Weak measurement and the traversal time problem

TL;DR

This paper explores how weak measurement theory can address the traversal time problem in quantum mechanics, clarifying ambiguities and proposing methods to determine higher moments, while discussing interpretational challenges.

Contribution

It applies weak measurement formalism to the traversal time problem, expressing known methods within this framework and proposing a new approach to measure higher moments of traversal time.

Findings

Weak measurement clarifies traversal time ambiguities

Expresses Larmor clock in weak measurement formalism

Proposes method for higher moments of traversal time

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.