Relativistic Velocity Space, Wigner Rotation and Thomas Precession

Alexander L. Kholmetskii, Tolga Yarman

Constantin I. Mocanu

Grigorii B. Malykin

In 1913, É. Borel (1871–1956) considered the relativistic kinematic rotation of a body that arises in the course of its orbital motion. In order to determine the angular velocity of this rotation, Borel introduced the notion of a kinematic space and applied the Gauss-Bonnet formula for a sphere of a unit radius. However, at that time, his results did not find practical applications and, soon, were forgotten. After the discovery of electron spin by S.A. Goudsmit and G.E. Uhlenbeck in 1925, real interest in this phenomenon was rekindled, and it was considered once again by L.H. Thomas in 1926–1927, being termed the Thomas precession. The Thomas precession manifests itself mostly in optical phenomena.

V. I. Ritus

An account is given of the Wigner concept of particle spin and velocity rotations and of the variation of the angle between them under Lorentz transformations with noncollinear velocities. It is shown that Moller's description of spin rotation can be reduced to the Wigner rotation, and Moller's formula for the angle of spin rotation in the curvilinear motion of a particle is corrected. The permutation asymmetry of the relativistic velocity addition law distinguishes the Wigner sequence of Lorentzian boosts by its applicability to the description of spin and velocity rotations in curvilinear motion.

Veiko Palge, Jacob Dunningham, Yuji Hasegawa

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.

Joseph Shaffer