Schroedinger-picture correlation functions for nonlinear evolutions

Abstract

The well known interpretational difficulties with nonlinear Schrödinger and von Neumann equations can be reduced to the problem of computing multiple-time correlation functions in the absence of Heisenberg picture. Having no Heisenberg picture one often resorts to Zeno-type reasoning which explicitly involves the projection postulate as a means of computing conditional and joint probabilities. Although the method works well in linear quantum mechanics, it completely fails for nonlinear evolutions. We propose an alternative way of performing the same task in linear quantum mechanics and show that the method smoothly extends to the nonlinear domain. The trick is to use appropriate time-dependent Hamiltonians which involve "switching-off functions". We apply the technique to the EPR problem in nonlinear quantum mechanics and show that paradoxes of Gisin and Polchinski disappear.