Weak measurement and the traversal time problem

Abstract

The theory of weak measurement, proposed by Aharonov and coworkers, has been applied by Steinberg to the long-discussed traversal time problem. The uncertainty and ambiguity that characterize this concept from the perspective of von Neumann measurement theory apparently vanish, and joint probabilities and conditional averages become meaningful concepts. We express the Larmor clock and some other well-known methods in the weak measurement formalism. We also propose a method to determine higher moments of the traversal time distribution in terms of the outcome of a gedanken experiment, by introducing an appropriate operator. Since the weak measurement approach can sometimes lead to unphysical results, for example average negative reflection times and higher moments, the interpretation of the results obtained remains an open problem.