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arXiv:1604.03389 · Physics Letters A

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

Veiko Palge, Jacob Dunningham, Yuji Hasegawa, Christian Pfeifer

Published Mar 30, 2025• 0 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2025.130490

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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 examine the behaviour of the maximally entangled Bell state of two spin 1 massive particles under relativistic transformations. On the basis of explicit calculations of the Wigner rotation and the use of transformation properties of Dirac spinors, we establish that the constituent particles of the Bell state undergo momentum dependent rotation of the spin orientations characterized by the Wigner angle φW = tan −1 sinhsinh τ cosh � +cosh τ . However, since local unitarity is retained in the process, the corresponding entanglement fidelity is not lost. c
Abstract: We examine the behaviour of the maximally entangled Bell state of two spin 12 massive particles under relativistic transformations. On the basis of explicit calculations of the Wigner rotation and the use of transformation properties of Dirac spinors, we establish that the constituent particles of the Bell state undergo momentum dependent rotation of the spin orientations characterized by the Wigner angle φW = tan−1 sinh sinh τcosh+cosh τ. However, since local unitarity is retained in the process, the corresponding entanglement fidelity is not lost.