Narrow Results

Although for some nonlocal variables the standard quantum measurements which are reliable, instantaneous, and nondemolition, are impossible, demolition reliable instantaneous measurements of all variables are possible. It is shown that this is correct also in the framework of the time-symmetric quantum formalism, i.e. nonlocal variables of composite quantum systems with quantum states evolving both forward and backward in time are measurable in a demolition way. The result follows from the possibility to reverse with certainty the time direction of backward evolving quantum states.

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.