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In this work we build a quantum logic that allows us to refer to physical magnitudespertaining to different contexts from a fixed one without the contradictionswith quantum mechanics expressed in no-go theorems. This logic arises from consideringa sheaf over a topological space associated with the Boolean sublattices ofthe ortholattice of closed subspaces of the Hilbert space of the physical system.Different from standard quantum logics, the contextual logic maintains a distributivelattice structure and a good definition of implication as a residue of theconjunction
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JOURNAL OF MATHEMATICAL PHYSICS 46, 012102 (2005)
Contextual logic for quantum systems Graciela Domenecha) Instituto de Astronomía y Física del Espacio (IAFE), Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires, Argentina
Hector Freytesb) Escuela de Filosofía - Universidad Nacional de Rosario, Entre Ríos 758, 2000, Rosario, Argentina (Received 21 May 2004; accepted 20 September 2004; published online 27 December 2004)
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. [DOI: 10.1063/1.1819525]
I. INTRODUCTION
Quantum mechanics has profound conceptual difficulties that may be posed in several ways. Nonetheless, almost every problem in the relation between the mathematical formalism and what may b