  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.

Quantum Physics