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Definitions of time symmetry and examples of time-directed behaviour are discussed in the framework of discrete Markov processes. It is argued that typical examples of time-directed behaviour can be described using time-symmetric transition probabilities. Some current arguments in favour of a distinction between past and future on the basis of probabilistic… (More)

The symmetries of the wavefunction for identical particles, including anyons, are given a rigorous non-relativistic derivation within pilot-wave formulations of quantum mechanics. In particular, parastatistics are excluded. The result has a rigorous generalisation to n particles and to spinorial wavefunctions. The relation to other non-relativistic… (More)

The philosophical debate about quantum logic between the late 1960s and the early 1980s was generated mainly by Putnam’s claims that quantum mechanics empirically motivates introducing a new form of logic, that such an empirically founded quantum logic is the ‘true’ logic, and that adopting quantum logic would resolve all the paradoxes of quantum mechanics.… (More)

In de Broglie and Bohm’s pilot-wave theory, as is well known, it is possible to consider alternative particle dynamics while still preserving the |ψ| distribution. I present the analogous result for Nelson’s stochastic theory, thus characterising the most general diffusion processes that preserve the quantum equilibrium distribution, and discuss the analogy… (More)

Technical results about the time dependence of eigenvectors of reduced density operators are considered, and the relevance of these results is discussed for modal interpretations of quantum mechanics which take the corresponding eigenprojections to represent definite properties. Continuous eigenvectors can be found if degeneracies are avoided. We show that,… (More)

Nelson’s programme for a stochastic mechanics aims to derive the wave function and the Schrödinger equation from natural conditions on a diffusion process in configuration space. If successful, this programme might have some advantages over the better-known deterministic pilot-wave theory of de Broglie and Bohm. The essential points of Nelson’s strategy are… (More)

I discuss the interpretation of spontaneous collapse theories, with particular reference to Bell’s suggestion that the stochastic jumps in the evolution of the wave function should be considered as local beables of the theory. I develop this analogy in some detail for the case of non-relativistic GRW-type theories, using a generalisation of Bell’s notion of… (More)

Putnam gives a strongly realist account of quantum logic. This has been criticised as suggesting a hidden variable interpretation for quantum mechanics. Friedman and Glymour have done this in the framework of noncontextual hidden variable theories, which, however, does not fully represent Putnam's ideas. Here Putnam's approach to quantum logic is understood… (More)

I review the formalism of classical extensions of quantum mechanics introduced by Beltrametti and Bugajski, and compare it to the classical representations discussed e.g. by Busch, Hellwig and Stulpe and recently used by Fuchs in his discussion of quantum mechanics in terms of standard quantummeasurements. I treat the problem of finding Bayesian analogues… (More)

This paper relates both to the metaphysics of probability and to the physics of time asymmetry. Using the formalism of decoherent histories, it investigates whether intuitions about intrinsic time directedness that are often associated with probability can be justified in the context of no-collapse approaches to quantum mechanics. The standard (two-vector)… (More)