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A Topological Study of Contextuality and Modality in Quantum Mechanics

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Abstract

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.

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Author notes

  1. Hector Freytes

    Present address: Instituto Argentino de Matemática, Saavedra 15, Buenos Aires, Argentina

Authors and Affiliations

  1. Instituto de Astronomía y Física del Espacio (IAFE), Casilla de Correo 67, Sucursal 28, 1428, Buenos Aires, Argentina

    Graciela Domenech

  2. Dipartimento di Scienze e Pedagogiche e Filosofiche, Università degli Studi di Cagliari, Via Is Mirrionis 1, 09123, Cagliari, Italy

    Hector Freytes

  3. Center Leo Apostel (CLEA), Brussels Free University, Krijgskundestraat 33, 1160, Brussels, Belgium

    Graciela Domenech & Christian de Ronde

  4. Foundations of the Exact Sciences (FUND), Brussels Free University, Krijgskundestraat 33, 1160, Brussels, Belgium

    Christian de Ronde

Authors
  1. Graciela Domenech
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  2. Hector Freytes
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  3. Christian de Ronde
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Corresponding author

Correspondence to Graciela Domenech.

Additional information

Graciela Domenech is a fellow of the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET). Hector Freytes is a fellow of the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET).

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Domenech, G., Freytes, H. & de Ronde, C. A Topological Study of Contextuality and Modality in Quantum Mechanics. Int J Theor Phys 47, 168–174 (2008). https://doi.org/10.1007/s10773-007-9595-8

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  • DOI: https://doi.org/10.1007/s10773-007-9595-8

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