The Stochastic-Quantum Correspondence

Jacob A. Barandes

doi:10.31389/pop.186

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arXiv · 2302.10778

The Stochastic-Quantum Correspondence

Jacob A. Barandes

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Abstract

This paper argues that every quantum system can be understood as a sufficiently general kind of stochastic process unfolding in an old-fashioned configuration space according to ordinary notions of probability. This argument is based on an exact correspondence between the class of `indivisible' stochastic processes and quantum theory. This new stochastic-quantum correspondence demotes the wave function from a primary ontological ingredient to a secondary mathematical tool, and yields a deflationary account of exotic quantum phenomena, such as interference, decoherence, entanglement, noncommutative observables, and wave-function collapse. At a more practical level, the stochastic-quantum correspondence leads to a novel reconstruction of quantum theory, alongside the Hilbert-space, path-integral, and quasiprobability representations, and also provides a framework for using Hilbert-space methods to formulate highly generic, non-Markovian types of stochastic dynamics, with potential applications throughout the sciences.

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Jacob A. Barandes. 2023-02-20. The Stochastic-Quantum Correspondence. https://doi.org/10.31389/pop.186

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