Fibred contextual quantum physics

Raynaud, Guillaume (2014). Fibred contextual quantum physics. University of Birmingham. Ph.D.

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Abstract

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.

Type of Work:

Thesis (Doctorates > Ph.D.)

Award Type:

Doctorates > Ph.D.

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