12 research outputs found
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