) Language, quantum, music. Kluwer, DordrechtGoogle Scholar
  12. dalla Chiara M. L., di Francia G. T. (1993) Individuals, kinds and names in physics. In: Corsi G., dalla Chiara M. L., Ghirardi G. C. (Eds.) Bridging the gap: Philosophy, mathematics and physics. Kluwer, DordrechtGoogle Scholar
  13. dalla Chiara M. L., di Francia G. T. (1995) Identity questions from quantum theory. In: Gavroglu K., Stachel J., Wartofski M. W. (Eds.) Physics, philosophy and the scientific community. Kluwer, DorrechtGoogle Scholar
  14. Dieks D. (2007) Probability in modal interpretations of quantum mechanics. Studies in History and Philosophy of Modern Physics 19: 292–310CrossRefGoogle Scholar
  15. Dieks, D., & Lombardi, O. (2012). Modal interpretations of quantum mechanics. In E. N. Zalta (Ed.) The Stanford encyclopedia of philosophy (fall 2012 edn.). Retrieved October 27, 2012 from http://plato.stanford.edu, forthcoming.
  16. Dieks, D., Vermaas, P. (Eds.) (1998) The modal interpretation of quantum mechanics. Kluwer Academic Publishers, DordrechtGoogle Scholar
  17. French S. (1998) On the withering away of physical objects. In: Castellani E. (Ed.) Interpreting bodies: Classical and quantum objects in modern physics. Princeton University Press, Princeton, pp 93–113Google Scholar
  18. French S., Krause D. (2006) Identity in physics: A historical, philosophical and formal analysis. Oxford University Press, OxfordCrossRefGoogle Scholar
  19. Harshman N. L., Wickramasekara S. (2007) Galilean and dynamical invariance of entanglement in particle scattering. Physical Review Letters 98: 080406CrossRefGoogle Scholar
  20. Kneale W., Kneale M. (1962) The development of logic. Clarendon Press, OxfordGoogle Scholar
  21. Kochen S., Specker E. (1967) The problem of hidden variables in quantum mechanics. Journal of Mathematics and Mechanics 17: 59–87Google Scholar
  22. Krause D. (1992) On a quasi-set theory. Notre Dame Journal of Formal Logic 33: 402–411CrossRefGoogle Scholar
  23. Lévi-Leblond J. M. (1974) The pedagogical role and epistemological significance of group theory in quantum mechanics. Nuovo Cimento 4: 99–143Google Scholar
  24. Lombardi O., Castagnino M. (2008) A modal-Hamiltonian interpretation of quantum mechanics. Studies in History and Philosophy of Modern Physics 39: 380–443CrossRefGoogle Scholar
  25. Lombardi O., Castagnino M., Ardenghi J. S. (2010) The modal-Hamiltonian interpretation and the Galilean covariance of quantum mechanics. Studies in History and Philosophy of Modern Physics 41: 93–103CrossRefGoogle Scholar
  26. Loux M. (1998) Metaphysics: A contemporary introduction. Routledge, LondonCrossRefGoogle Scholar
  27. Maudlin T. (1998) Part and whole in quantum mechanics. In: Castellani E. (Ed.) Interpreting bodies: Classical and quantum objects in modern physics. Princeton University Press, Princeton, pp 46–60Google Scholar
  28. Menzel, C. (2007). Actualism. In: E. N. Zalta (Ed.) The Stanford encyclopedia of philosophy (spring 2007 edn.). Retrieved June 4, 2007 from http://plato.stanford.edu/archives/spr2007/entries/actualism/.
  29. Post H. (1963) Individuality and physics. Listener 70: 534–537Google Scholar
  30. Redhead M., Teller P. (1992) Particle labels and the theory of indistinguishable particles in quantum mechanics. British Journal for the Philosophy of Science 43: 201–218CrossRefGoogle Scholar
  31. Tarski A. (1941) On the calculus of relations. The Journal of Symbolic Logic 6: 73–89CrossRefGoogle Scholar
  32. Teller P. (1998) Quantum mechanics and haecceities. In: Castellani E. (Ed.) Interpreting bodies: Classical and quantum objects in modern physics. Princeton University Press, Princeton, pp 114–141Google Scholar
  33. van Fraassen B. C. (1972) A formal approach to the philosophy of science. In: Colodny R. (Ed.) Paradigms and paradoxes: The philosophical challenge of the quantum domain. University of Pittsburgh Press, Pittsburgh, pp 303–366Google Scholar
  34. van Fraassen B. C. (1974) The Einstein–Podolsky–Rosen paradox. Synthese 29: 291–309CrossRefGoogle Scholar
  35. van Fraassen B. C. (1991) Quantum mechanics: An empiricist view. Clarendon Press, OxfordCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Newton da Costa
    • 1
  • Olimpia Lombardi
    • 2
  • Mariano Lastiri
    • 3
  1. 1.Universidade Federal de Santa CatarinaFlorianopolisBrazil
  2. 2.CONICETUniversidad de Buenos AiresBuenos AiresArgentina
  3. 3.CONICETUniversidad Nacional de Tres de FebreroBuenos AiresArgentina

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