A Topological Study of Contextuality and Modality in Quantum Mechanics |
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| Authors: | Graciela Domenech Hector Freytes Christian de Ronde |
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| Institution: | (1) Instituto de Astronomía y Física del Espacio (IAFE), Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires, Argentina;(2) Dipartimento di Scienze e Pedagogiche e Filosofiche, Università degli Studi di Cagliari, Via Is Mirrionis 1, 09123 Cagliari, Italy;(3) Present address: Instituto Argentino de Matemática, Saavedra 15, Buenos Aires, Argentina;(4) Center Leo Apostel (CLEA), Brussels Free University, Krijgskundestraat 33, 1160 Brussels, Belgium;(5) Foundations of the Exact Sciences (FUND), Brussels Free University, Krijgskundestraat 33, 1160 Brussels, Belgium |
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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.
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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| Keywords: | Contextuality Sheaves Modal Quantum logic |
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