PhD students of Steve Vickers: Guillaume Raynaud

Guillaume Raynaud completed his PhD thesis "Fibred Contextual Quantum Physics" in 2014 at the School of Computer Science, University of Birmingham, under my supervision.

ABSTRACT

"Fibred Contextual Quantum Physics"

PhD Thesis, School of Computer Science, University of Birmingham, 2014. 137 pages.

Summary

Inspired by the recast of the quantum mechanics in a toposical framework, we develop a contextual quantum mechanics using only the geometric mathematics to propose a quantum contextuality adaptable in every topos. The contextuality adopted here corresponds to the belief that the quantum world must only be seen from the classical viewpoints à la Bohr and consequently putting forth the notion of a context, while retaining a realist understanding. Mathematically, the cardinal object is a spectral Stone bundle $\Sigma \rightarrow \mathcal{B}$ (between stablycompact locales) permitting a treatment of the kinematics, fibre by fibre and fully point-free. In leading naturally to a new notion of point, the geometricity permits to understand those of the base space $\mathcal{B}$ as the contexts $C$ - the commutative C*-algebras of a incommutative C*-algebra - and those of the spectral locale $\Sigma$ as the couples $(C,\psi)$, with $\psi$ 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 $\mathcal{B}$ and $\Sigma$ 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.