A topological study of contextuality and modality in quantum mechanics
Kochen-Specker theorem rules out the non-contextual assignment of values to physical magnitudes. Here we enrich the usual orthomodular structure of quantum mechanical propositions with modal operators. This enlargement allows to refer consistently to actual and possible properties of the system. By...
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| Formato: | Capítulo de libro |
| Lenguaje: | Inglés |
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2008
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| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
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| LEADER | 06066caa a22006857a 4500 | ||
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| 001 | PAPER-22504 | ||
| 003 | AR-BaUEN | ||
| 005 | 20250226084436.0 | ||
| 008 | 190411s2008 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-37849036063 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Domenech, Graciela | |
| 245 | 1 | 2 | |a A topological study of contextuality and modality in quantum mechanics |
| 260 | |c 2008 | ||
| 270 | 1 | 0 | |m Domenech, G.; Instituto de Astronomía y Física del Espacio (IAFE), Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires, Argentina; email: domenech@iafe.uba.ar |
| 504 | |a Birkhoff, G., Von Neuman, J., The logic of quantum mechanics (1936) Ann. Math., 27, pp. 823-843 | ||
| 504 | |a Dalla Chiara, M.L., Beltrametti, E.G., Van Fraassen, B.C., Some metalogical pathologies of Quantum Logic (1981) Current Issues in Quantum Logic, pp. 147-159. , Plenum New York | ||
| 504 | |a Dalla Chiara, M.L., Giuntini, R., Greechie, R., (2004) Reasoning in Quantum Theory. Sharp and Unsharp Quantum Logic, , Kluwer Academic Dordrecht | ||
| 504 | |a Dieks, D., The formalism of quantum theory: An objective description of reality (1988) Ann. Phys., 7, pp. 174-190 | ||
| 504 | |a Dieks, D., Quantum mechanics without the projection postulate and its realistic interpretation (1989) Found. Phys., 19, pp. 1397-1423 | ||
| 504 | |a Dieks, D., Quantum mechanics: An intelligible description of reality? (2005) Found. Phys., 35, pp. 399-415 | ||
| 504 | |a Domenech, G., Freytes, H., Contextual logic for quantum systems (2005) J. Math. Phys., 46, pp. 0121021-0121029 | ||
| 504 | |a Domenech, G., Freytes, H., De Ronde, C., Scopes and limits of modality in quantum mechanics (2006) Ann. Phys., 15, pp. 853-860 | ||
| 504 | |a Van Fraassen, B.C., Beltrametti, E.G., Van Fraassen, B.C., A modal interpretation of quantum mechanics (1981) Current Issues in Quantum Logic, pp. 229-258. , Plenum New York | ||
| 504 | |a Van Fraassen, B.C., (1991) Quantum Mechanics: An Empiricist View, , Clarendon Oxford | ||
| 504 | |a Goldblatt, R., Orthomodularity is not elementary (1984) J. Symb. Log., 49, pp. 401-404 | ||
| 504 | |a Goldblatt, R., (1986) Topoi: The Categorical Analysis of Logic, , Elsevier Amsterdam | ||
| 504 | |a Isham, C., Butterfield, J., A topos perspective on the Kochen-Specker theorem: I (1998) Int. J. Theor. Phys., 37, pp. 2669-2773 | ||
| 504 | |a Janowitz, M.F., Quantifiers and orthomodular lattices (1963) Pac. J. Math., 13, pp. 1241-1249 | ||
| 504 | |a Jauch, J.M., (1968) Foundations of Quantum Mechanics, , Addison-Wesley Reading | ||
| 504 | |a Kalmbach, G., (1983) Orthomodular Lattices, , Academic Press London | ||
| 504 | |a Kochen, S., Specker, E.P., The problem of hidden variables in quantum mechanics (1967) J. Math. Mech., 17, pp. 9-87 | ||
| 504 | |a Mac Lane, S., Moerdijk, I., (1992) Sheaves in Geometry and Logic: A First Introduction to Topos Theory, , Springer Berlin | ||
| 504 | |a Maeda, F., Maeda, S., (1970) Theory of Symmetric Lattices, , Springer Berlin | ||
| 504 | |a Sikorski, R., A theorem on extensions of homomorphism (1948) Ann. Soc. Pol. Math., 21, pp. 332-335 | ||
| 506 | |2 openaire |e Política editorial | ||
| 520 | 3 | |a Kochen-Specker theorem rules out the non-contextual assignment of values to physical magnitudes. Here we enrich the usual orthomodular structure of quantum mechanical propositions with modal operators. This enlargement allows to refer consistently to actual and possible properties of the system. By means of a topological argument, more precisely in terms of the existence of sections of sheaves, we give an extended version of Kochen-Specker theorem over this new structure. This allows us to prove that contextuality remains a central feature even in the enriched propositional system. © 2007 Springer Science+Business Media, LLC. |l eng | |
| 536 | |a Detalles de la financiación: Secretaría de Ciencia y Técnica, Universidad de Buenos Aires | ||
| 536 | |a Detalles de la financiación: Agencia Nacional de Promoción Científica y Tecnológica, 6461/05 | ||
| 536 | |a Detalles de la financiación: Consejo Nacional de Investigaciones Científicas y Técnicas | ||
| 536 | |a Detalles de la financiación: Acknowledgements We wish to thank the valuable comments from an anonymous referee. This work was partially supported by the following grants: PICT 04-17687 (ANPCyT), PIP No. 6461/05 (CONICET), UBACyT Nos. X081 and X204. | ||
| 593 | |a Instituto de Astronomía y Física del Espacio (IAFE), Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires, Argentina | ||
| 593 | |a Dipartimento di Scienze e Pedagogiche e Filosofiche, Università degli Studi di Cagliari, Via Is Mirrionis 1, 09123 Cagliari, Italy | ||
| 593 | |a Instituto Argentino de Matemática, Saavedra 15, Buenos Aires, Argentina | ||
| 593 | |a Center Leo Apostel (CLEA), Brussels Free University, Krijgskundestraat 33, 1160 Brussels, Belgium | ||
| 593 | |a Foundations of the Exact Sciences (FUND), Brussels Free University, Krijgskundestraat 33, 1160 Brussels, Belgium | ||
| 690 | 1 | 0 | |a CONTEXTUALITY |
| 690 | 1 | 0 | |a MODAL |
| 690 | 1 | 0 | |a QUANTUM LOGIC |
| 690 | 1 | 0 | |a SHEAVES |
| 700 | 1 | |a Freytes, H. | |
| 700 | 1 | |a De Ronde, C. | |
| 773 | 0 | |d 2008 |g v. 47 |h pp. 168-174 |k n. 1 |p Int. J. Theor. Phys. |x 00207748 |w (AR-BaUEN)CENRE-5330 |t International Journal of Theoretical Physics | |
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