Quantum Measure Theory: A New Interpretation

Quantum measure theory can be introduced as a histories based reformulation (and generalisation) of Copenhagen quantum mechanics in the image of classical stochastic theories. These classical models lend themselves to a simple interpretation in which a single history (a single element of the sample space) is deemed to be 'real'; we require only that this real history should not be ruled out by the dynamics, the axioms of which ensure that not all histories are precluded. However, applying this interpretation naively to quantum measure theory we can find experimentally realisable systems (notably the Peres-Kochen-Specker system) in which every history is ruled out by the dynamics, challenging us to formulate a deeper realist framework. Our first response is to hold on to our existing interpretative framework and attempt a revision of the dynamics that would reduce quantum measure theory to a classical dynamics. We explore this approach by examining the histories formulation of a stochastic-collapse model on a simple (discrete) null-lattice, concluding that the drawbacks of this approach outweigh the benefits. Our second response is to abandon our classically inspired interpretation in favour of Sorkin's 'co-events', a more general ontology that still allows for strict realism. In this case the 'potentially real' objects of the theory (the 'beables' in Bell's language) are not individual histories but truth valuation maps, or co-events. We develop & evaluate various co-event schemes that have been suggested to date, finally adopting the multiplicative scheme; the current working model of co-event theory and a promising interpretation of quantum measure theory, though still a work in progress. We conclude by exploring the expression of the dynamics & predictions in this new framework.Comment: Thesis, 155 page

Dynamical Wave Function Collapse Models in Quantum Measure Theory

The structure of Collapse Models is investigated in the framework of Quantum Measure Theory, a histories-based approach to quantum mechanics. The underlying structure of coupled classical and quantum systems is elucidated in this approach which puts both systems on a spacetime footing. The nature of the coupling is exposed: the classical histories have no dynamics of their own but are simply tied, more or less closely, to the quantum histories.Comment: 20 pages, 1 figure. Revised after refereein

Dynamics & Predictions in the Co-Event Interpretation

Sorkin has introduced a new, observer independent, interpretation of quantum mechanics that can give a successful realist account of the 'quantum microworld' as well as explaining how classicality emerges at the level of observable events for a range of systems including single time 'Copenhagen measurements'. This 'co-event interpretation' presents us with a new ontology, in which a single 'co-event' is real. A new ontology necessitates a review of the dynamical & predictive mechanism of a theory, and in this paper we begin the process by exploring means of expressing the dynamical and predictive content of histories theories in terms of co-events.Comment: 35 pages. Revised after refereein

Twistor form of massive 6D superparticle

The massive six-dimensional (6D) superparticle with manifest (n, 0) supersymmetry is shown to have a supertwistor formulation in which its “hidden” (0, n) supersymmetry is also manifest. The mass-shell constraint is replaced by Spin(5) spin-shell constraints which imply that the quantum superparticle has zero superspin; for n = 1 it propagates the 6D Proca supermultiplet.PKT acknowledges support from the UK Science and Technology Facilities Council (grant ST/L000385/1). AJR is supported by a grant from the London Mathematical Society.This is the final version of the article. It was first available from IOP Science via http://dx.doi.org/10.1088/1751-8113/49/2/02540

The Kochen-Specker Theorem Revisited in Quantum Measure Theory

The Kochen-Specker Theorem is widely interpreted to imply that non-contextual hidden variable theories that agree with the predictions of Copenhagen quantum mechanics are impossible. The import of the theorem for a novel observer independent interpretation of quantum mechanics, due to Sorkin, is investigated.Comment: 17 pages. Revised after refereein