Thomas-Wigner rotation and Thomas precession: Actualized approach (original) (raw)

Elementary analysis of the special relativistic combination of velocities, Wigner rotation and Thomas precession

European Journal of Physics, 2011

The purpose of this paper is to provide an elementary introduction to the qualitative and quantitative results of velocity combination in special relativity, including the Wigner rotation and Thomas precession. We utilize only the most familiar tools of special relativity, in arguments presented at three differing levels: (1) utterly elementary, which will suit a first course in relativity; (2) intermediate, to suit a second course; and (3) advanced, to suit higher level students. We then give a summary of useful results, and suggest further reading in this often obscure field.

Relativistic velocity space, Wigner rotation, and Thomas precession

American Journal of Physics, 2004

We develop a relativistic velocity space called rapidity space from the single assumption of Lorentz invariance, and use it to visualize and calculate effects resulting from the successive application of non-collinear Lorentz boosts. In particular, we show how rapidity space provides a geometric approach to Wigner rotation and Thomas precession in the same way that space-time provides a geometrical approach to kinematic effects in special relativity.

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

Scientific Reports

It is demonstrated that the 3-vector \varvec{S}Scurrentlyassociatedtothespininaninertialframedoesnotcontract,butratherdilates,inthedirectionofthevelocity.ThecorrectvectorS currently associated to the spin in an inertial frame does not contract, but rather dilates, in the direction of the velocity. The correct vectorScurrentlyassociatedtothespininaninertialframedoesnotcontract,butratherdilates,inthedirectionofthevelocity.Thecorrectvector\varvec{T}$$ T 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.

Thomas Precession in Spacetime Geometries

The authors of a recently published paper (Sonego S and Pin M 2005 Eur. J. Phys. 26 851-6) have erroneously asserted that Einstein's velocity addition law is associative. Moreover, they have attributed the alleged associativity of Einstein's velocity addition law to 'The relativity principle[, which] requires that [Einstein's velocity addition] gives the composition law of a group'. Accordingly, we note that Einstein's velocity addition is non-associative and demonstrate that the breakdown of associativity and commutativity in Einstein's velocity addition law results from the presence of Thomas precession.

The relativistic velocity composition paradox and the Thomas rotation

Foundations of Physics, 1989

The relativistie velocity composition paradox of Moeanu and its resolution are presented. The paradox, which rests on the bizarre and counterintuitive noncommutativity of the relativistic velocity composition operation, when applied to noncollinear admissible velocities, led Mocanu to claim that there are "some difficulties within the framework of relativistic electrodynamics. "' The paradox is resolved in this article by means of the Thomas rotation, shedding light on the role played by composite velocities in special relativity, as opposed to the role they play in Galilean relativity.

Does Thomas-Wigner rotation show the fallacy of " Lorentz rotation "

As a result of the composition of non-collinear relativistic velocities, apart from the resultant velocity, a component of turn is obtained which is called the Thomas-Wigner rotation. The paper discusses the Lorentz transformation using the paravector calculus. It has been shown that any " Lorentz rotation " is a combination of real velocity and a Euclidean rotation, and that as a result of the composition of appropriately selected velocities any object can rotate in place, which may indicate the fallacy of the idea of the " Lorentz rotation " .

Thomas rotation and Thomas precession

2005

Exact and simple calculation of Thomas rotation and Thomas precessions along a circular world line is presented in an absolute (coordinatefree) formulation of special relativity. Besides the simplicity of calculations the absolute treatment of spacetime allows us to gain a deeper insight into the phenomena of Thomas rotation and Thomas precession.

The Thomas Precession and the Transformation to Rotating Frames

2002

The Thomas precession is calculated using three different transformations to the rotating frame. It is shown that for sufficiently large values of v/c, important differences in the predicted angle of precession appear, depending on the transformation used. For smaller values of v/c these differences might be measured by extending the time of observation.

Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession

Springer eBooks, 2002

To my Mother Chayah Sarah and to the memory of my Father Chayim Yehudah and to my Son Ofer for their love and support, and to Rabbi Yom-Tov Lipman-Heler ben Nathan Halevy, Ba'al Hatosafot Yom-Tov, born in 1579 in the city of Valershtein, Bavaria, and died in 1654 in the city of krakow, Galitzia, who was the first known mathematician in the author's family tree. This book is dedicated to: (i) Llewellyn H. Thomas (1902-1992); and (ii) the development of greater understanding of the central role that the Thomas gyration plays in relativity physics, in nonassociative algebra, in non-Euclidean geometry and, particularly, in the theory of gyrogroups and gyrovector spaces.