A new conceptual scheme for the interpretation of the improper mixtures in quantum mechanics
DOI:
https://doi.org/10.1590/S1678-31662013000100005Keywords:
Quantum logic, Improper mixtures, Convex setsAbstract
In this article, we analyze the meaning of density matrices within the formalism of quantum mechanics. We discuss the problem of compound systems in the context of quantum logic as well as the interpretation of improper mixtures. Taking into account the development of convex quantum logic, we present an analysis of the formal structure of the theory which we will argue, must be taken into account when developing a new conceptual scheme for the interpretation of quantum mixtures.Downloads
References
Alber, G. et al. (Ed.). Quantum information. Berlin: Springer, 2001. (Springer Tracts in Modern Physics, 173.)
Bengtsson, I. & Zyczkowski, K. Geometry of quantum states: an introduction to quantum entanglement. Cambridge: Cambridge University Press, 2006.
Birkhoff G. & von Neumann, J. The logic of quantum mechanics. Annals of Mathematics, 37, p. 823-43, 1936.
Bitbol, M. Mechanique quantique, une introduction philosophique. Paris: Champs Flamarion, 1997.
Bohm, D. A suggested interpretations of the quantum theory in terms of “hidden variables”. Part I. Physical Review, 85, p. 166-79, 1952a.
Bohm, D. A suggested interpretations of the quantum theory in terms of “hidden variables”. Part II. Physical Review, 85, p. 180-93, 1952b.
Bokulich, A. Open or closed? Dirac, Heisenberg, and the relation between classical and quantum mechanics. Studies in History and Philosophy of Modern Physics, 35, p. 377-96, 2004.
Dalla Chiara, M. L.; Giuntinni, R. & Greechie, R. Reasoning in quantum theory. Dordrecht: Kluwer Academic Publishers, 2004.
de Ronde, C. El enfoque de descripciones complementarias: en búsqueda de un desarrollo expresivo de la realidad física. Perspectivas Metodológicas, 9, p. 126-38, 2009.
de Ronde, C. For and against metaphysics in the modal interpretation of quantum mechanics. Philosophica, 83, p. 85-117, 2010.
de Ronde, C. The contextual and modal character of quantum mechanics. Utrecht, 2011. Tesis (Doctorado en Física). Utrecht University.
de Ronde, C. La noción de potencialidad en la interpretación modal de la mecánica cuántica. Scientiae Studia, 10, p. 137-64, 2012.
de Ronde, C. & Bontems, V. La notion d’entité en tant qu’obstaclé épistémologique: Bachelard, la mécanique quantique et la logique. Bulletin des Amis de Gaston Bachelard, 13, p. 12-38, 2011.
de Ronde, C. & Fleisner, A. Sobre teorías cerradas y paradigmas: un dialogo entre Werner Heisenberg y Thomas Kuhn. Actas del 1er Congreso de la Sociedad Filosófica Uruguaya, 2012.
de Ronde, C.; Freytes, H & Domenech, G., Interpreting the modal Kochen-Specker theorem: possibility and many worlds in quantum mechanics. En prensa.
D’Espagnat, B. Conceptual foundations of quantum mechanics, Massachusetts: Benjaming Reading, 1976.
D’Espagnat, B. Reply to K. A. Kirkpatrick. ArXiv: quant-ph0111081, 2001.
Dickson, M. & Dieks, D. Modal interpretations of quantum mechanics. In: Zalta, E. N. (Ed.). The Stanford Encyclopedia of Philosophy, 2002. Disponible en: <http://plato.stanford.edu/archives/ win2002/entries/qm-modal/>. Acceso en: 20 oct. 2012.
Dirac, P. A. M. The principles of quantum mechanics. 4 ed. London: Oxford University Press, 1974.
Domenech, G., Holik, F. & Massri, C. A quantum logical and geometrical approach to the study of improper mixtures. Journal Mathematical Physics, 51, p. 521081-7, 2010.
Fine, A. The shaky game. Chicago: University of Chicago Press, 1986.
Fuchs, C. & Peres, A. Quantum theory needs no “interpretation”. Physics Today, 53, p. 70-2, 2000.
Ghirardi, G. C., Rimini, A. & Weber, T. Unified dynamics for microscopic and macroscopic systems. Physical Review D, 34, p. 470-91, 1986.
Healey, R. Holism and nonseparability in physics. In: Zalta, E. N. (Ed.). The Stanford Encyclopedia of Philosophy, 2002. Disponible en: <http://plato.stanford.edu/entries/physicsp-holism/>. Acceso en: 20 oct. 2012.
Holik, F. Compound quantum systems: an algebraic approach. Buenos Aires, 2010. Tesis (Doctorado en Física). Universidad de Buenos Aires.
Holik, F.; Massri, C. & Ciancaglini, N. Convex quantum logic. International Journal of Theoretical Physics, 51, p. 1600-20, 2012.
Horodecki, M.; Horodecki, P. & Horodecki, R. Mixed-state entanglement and quantum communication. In: Alber, G. et al. (Ed.). Quantum information. Berlin: Springer, 2001. (Springer Tracts in Modern Physics, v. 173.). p. 151-65.
Howard, D. Was Einstein really a realist? Perspectives on Science, 1, p. 204-51, 1993.
Howard, D. Einstein, Kant, and the origins of logical empiricism. In: Salmon, W. & Wolters, G. (Ed.). Logic, language, and the structure of scientific theories. Pittsburgh: University of Pittsburgh Press, 1994. (Proceedings of the Carnap-Reichenbach centennial, University of Konstanz, 21-24 May 1991.). p. 45-105.
Jauch. J. M. Foundations of quantum mechanics. Cambridge: Addison-Wesley, 1968.
Kochen, S. A new interpretation of quantum mechanics. In: Lathi, P. & Mittelslaedt, P. (Ed.). Symposium on the foundations of modern Physics 1985. Johensuu: World Scientific, 1985. p. 151-69.
Kochen, S. & Specker, E. On the problem of hidden variables in quantum mechanics. Journal of Mathematics and Mechanics, 17, p. 59-87, 1967.
Lathi, P. & Mittelslaedt, P. (Ed.). Symposium on the foundations of modern Physics 1985. Johensuu: World Scientific, 1985.
Mittelstaedt, P. The interpretation of quantum mechanics and the measurement process. Cambridge: Cambridge University Press, 1998.
Piron, C. Foundations of quantum physics, Cambridge: Addison-Wesley, 1976.
Rédei, M. Quantum logic in algebraic approach. Dordrecht: Kluwer Academic Publishers, 1998.
Salmon, W. & Wolters, G. (Ed.). Logic, language, and the structure of scientific theories. Pittsburgh: University of Pittsburgh Press, 1994. (Proceedings of the Carnap-Reichenbach centennial, University of Konstanz, 21-24 May 1991.)
Van Fraassen, B. C. Quantum mechanics: an empiricist view, Oxford: Clarendon, 1991.
Werner, R. Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. Physical Review A, 40, p. 4277-81, 1989.
Zalta, E. N. (Ed.). The Stanford Encyclopedia of Philosophy. Standford: Standford University Press, 2008. 10 v.
Downloads
Published
Issue
Section
License
Copyright (c) 2013 Scientiae Studia
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
A revista detém os direitos autorais de todos os textos nela publicados. Os autores estão autorizados a republicar seus textos mediante menção da publicação anterior na revista. A revista adota a Licença Creative Commons Attribution-NonCommercial-ShareAlike 4.
