Related papers: A Topos Formulation of Consistent Histories
The Two-State-Vector formalism and the Entangled Histories formalism are attempts to better understand quantum correlations in time. The main objective of this paper is to show that, with appropriately defined scalar products, both…
The Kochen-Specker theorem asserts the impossibility of assigning values to quantum quantities in a way that preserves functional relations between them. We construct a new type of valuation which is defined on all operators, and which…
Sorkin's coevents can be thought of as the `beables' of a quantum histories theory; in this paper we study the 'logical' implications of taking this claim at face value, constructing a propositional lattice for the space of coevents…
In a recent paper by the author, a new approach was suggested for quantising space-time, or space. This involved developing a procedure for quantising a system whose configuration space--or history-theory analogue--is the set of objects in…
In consistent history quantum theory, a description of the time development of a quantum system requires choosing a framework or consistent family, and then calculating probabilities for the different histories which it contains. It is…
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…
The predictions of the Bohmian and the decoherent (or consistent) histories formulations of the quantum mechanics of a closed system are compared for histories -- sequences of alternatives at a series of times. For certain kinds of…
From a logical point of view, Stone duality for Boolean algebras relates theories in classical propositional logic and their collections of models. The theories can be seen as presentations of Boolean algebras, and the collections of models…
A modification of the covariant theory is proposed in which the self-energy of the system, corresponding to time-like degrees of freedom in the configuration space, preserves the classical law of change in quantum theory. As a result,…
We pursue the view that quantum theory may be an emergent structure related to large space-time scales. In particular, we consider classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a…
The overwhelming majority of the attempts in exploring the problems related to quantum logical structures and their interpretation have been based on an underlying set-theoretic syntactic language. We propose a transition in the involved…
Over the last two decades, there has been an extensive study on logical formalisms for specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although numerous logics have…
Time-symmetric cosmological theories, in which the initial and final states are arranged to have similar features or are independently fixed, have been quite extensively discussed in the literature. However, a more general and perhaps more…
The decoherent (consistent) histories formalism has been proposed as a means of eliminating measurements as a fundamental concept in quantum mechanics. In this formalism, probabilities can be assigned to any description which satisfies a…
An analysis using classical stochastic processes is used to construct a consistent system of quantum counterfactual reasoning. When applied to a counterfactual version of Hardy's paradox, it shows that the probabilistic character of quantum…
The quantum mechanics of closed systems such as the universe is formulated using an extension of familiar probability theory that incorporates negative probabilities. Probabilities must be positive for sets of alternative histories that are…
We investigate quantum correlations in time in different approaches. We assume that temporal correlations should be treated in an even-handed manner with spatial correlations. We compare the pseudo-density matrix formalism with several…
Quantum set theory (QST) and topos quantum theory (TQT) are two long running projects in the mathematical foundations of quantum mechanics that share a great deal of conceptual and technical affinity. Most pertinently, both approaches…
Recently, several authors have criticized the time-symmetrized quantum theory originated by the work of Aharonov et al. (1964). The core of this criticism was a proof, appearing in various forms, which showed that the counterfactual…
The scope of the paper has been broadened to include a more complete discussion of the following topics: The derivation of composition laws in quantum cosmology. The connection between the existence of a composition law in the sum over…