Proposal for an experiment to verify Wigner's rotation at non-relativistic speeds with massive spin-$1/2$ particles

TL;DR

This paper proposes a feasible experiment using cold neutrons to verify Wigner's rotation at non-relativistic speeds, highlighting its cumulative nature and potential for laboratory testing.

Contribution

It introduces a novel experimental approach to observe Wigner's rotation at low velocities, which was previously thought to require relativistic speeds.

Findings

Wigner rotation can be observed at velocities around 10^3 m/s.

Long propagation times enable detection of cumulative Wigner rotation effects.

The experiment is feasible with current cold neutron technology.

Abstract

The Wigner rotation of quantum particles with spin is one of the fascinating consequences of interplay between special relativity and quantum mechanics. In this paper we show that a direct experimental verification of Wigner's rotation is in principle accessible in the regime of non-relativistic velocities at $\sim 10^3$ m/s for massive spin-$1/2$ particles. We discuss how the experiment could be carried out in a laboratory using cold neutrons. The measurement at non-relativistic velocities becomes possible through letting neutrons propagate for a sufficiently long time because Wigner rotation is a cumulative effect.