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

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-$1\mathrm{/}2$ 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.