The relativistic velocity composition paradox and the Thomas rotation (original) (raw)
References and notes
Constantin I. Mocanu, “Some difficulties within the framework of relativistic electrodynamics,”Arch. Elektrotech.69, 97–110 (1986). Google Scholar
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L. H. Thomas, “The motion of the spinning electron,”Nature (London)117, 514 (1926); “The kinematics of an electron with an axis,”Philos. Mag.3, 1–22 (1927); see also Ref. 28. Google Scholar
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Presently, most books on STR make no mention of the Thomas rotation (or precession). Several outstanding exceptions are: E. F. Taylor and J. A. Wheeler,Spacetime Physics, H. M. Foley and M. A. Ruderman, eds. (Freeman, San Francisco, 1966); M. C. Møller,The Theory of Relativity (Clarendon Press, Oxford, 1952); J. D. Jackson,Classical Electrodynamics (Wiley, New York, 1975); and H. P. Robertson and T. W. Noonan,Relativity and Cosmology (Saunders, Philadelphia, 1968). Several articles on the Thomas precession (rotation) are listed in Refs. 8–22. Google Scholar
Lanfranco Belloni and Cesare Reina, “Sommerfeld's way to the Thomas precession,”Eur. J. Phys.7, 55–61 (1986). Google Scholar
Ari Ben-Menahem, “Wigner's rotation revisited,”Am. J. Phys.53, 62–66 (1985). In this article, as well as in several others, the Thomas rotation is referred to as the_Wigner rotation_. The use of the term “Wigner rotation” for the description of the Thomas rotation apparently came into the English literature from a text by S. Gasiorowicz,Elementary Particle Physics (Wiley, New York, 1967), p. 74, who copied the term from the German literature. An objection to the use of this term for the description of the Thomas rotation is based on the claim that the “correct” Wigner rotation is the Thomas rotation measured in the frame in which the accelerated particle is at rest; see Ref. 25 of Ref. 28. Google Scholar
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David Shelupsky, “Derivation of the Thomas precession formula,”Am. J. Phys.35, 650–651 (1967). Google Scholar
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See, for instance, V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitaevskii,Quantum Electrodynamics, trans. by J. B. Sykes and J. S. Bell (Pergamon Press, New York, 1982), p. 126. Google Scholar
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A. A. Ungar, “Thomas rotation and the parametrization of the Lorentz transformation group,”Found. Phys. Lett.1, 57–89 (1988). Google Scholar
A. A. Ungar, “The Thomas rotation formalism underlying a nonassociative group structure for relativistic velocities,”Appl. Math. Lett.1, 403–405 (1988). Google Scholar
A. A. Ungar, “The relativistic noncommutative nonassociative group of velocities and the Thomas rotation,”Results Math.16, 168–179 (1989). Google Scholar
M. C. Møller,The Theory of Relativity (Clarendon Press, Oxford, 1952), p. 42. Google Scholar
A. A. Ungar, “Weakly associative groups,” preprint.
H. Wefelscheid,Proc. Edinburgh Math. Soc.23, 9 (1980); W. Kerby and H. Wefelscheid, “The maximal sub near-field of a near-domain,”J. Algebra28, 319–325 (1974); H. Wähling,Theorie der Fastkörper (Thales, W. Germany, 1987), and references therein. Google Scholar