Evolving Realities for Quantum Measure Theory

Abstract: We introduce and explore Rafael Sorkin's \textit{evolving co-event scheme}: a theoretical framework for determining completely which events do and do not happen in evolving quantum, or indeed classical, systems. The theory is observer-independent and constructed from discrete histories, making the framework a potential setting for discrete quantum cosmology and quantum gravity, as well as ordinary discrete quantum systems. The foundation of this theory is Quantum Measure Theory, which generalises (classical) measure theory to allow for quantum interference between alternative histories; and its co-event interpretation, which describes whether events can or can not occur, and in what combination, given a system and a quantum measure. In contrast to previous co-event schemes, the evolving co-event scheme is applied in stages, in the stochastic sense, without any dependence on later stages, making it manifestly compatible with an evolving block view. It is shown that the co-event realities produced by the basic evolving scheme do not depend on the inclusion or exclusion of zero measure histories in the history space, which follows non-trivially from the basic rules of the scheme. It is also shown that this evolving co-event scheme will reduce to producing classical realities when it is applied to classical systems.