Review of Stochastic Mechanics

Department of Mathematics
Princeton University

Stochastic mechanics is a theory that pictures non-relativistic quantum mechanics in terms of classical Markov processes on configuration space. It is described in two of my books, "Dynamical Theories of Brownian Motion" (1967) and "Quantum Fluctuations" (1985), both published by Princeton University Press and available at http://math.princeton.edu/~nelson/books.html, and in many papers by mathematicians and physicists, primarily in Italy and the United States, cited in the references to the second book.
I shall describe various successes of the theory, and two failures that prevent it from being considered as a theory of quantum mechanics as an emergent phenomenon.
Computations in quantum mechanics are notoriously difficult on a classical computer. The talk concludes with some considerations of the possibility of using stochastic mechanics as a computational device on a classical computer with randomization.