a Conceptual Introduction to Nelson's Mechanics

Nelson's programme for a stochastic mechanics aims to derive the wave function and the Schrödinger equation from natural conditions on a diffusion process in configuration space. If successful, this programme has some potential advantages, which are briefly sketched, over the better-known deterministic pilot-wave theory of de Broglie and Bohm. The essential points of Nelson's strategy are then reviewed, with particular emphasis on conceptual issues relating to the role of time symmetry. The main problem in Nelson's approach is the lack of strict equivalence between the coupled Madelung equations and the Schrödinger equation. After a brief discussion, the paper concludes with a sketch of two possible strategies for trying to overcome this problem.