Wilce, Alexander
(2019)
Dynamical states and the conventionality of (non-) classicality.
[Preprint]
Abstract
Itamar Pitowsky long championed the view that quantum mechanics (QM) is best understood as a non-classical probability theory. Here, I want to offer some modest caveats. One is that QM is best seen, not as a new probability theory, but as something narrower, namely, a particular probabilistic theory --- roughly, a class of probabilistic models, selected from within a much more general framework. It is this general framework that, if anything, deserves to be regarded as a ``non-classical" probability theory. However, as I will also argue, this framework represents a very conservative extension of classical probability theory, essentially just eliding a tacit, and contingent, assumption in the latter that measurements or experiments can always be performed together. Moreover, for individual probabilistic models, and even for probabilistic theories, the distinction between ``classical" and a ``non-classical" is largely a conventional one, bound up with the question of what one means by the state of a system. In fact, for systems with a high degree of symmetry, including quantum mechanics, it is possible to interpret general probabilistic models as having a perfectly classical probabilistic structure, but an additional dynamical structure: states, rather than corresponding simply to probability measures, are represented as certain probability measure-valued functions on the system's symmetry group, and thus, as fundamentally dynamical objects. Conversely, a classical probability space equipped with reasonably well-behaved family of such ``dynamical states" can be interpreted as a generalized probabilistic model in a canonical way. It is noteworthy that this ``dynamical" representation is not a conventional hidden-variables representation, and the question of what one means by ``non-locality" in this setting is not entirely straightforward.
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