On the Weak Measurement of Velocity in Bohmian Mechanics

TL;DR

This paper discusses the use of weak measurements to determine particle velocity in Bohmian mechanics, arguing that such measurements can indeed be considered genuine within this framework despite prior claims of non-measurability.

Contribution

It clarifies how weak measurements can serve as genuine velocity measurements in Bohmian mechanics, resolving apparent contradictions with previous non-measurability results.

Findings

Weak measurements can measure Bohmian velocity.

The paper reconciles measurement concepts in Bohmian mechanics.

It clarifies the role of weak measurements in quantum theory.

Abstract

In a recent article (New Journal of Physics 9, 165, 2007), Wiseman has proposed the use of so-called weak measurements for the determination of the velocity of a quantum particle at a given position, and has shown that according to quantum mechanics the result of such a procedure is the Bohmian velocity of the particle. Although Bohmian mechanics is empirically equivalent to variants based on velocity formulas different from the Bohmian one, and although it has been proven that the velocity in Bohmian mechanics is not measurable, we argue here for the somewhat paradoxical conclusion that Wiseman's weak measurement procedure indeed constitutes a genuine measurement of velocity in Bohmian mechanics. We reconcile the apparent contradictions and elaborate on some of the different senses of measurement at play here.