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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Explore related subjects
Discover the latest articles and news from researchers in related subjects, suggested using machine learning.References
Ardenghi J. S., Lombardi O. (2011) The modal-Hamiltonian interpretation of quantum mechanics as a kind of “atomic” interpretation. Physics Research International 2011: 379–604
Ardenghi J. S., Castagnino M., Lombardi O. (2009) Quantum mechanics: Modal interpretation and Galilean transformations. Foundations of Physics 39: 1023–1045
Ballentine L. (1998) Quantum mechanics: A modern development. World Scientific, Singapore
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 1331–1367
Brown H., Holland P. (1999) The Galilean covariance of quantum mechanics in the case of external fields. American Journal of Physics 67: 204–214
Bunge M. (1977) Treatise on basic philosophy, Vol. 3: Ontology I. Reidel, Dordrecht
Butterfield J. (1993) Interpretation and identity in quantum theory. Studies in History and Philosophy of Science 24: 443–476
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, Paris
da Costa N., Krause D. (1994) Schrödinger logics. Studia Logica 53: 533–550
da Costa N., Krause D. (1997) An intensional Schrödinger logic. Notre Dame Journal of Formal Logic 38: 179–194
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, Dordrecht
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, Dordrecht
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, Dorrecht
Dieks D. (2007) Probability in modal interpretations of quantum mechanics. Studies in History and Philosophy of Modern Physics 19: 292–310
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.
Dieks, D., Vermaas, P. (Eds.) (1998) The modal interpretation of quantum mechanics. Kluwer Academic Publishers, Dordrecht
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 93–113
French S., Krause D. (2006) Identity in physics: A historical, philosophical and formal analysis. Oxford University Press, Oxford
Harshman N. L., Wickramasekara S. (2007) Galilean and dynamical invariance of entanglement in particle scattering. Physical Review Letters 98: 080406
Kneale W., Kneale M. (1962) The development of logic. Clarendon Press, Oxford
Kochen S., Specker E. (1967) The problem of hidden variables in quantum mechanics. Journal of Mathematics and Mechanics 17: 59–87
Krause D. (1992) On a quasi-set theory. Notre Dame Journal of Formal Logic 33: 402–411
Lévi-Leblond J. M. (1974) The pedagogical role and epistemological significance of group theory in quantum mechanics. Nuovo Cimento 4: 99–143
Lombardi O., Castagnino M. (2008) A modal-Hamiltonian interpretation of quantum mechanics. Studies in History and Philosophy of Modern Physics 39: 380–443
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: 93–103
Loux M. (1998) Metaphysics: A contemporary introduction. Routledge, London
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 46–60
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/.
Post H. (1963) Individuality and physics. Listener 70: 534–537
Redhead M., Teller P. (1992) Particle labels and the theory of indistinguishable particles in quantum mechanics. British Journal for the Philosophy of Science 43: 201–218
Tarski A. (1941) On the calculus of relations. The Journal of Symbolic Logic 6: 73–89
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 114–141
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 303–366
van Fraassen B. C. (1974) The Einstein–Podolsky–Rosen paradox. Synthese 29: 291–309
van Fraassen B. C. (1991) Quantum mechanics: An empiricist view. Clarendon Press, Oxford
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
da Costa, N., Lombardi, O. & Lastiri, M. A modal ontology of properties for quantum mechanics. Synthese 190, 3671–3693 (2013). https://doi.org/10.1007/s11229-012-0218-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11229-012-0218-4