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Abstract:

In this work we build a quantum logic that allows us to refer to physical magnitudes pertaining to different contexts from a fixed one without the contradictions with quantum mechanics expressed in no-go theorems. This logic arises from considering a sheaf over a topological space associated with the Boolean sublattices of the ortholattice of closed subspaces of the Hilbert space of the physical system. Different from standard quantum logics, the contextual logic maintains a distributive lattice structure and a good definition of implication as a residue of the conjunction. © 2005 American Institute of Physics.

Registro:

Documento: Artículo
Título:Contextual logic for quantum systems
Autor:Domenech, G.; Freytes, H.
Filiación:Inst. de Astron. y Fis. del Espacio, Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires, Argentina
Escuela de Filosofía, Universidad National de Rosario, Entre Ríos 758, 2000, Rosario, Argentina
Consejo Nac. de Invest. Cie. y Tec., Argentina
Año:2005
Volumen:46
Número:1
DOI: http://dx.doi.org/10.1063/1.1819525
Título revista:Journal of Mathematical Physics
Título revista abreviado:J. Math. Phys.
ISSN:00222488
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222488_v46_n1_p_Domenech

Referencias:

  • Aerts, D., Quantum mechanics; structures, axioms and paradoxes (1999) Quantum Structures and the Nature of Reality: The Indigo Book of the Einstein Meets Margritte Series, , edited by D. Aerts and J. Pykacz (Kluwer Academic, Dordrecht)
  • Aerts, D., Colebunders, E., Van Der Voorde, A., Van Steirteghem, B., State property systems and closure spaces: A study of categorical equivalence (1999) Int. J. Theor. Phys., 38, pp. 359-385
  • Balbes, R., Dwinger, Ph., (1974) Distributive Lattices, , University of Missouri Press, Columbia, MO
  • Birkhoff, G., (1967) Lattice Theory, 3rd Ed., , American Mathematical Society, Providence, RI
  • Birkhoff, G., Von Neumann, J., The logic of quantum mechanics (1936) Ann. Math., 37, pp. 823-843
  • Butterfield, J., Isham, C., A topos perspective on the Kochen-Specker theorem: IV (2002) Int. J. Theor. Phys., 41, pp. 613-639
  • Coecke, B., Moore, D.J., Wilce, A., Operational quantum logic: An overview (2000) Current Research in Operational Quantum Logic, , edited by B. Coecke, D. J. Moore, and A. Wilce (Kluwer Academic, Dordecht)
  • Coecke, B., Moore, D.J., Smets, S., Logic of dynamics and dynamics of logic; some paradigm examples (2001) Logic, Epistemology and the Unity of Science, , edited by D. Gabbay, S. Rahman, J. M. Torres, and J. P. Van Bendegem (Kluwer Academic, Dordrecht)
  • Dalla Chiara, M.L., Giuntini, R., Quantum logic (2001) Handbook of Philosophical Logic, 6. , edited by G. Gabbay and F. Guenther (Kluwer, Dordrecht)
  • Dirac, P.A.M., (1958) The Principle of Quantum Mechanics, , Oxford University Press, Oxford
  • Goldblatt, R., (1986) Tapoi: The Categorial Analysis of Logic, , Elsevier Science, Amsterdam
  • Hamilton, J., An obstruction based approach to the Kochen-Specker theorem (2000) J. Phys. A, 33, pp. 3783-3794
  • Hamilton, J., Isham, C., Butterfield, J., A Topos Perspective on the Kochen-specker Theorem: III, , quant-ph/ 9911020
  • Isham, C., Topos theory and consistent histories: The internal logic of the set of all consistent sets (1997) Int. J. Theor. Phys., 36, pp. 785-814
  • Isham, C., Butterfield, J., A topos perspective on the Kochen-Specker theorem. I (1998) Int. J. Theor. Phys., 37, pp. 2669-2773
  • Isham, C., Butterfield, J., A topos perspective on the Kochen-Specker theorem. II (1999) Int. J. Theor. Phys., 38, pp. 827-859
  • Kochen, S., Specker, E.P., The problem of hidden variables in quantum mechanics (1967) J. Math. Mech., 17, pp. 9-87
  • Mac Lane, S., Moerdijk, I., (1992) Sheaves in Geometry and Logic: A First Introduction to Topos Theory, , Springer, Berlin
  • Maeda, F., Maeda, S., (1970) Theory of Symmetric Lattices, , Springer, Berlin

Citas:

---------- APA ----------
Domenech, G. & Freytes, H. (2005) . Contextual logic for quantum systems. Journal of Mathematical Physics, 46(1).
http://dx.doi.org/10.1063/1.1819525
---------- CHICAGO ----------
Domenech, G., Freytes, H. "Contextual logic for quantum systems" . Journal of Mathematical Physics 46, no. 1 (2005).
http://dx.doi.org/10.1063/1.1819525
---------- MLA ----------
Domenech, G., Freytes, H. "Contextual logic for quantum systems" . Journal of Mathematical Physics, vol. 46, no. 1, 2005.
http://dx.doi.org/10.1063/1.1819525
---------- VANCOUVER ----------
Domenech, G., Freytes, H. Contextual logic for quantum systems. J. Math. Phys. 2005;46(1).
http://dx.doi.org/10.1063/1.1819525