On the relativistic velocity composition paradox and the Thomas rotation

@article{Mocanu1992OnTR,
  title={On the relativistic velocity composition paradox and the Thomas rotation},
  author={Costel - Iulian Mocanu},
  journal={Foundations of Physics Letters},
  year={1992},
  volume={5},
  pages={443-456}
}
  • C. Mocanu
  • Published 1 October 1992
  • Physics
  • Foundations of Physics Letters
The non-commutativity and the non-associativity of the composition law of the non-colinear velocities lead to an apparent paradox, which in turn is solved by the Thomas rotation. A 3×3 parametric, unimodular and orthogonal matrix elaborated by Ungar is able to determine the Thomas rotation. However, the algebra involved in the derivation of the Thomas rotation matrix is overwhelming. The aim of this paper is to present a direct derivation of the Thomas angle as the angle between the composite… 

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References

SHOWING 1-10 OF 28 REFERENCES

The Relativistic Noncommutative Nonassociative Group of Velocities and the Thomas Rotation

The bizarre and counterintuitive noncommutativity and nonassociativity of the relativistic composition of nonparallel admissible velocities is sometimes interpreted as a peculiarity of special theory

The relativistic velocity composition paradox and the Thomas rotation

The relativistic velocity composition paradox of Mocanu and its resolution are presented. The paradox, which rests on the bizarre and counterintuitive non-communtativity of the relativistic velocity

Successive Lorentz transformations of the electromagnetic field

A velocity-orientation formalism to deal with compositions of successive Lorentz transformations, emphasizing analogies shared by Lorentz and Galilean transformations, has recently been developed.

Thomas rotation and the parametrization of the Lorentz transformation group

Two successive pure Lorentz transformations are equivalent to a pure Lorentz transformation preceded by a 3×3 space rotation, called a Thomas rotation. When applied to the gyration of the rotation

The Thomas precession and velocity-space curvature

The motion of a physical system acted upon by external torqueless forces causes the relativistic Thomas precession of the system’s spin vector, relative to an inertial frame. A time‐dependent force

Axiomatic approach to the nonassociative group of relativistic velocities

The bizarre and counterintuitive noncommutativity and nonassociativity of the relativistic composition of noncollinear velocities is attributed to the presence of the Thomas rotation. The Thomas

Weakly Associative Groups

The space ℝc3 of 3-dimensional relativistically admissible velocities possesses (i) a binary operation which represents the relativistic velocity composition law; and (ii) a mapping from the

The Thomas Precession

This paper is intended to give a simple physical understanding of the kinematic effect referred to as the Wigner rotation or, when applied to an orbiting object, the Thomas precession. Since this is

Thomas precession and its associated grouplike structure

Mathematics phenomena and discovers the secret analogies which unite them. Joseph Fourier. Where there is physical significance, there is pattern and mathematical regularity. The aim of this article