Bacciagaluppi, Guido A Conceptual Introduction to Nelson’s Mechanics. World Scientific, Singapore.
Nelson’s programme for a stochastic mechanics aims to derive the
wave function and the Schroedinger equation from natural conditions
on a diffusion process in configuration space. If successful, this pro-
gramme might have some advantages over the better-known determin-
istic pilot-wave theory of de Broglie and Bohm. The essential points
of Nelson’s strategy are reviewed, with particular emphasis on concep-
tual issues relating to the role of time symmetry. The main problem
in Nelson’s approach is the lack of strict equivalence between the cou-
pled Madelung equations and the Schroedinger equation. After a brief
discussion, the paper concludes with a possible suggestion for trying to overcome this problem.
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