How to measure the momentum of single quanta

TL;DR

This paper reviews how momentum of single quantum particles is measured in practice, highlighting the limitations of traditional measurement theory and proposing improvements in teaching based on real experimental methods.

Contribution

It critically examines real momentum measurement experiments and suggests ways to better teach quantum measurement concepts through practical examples.

Findings

Most momentum measurements involve position inference.

Traditional von Neumann measurement theory does not fully apply.

Improved teaching methods based on real experiments are proposed.

Abstract

The von Neumann theory of measurement, based on an entanglement of the quantum observable with a classical machine followed by decoherence or collapse, does not readily apply to most measurements of momentum. Indeed, how we measure the momentum of a quantum particle is not even discussed in most quantum mechanics textbooks. Instead, we often teach the lore that position and momentum cannot be measured at the same time. Yet, most ways to measure momentum actually involve measuring position to infer momentum. In this tutorial review, I examine real experiments that measure momentum and describe how one can improve our teaching of the theory of measurement when we focus on real experiments, rather than abstract mathematical models of measurement.