# 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.