Elementary analysis of the special relativistic combination of velocities, Wigner rotation and Thomas precession (original) (raw)
Related papers
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.
Thomas-Wigner rotation and Thomas precession: Actualized approach
Thomas-Wigner rotation and Thomas precession: Actualized approach, 2014
We show that the explanation of Thomas-Wigner rotation (TWR) and Thomas precession (TP) in the framework of special theory of relativity (STR) contains a number of points of inconsistency, in particular, with respect to physical interpretation of the Einstein velocity composition law in successive space-time transformations. In addition, we show that the common interpretation of TP falls into conflict with the causality principle. In order to eliminate such a conflict, we suggest considering the velocity parameter, entering into expression for the frequency of TP, as being always related to a rotation-free Lorentz transformation. Such an assumption (which actually resolves any causal paradoxes with respect to TP), comes however to be in contradiction with the spirit of STR. The results obtained are discussed.
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.
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.
Alternative realization for the composition of relativistic velocities
The Nature of Light: What are Photons? IV, 2011
The reciprocity principle requests that if an observer, say in the laboratory, sees an event with a given velocity, another observer at rest with the event must see the laboratory observer with minus the same velocity. The composition of velocities in the Lorentz-Einstein scheme does not fulfill the reciprocity principle because the composition rule is neither commutative nor associative. In other words, the composition of two non-collinear Lorentz boosts cannot be expressed as a single Lorentz boost but requires in addition a rotation. The Thomas precession is a consequence of this composition procedure. Different proposals such as gyro-groups have been made to fulfill the reciprocity principle.
Classical Mechanics, Second Edition, 2013
Special Relativity is taught to physics sophomores at Johns Hopkins University in a series of eight lectures. Lecture 1 covers the principle of relativity and the derivation of the Lorentz transform. Lecture 2 covers length contraction and time dilation. Lecture 3 covers Minkowski diagrams, simultaneous events and causally connected events, as well as velocity transforms. Lecture 4 covers energy and momentum of particles and introduces 4-vectors. Lecture 5 covers energy and momentum of photons and collision problems. Lecture 6 covers Doppler effect and aberration. Lecture 7 covers relativistic dynamics. Optional Lecture 8 covers field transforms. The main purpose of these notes is to introduce 4-vectors and the matrix notation and to demonstrate their use in solving standard problems in Special Relativity. The prerequisites for the class are calculus-based Classical Mechanics and Electricity & Magnetism, and Linear Algebra is highly recommended.
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.
A Brief Review of Special Relativity
International Journal of Theoretical and Mathematical Physics, 2019
This review is dedicated to those which already have understood special relativity (SR), but designated to these which still have not. From the kinematical context and EM pretext, as the starting bases, the simplest methodology of the initial constitution of SR is here presented. Some inconsistencies of the adopted premises, applied procedures and thus obtained results are clearly pointed at. Apart from the alleged dependence of the relative time on the mutual motion of the two frames, it would also depend on the object position, determined in its own arbitrarily adopted frame! Some reinterpretations of the known empirical facts call in question the empirical bases of SR. The scientific wander was conditioned by the incomplete EM theory, tried to make up by a sequence of the ideal symmetries.
Relativityworkshop.com, 2018
This scientic article develops the theory of relativity regardless of the principles "constancy of light speed", "homogeneity and isotropy of space", and "timing of clocks" in a minkowskian space-time on the basis of electromagnetic fields and reference frames features. In this article we do not think into the invariance of Maxwell equations. It is proved that in this context, orthogonal transformation preserves the skew-adjoint property of electromagnetic field. Thereby it is derived the Lorentz transformations and (in part II) the Lorentz boost. Some possible appealing generalizations arise from the hints that appear in the analysis of this work. * c General Register of Intellectual Property ; Dossier 09/RTPI-03090.4/2018 Madrid(Spain) April 20th 2018 ; M-002741/2018 † Article on line published in the website relativityworkshop.com ‡ The theory of relativity is rediscovered from new standpoints and principles.