Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2210.10635 · Scientific Reports

Nonlinear effects in Thomas precession due to the interplay of Lorentz contraction and Thomas–Wigner rotation

Antonio Di Lorenzo

Published Oct 6, 2022• 0 citations
arXivHTMLPDF

Abstract

It is demonstrated that the 3-vector [Formula: see text] currently associated to the spin in an inertial frame does not contract, but rather dilates, in the direction of the velocity. The correct vector [Formula: see text] is individuated. The equation of motion for the two vectors is shown to contain two terms, a common linear rotation, identified with Thomas precession, and also a nonlinear rotation depending on the direction of the spin itself.

DOI
10.1038/s41598-022-20942-w

Related papers

Effect of relativistic spin rotation for one- and two-particle spin states

Richard Lednicky, Vladimir Lvovich Lyuboshitz, Vladimir Lvovich Lyuboshitz

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.

arXiv:hep-ph/0311081•Nov 6, 2003•0 citations

Thomas precession and the Bacry paradox

Alexander L. Kholmetskii, O. Missevitch, Tolga Yarman

We show that in the derivation of the frequency of Thomas precession, the fact of implementation of rotation-free Lorentz transformations between a laboratory frame, KL, and Lorentz frames K(t) co-moving with a particle with spin at any time moments, t, has principal importance. Choosing for the observation of the particle’s motion any other inertial frame, K, related with KL by the rotation-free transformation, we have to realize that the transformations between K and K(t) at any t are no longer rotation-free. This way we provide a resolution of the known paradox by Bacry (H. Bacry. Nuovo Cimento, 26, 1164 (1962)) and suggest a reinterpretation of the Thomas precession, which is further discussed.

Canadian Journal of Physics•May 16, 2014•4 citations

On the difference between Wigner's and Møller's approaches to the description of Thomas precession

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.

Physics-Uspekhi•Jan 31, 2007•23 citations

Effect of the relativistic spin rotation on two-particle spin composition

Richard Lednicky, Vladimir Lvovich Lyuboshitz, Vladimir Lvovich Lyuboshitz

The effect of the relativistic spin rotation on two-particle spin states, conditioned by the setting of the spins of the particles in their rest frames and by the noncommutativity of the Lorentz transformations along noncollinear directions, is discussed. Particularly, the transition from the center-of-mass system (c.m.s.) of two spin-1∕2 particles to the laboratory is considered. When the vectors of the c.m.s. particle velocities are not collinear with the velocity vector of the c.m.s., the angles of the relativistic spin rotation for the two particles are different. As a result, the relative fractions of the singlet and triplet states in the relativistic system of two spin-1∕2 particles with a nonzero vector of relative momentum depend on the concrete frame in which the two-particle system is analyzed.

arXiv:hep-ph/0302136•Physical Review A•Mar 15, 2004•2 citations

A Method of É. Borel for calculation of the Thomas precession: The geometric phase in relativistic kinematic velocity space and its applications in optics

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.

Optics and Spectroscopy•Feb 1, 2013•0 citations

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

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.

•Apr 12, 2016•0 citations
It is demonstrated that the 3-vector [Formula: see text] currently associated to the spin in an inertial frame does not contract, but rather dilates, in the direction of the velocity. The correct vector [Formula: see text] is individuated. The equation of motion for the two vectors is shown to contain two terms, a common linear rotation, identified with Thomas precession, and also a nonlinear rotation depending on the direction of the spin itself.
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.
We show that in the derivation of the frequency of Thomas precession, the fact of implementation of rotation-free Lorentz transformations between a laboratory frame, KL, and Lorentz frames K(t) co-moving with a particle with spin at any time moments, t, has principal importance. Choosing for the observation of the particle’s motion any other inertial frame, K, related with KL by the rotation-free transformation, we have to realize that the transformations between K and K(t) at any t are no longer rotation-free. This way we provide a resolution of the known paradox by Bacry (H. Bacry. Nuovo Cimento, 26, 1164 (1962)) and suggest a reinterpretation of the Thomas precession, which is further discussed.
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.
The effect of the relativistic spin rotation on two-particle spin states, conditioned by the setting of the spins of the particles in their rest frames and by the noncommutativity of the Lorentz transformations along noncollinear directions, is discussed. Particularly, the transition from the center-of-mass system (c.m.s.) of two spin-1∕2 particles to the laboratory is considered. When the vectors of the c.m.s. particle velocities are not collinear with the velocity vector of the c.m.s., the angles of the relativistic spin rotation for the two particles are different. As a result, the relative fractions of the singlet and triplet states in the relativistic system of two spin-1∕2 particles with a nonzero vector of relative momentum depend on the concrete frame in which the two-particle system is analyzed.
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.
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.