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Proposal for verifying Wigner's rotation with massive spin-$1/2$ particles at non-relativistic speeds

Veiko Palge, Jacob Dunningham, Yuji Hasegawa

Published Apr 12, 2016• 0 citations
OpenAlex

Abstract

In quantum physics Wigner's rotation is commonly regarded as confirmed by the Thomas precession in a hydrogen like atom. 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 $2 \cdot 10^3\,$m/s and propose an experiment using thermal neutrons. The experiment can be carried out in a laboratory and it provides a test of relativity in the quantum domain.

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Proposal for verifying Wigner's rotation with massive spin-1/21/21/2 particles at non-relativistic speeds
In quantum physics Wigner's rotation is commonly regarded as confirmed by the Thomas precession in a hydrogen like atom. 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 2⋅103 2 \cdot 10^3\,2⋅103m/s and propose an experiment using thermal neutrons. The experiment can be carried out in a laboratory and it provides a test of relativity in the quantum domain.
We present a new treatment for the spin of a massive relativistic particle in the context of quantum information based on a physical interpretation of the Wigner rotations, obtaining different results in relation to previous works. We are led to the conclusion that it is not possible to define a reduced density matrix for the particle spin and that the Pauli–Lubanski (or similar) spin operators are not suitable for describing measurements where the spin couples to an electromagnetic field in the measuring apparatus. These conclusions contradict the assumptions made by most of the previous papers on the subject. We also propose an experimental test of our formulation.
A still widely debated question in the field of relativistic quantum information is whether entanglement and the degree of violation of Bell's inequalities for massive relativistic particles are frame independent or not. At the core of this question is the effect that spin gets entangled with the momentum degree of freedom at relativistic velocities. Here, we show that Bell's inequalities for a pair of particles can be maximally violated in a special-relativistic regime, even without any postselection of the momentum of the particles. To this end, we use the methodology of quantum reference frames, which allows us to transform the problem to the rest frame of a particle, whose state can be in a superposition of relativistic momenta from the viewpoint of the laboratory frame. We show that, when the relative motion of two particles is noncollinear, the optimal measurements for violation of Bell's inequalities in the laboratory frame involve "coherent Wigner rotations." Moreover, the degree of violation of Bell's inequalities is independent of the choice of the quantum reference frame. Our results open up the possibility of extending entanglement-based quantum communication protocols to relativistic regimes.
Experimental tests of Bell-type inequalities distinguishing between quantum mechanics and local realistic theories remain of considerable interest if performed on massive particles, for which no conclusive result has yet been obtained. Only two-particle experiments may specifically test the concept of spatial nonlocality in quantum theory, whereas single-particle experiments may generally test the concept of quantum noncontextuality. Here we have performed the first Bell-type experiment with a beam of thermal-neutron pairs in the singlet state of spin, as originally suggested by J. S. Bell. These measurements confirm the quantum-theoretical predictions, in agreement with the results of the well-known polarization experiments carried out on optical photons years ago.
The effect of the relativistic spin rotation, conditioned by the setting of the spin in the rest frame of a particle and by the noncommutativity of the Lorentz transformations along noncolinear directions, is discussed. In connection with this, the Thomas precession of the spin polarization vector at the motion of a particle along a curvilinear trajectory is considered. The transformations of the correlation tensor components for a system of two spin-1/2 particles at the transition from the c.m.s. of the particle pair to the laboratory frame are investigated. When the particle laboratory velocities are not colinear, the relativistic spin rotation angles for these particles are different. As a result, the relative fractions of the singlet and triplet states in the relativistic system of two free spin-1/2 particles with a nonzero vector of relative momentum depend on the concrete frame in which this two-particle system is analyzed.