The theory of stochastic processes describes the phenomenological behavior of systems with definite configurations that evolve probabilistically in time. Quantum theory is a comprehensive mathematical apparatus for making measurement predictions when taking into account the microscopic constituents of various kinds of physical systems, from subatomic particles to superconductors. At an empirical level, both theories involve probabilities, and at the level of formalism, both employ vectors and matrices.
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There have been a number of previous attempts in the research literature to identify a fundamental relationship connecting stochastic process theory and quantum theory [1–7]. The most well-known of these approaches are due to Bopp [8–10], Fényes [11], and Nelson [12, 13]. Altogether different are stochastic-collapse models [14, 15], in which a quantum system’s wave function or density matrix is assumed to experience stochastic fluctuations through time.
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There have been a number of previous attempts in the research literature to identify a fundamental relationship connecting stochastic-process theory and quantum theory [1–7]. The most well-known of these approaches are due to Bopp [8–10], Fényes [11], and Nelson [12, 13]. Altogether different are stochastic-collapse models [14, 15], in which a quantum system’s wave function or density
matrix is assumed to experience stochastic fluctuations through time.