Fibred contextual quantum physics

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http://eprints.org/relation/isVersionOf http://etheses.bham.ac.uk/id/document/37342 http://eprints.org/relation/isVolatileVersionOf http://etheses.bham.ac.uk/id/document/37342 http://eprints.org/relation/isIndexCodesVersionOf http://etheses.bham.ac.uk/id/document/37342 archive 4031 disk0/00/00/16/85 2014-07-02 09:59:26 2019-01-23 09:54:39 2014-07-02 09:59:26 thesis show 0 Raynaud Guillaume Vickers Steven University of Birmingham Fibred contextual quantum physics unpub QA75 QC 10col_ephy Inspired by the recast of the quantum mechanics in a toposical framework, we develop a contextual quantum mechanics via the geometric mathematics to propose a quantum contextuality adaptable in every topos. The contextuality adopted corresponds to the belief that the quantum world must only be seen from the classical viewpoints à la Bohr consequently putting forth the notion of a context, while retaining a realist understanding. Mathematically, the cardinal object is a spectral Stone bundle Σ → B (between stably-compact locales) permitting a treatment of the kinematics, fibre by fibre and fully point-free. In leading naturally to a new notion of points, the geometricity permits to understand those of the base space B as the contexts C — the commutative C*–algebras of a incommutative C*–algebras — and those of the spectral locale Σ as the couples (C, ψ), with ψ a state of the system from the perspective of such a C. The contexts are furnished with a natural order, the aggregation order which is installed as the specialization on B and Σ thanks to (one part of) the Priestley's duality adapted geometrically as well as to the effectuality of the lax descent of the Stone bundles along the perfect maps. 2014-07 2014 graduation eng author This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder. public University of Birmingham School of Computer Science d_ph na 2014-07 graduation