I offer a response to the explanatory challenge, 'Why is time Markovian?' (i.e., why is it that the future is constrained by the present just as strictly as it is constrained by the entire history of the universe up to and including the present?). My response to this explanatory challenge does not rely on any claims about the ontology of time, undermining a recent empirical argument for Presentism which appeals to the fact that Presentism can be used to address (...) this explanatory challenge. My account shows that we can accept explanatory challenges of this sort, while denying that they lead to any strong metaphysical conclusions. (shrink)

The impossibility of an indeterministic evolution for standard relativistic quantum field theories, that is, theories in which all fields satisfy the condition that the generators of space-time translation have spectra in the forward light-cone, is demonstrated. The demonstration proceeds by arguing that a relativistically invariant theory must have a stable vacuum and then showing that stability of the vacuum, together with the requirements imposed by relativistic causality, entails deterministic evolution, if all degrees of freedom are standard degrees of freedom.

The development of causal modelling since the 1950s has been accompanied by a number of controversies, the most striking of which concerns the Markov condition. Reichenbach's conjunctive forks did satisfy the Markov condition, while Salmon's interactive forks did not. Subsequently some experts in the field have argued that adequate causal models should always satisfy the Markov condition, while others have claimed that non-Markovian causal models are needed in some cases. This paper argues for the second position by considering the (...) multi-causal forks, which are widespread in contemporary medicine (Section 2). A non-Markovian causal model for such forks is introduced and shown to be mathematically tractable (Sections 6, 7, and 8). The paper also gives a general discussion of the controversy about the Markov condition (Section 1), and of the related controversy about probabilistic causality (Sections 3, 4, and 5). (shrink)

This paper introduces an exact correspondence between a general class of stochastic systems and quantum theory. This correspondence provides a new framework for using Hilbert-space methods to formulate highly generic, non-Markovian types of stochastic dynamics, with potential applications throughout the sciences. This paper also uses the correspondence in the other direction to reconstruct quantum theory from physical models that consist of trajectories in configuration spaces undergoing stochastic dynamics. The correspondence thereby yields a new formulation of quantum theory, alongside the (...) Hilbert-space, path-integral, and quasiprobability formulations. In addition, this reconstruction approach opens up new ways of understanding quantum phenomena like interference, decoherence, entanglement, noncommutative observables, and wave-function collapse. (shrink)

This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called generalized stochastic systems, collectively encompass many important kinds of stochastic processes, including Markov chains and random dynamical systems. This paper then states and proves a new theorem that establishes a precise correspondence between any generalized stochastic system and a unitarily evolving quantum system. This theorem therefore leads to a new formulation of (...) quantum theory, alongside the Hilbert-space, path-integral, and quasiprobability formulations. The theorem also provides a first-principles explanation for why quantum systems are based on the complex numbers, Hilbert spaces, linear-unitary time evolution, and the Born rule. In addition, the theorem suggests that by selecting a suitable Hilbert space, together with an appropriate choice of unitary evolution, one can simulate any generalized stochastic system on a quantum computer, thereby potentially opening up an extensive set of novel applications for quantum computing. (shrink)

It is difficult to extract reliable criteria for causal locality from the limited ingredients found in textbook quantum theory. In the end, Bell humbly warned that his eponymous theorem was based on criteria that “should be viewed with the utmost suspicion.” Remarkably, by stepping outside the wave-function paradigm, one can reformulate quantum theory in terms of old-fashioned configuration spaces together with ‘unistochastic’ laws. These unistochastic laws take the form of directed conditional probabilities, which turn out to provide a hospitable foundation (...) for encoding microphysical causal relationships. This unistochastic reformulation provides quantum theory with a simpler and more transparent axiomatic foundation, plausibly resolves the measurement problem, and deflates various exotic claims about superposition, interference, and entanglement. Making use of this reformulation, this paper introduces a new principle of causal locality that is intended to improve on Bell's criteria, and shows directly that systems that remain at spacelike separation cannot exert causal influences on each other, according to that new principle. These results therefore lead to a general hidden-variables interpretation of quantum theory that is arguably compatible with causal locality. (shrink)