The Stochastic-Quantum Correspondence

• URL: http://arxiv.org/abs/2302.10778v3
• Date: Wed, 30 Jul 2025 04:34:14 GMT
• Title: The Stochastic-Quantum Correspondence
• Authors: Jacob A. Barandes,
• Abstract summary: This paper argues that every quantum system can be understood as a sufficiently general kind of unfolding process in an old-fashioned configuration space according to ordinary notions of probability.<n>At a more practical level, the quasi-quantum correspondence leads to a novel reconstruction of quantum theory, alongside the Hilbert-space, path-integral, andprobability representations, and also provides a framework for using Hilbert-space methods to formulate highly generic, non-Markovian types of dynamics.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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