The relativistic velocity composition paradox and the Thomas rotation

@article{Ungar1989TheRV,
  title={The relativistic velocity composition paradox and the Thomas rotation},
  author={Abraham Albert Ungar},
  journal={Foundations of Physics},
  year={1989},
  volume={19},
  pages={1385-1396}
}
  • A. Ungar
  • Published 1 November 1989
  • Physics
  • Foundations of Physics
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 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… 

Geometrical interpretation for relativistic composition of velocities and the Thomas precession

The relativistic composition of velocities is interpreted in terms of the rapidity triangle, as a generalization of the non-relativistic parallelogram rule. Some geometrical experiments are presented

The Expanding Minkowski Space

abstractUnder the common relativistic velocity composition law the relativistically admissible velocities form a weakly associative-commutative group (WACG) rather than an ordinary group. A study of

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 Mocanu paradox -- not at all paradoxical

Non-commutativity of the Einstein velocity addition, in case of non-collinear velocities, seemingly gives rise to a conflict with reciprocity principle. However, Thomas rotation comes at a rescue and

Alternative realization for the composition of relativistic velocities

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

Alternative realization for the composition of relativistic velocities

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

On a quasi-relativistic formula in polarization theory.

In a pure operatorial (nonmatrix) Pauli algebraic approach, this Letter shows that the Poincaré vector of the light transmitted by a dichroic device can be expressed as function of the Poincaré

Thomas rotation: a Lorentz matrix approach

The composition of two pure Lorentz transformations (boosts) parametrized by non-parallel velocities is equivalent to a boost combined with a pure spatial rotation - the Thomas rotation. Thirty years

Uniqueness of the Isotropic Frame and Usefulness of the Lorentz Transformation

According to the postulates of the special theory of relativity (STR), physical quantities such as proper times and Doppler shifts can be obtained from any inertial frame by regarding it as
...

References

SHOWING 1-10 OF 37 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

Lorentz Transformation and the Thomas Precession

The various kinematic effects of special relativity are here treated by considering iterations of the infinitesimal Lorentz transformation. There is only one relativistic effect that appears as a

The Motion of the Spinning Electron

IN a letter published in NATURE of February 20, p. 264, Messrs. Uhlenbeck and Goudsmit have shown how great difficulties which atomic theory had met in the attempt to explain spectral structure and

Relativistic motion of a charged particle, the Lorentz group, and the Thomas precession

The equation of motion of a classical charged particle in a homogeneous, static electromagnetic field is solved exactly in terms of a Lorentz transformation. All higher‐order corrections to the

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

Derivation of the Spin-Orbit Interaction

Many students find it paradoxical that spin-orbit coupling is discussed in nonrelativistic quantum mechanics although it is usually said to be a consequence of relativity. The resolution of this

Special relativity completed: The source of some 2s in the magnitude of physical phenomena

Some factors of 2 relate predictions made of relativistic systems by the special and the general theory. Conventional wisdom often assigns the source of the factors of 2 to complicated kinematical

The Lorentz group and the Thomas precession. II. Exact results for the product of two boosts

The product of two Lorentz boosts in different directions is equal to the product of a pure boost and a spatial rotation. To second order, the resulting boost is simply the sum of the individual

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