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From the history of physics


Noncommutative nature of the addition of noncollinear velocities in special relativity and the geometric phase method (commemorating the publication centennial of A Sommerfeld’s work)


Federal Research Center A.V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences, ul. Ulyanova 46, Nizhny Novgorod, 603000, Russian Federation

In 1909, Arnold Sommerfeld used geometric calculations to show that the relativistic addition of two noncollinear velocities on an imaginary-radius sphere is a noncommutative operation. Sommerfeld was the first to use the geometric phase method to calculate the angle between the resulting velocities depending on the order in which they are added. For this, he related the value of this angle to the excess of the spherical triangle formed by the two original velocities and their sum. In 1931, Sommerfeld applied his method to analyze the Thomas precession.

This article was written to commemorate the publication centennial of A Sommerfeld’s paper “Über die Zusammensetzung der Geschwindigkeiten in der Relativtheorie” (On the addition of velocities in relativity theory) in Physikalische Zeitschrift.

Fulltext pdf (122 KB)
Fulltext is also available at DOI: 10.3367/UFNe.0180.201009d.0965
PACS: 01.65.+g, 03.30.+p, 03.65.Vf (all)
DOI: 10.3367/UFNe.0180.201009d.0965
URL: https://ufn.ru/en/articles/2010/9/d/
000286041500004
2010PhyU...53..923M
Citation: Malykin G B "Noncommutative nature of the addition of noncollinear velocities in special relativity and the geometric phase method (commemorating the publication centennial of A Sommerfeld's work)" Phys. Usp. 53 923–927 (2010)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Малыкин Г Б «Некоммутативность сложения неколлинеарных скоростей в специальной теории относительности и метод геометрической фазы (к столетию со дня публикации работы А. Зоммерфельда)» УФН 180 965–969 (2010); DOI: 10.3367/UFNr.0180.201009d.0965

A. Sommerfeld is author of Physics-Uspekhi

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  1. G.B. Malykin, S.A. Kharlamov “Topological phase in classical mechanics” 46 957–965 (2003)
  2. G.B. Malykin, V.S. Savchuk, E.A. Romanets “Lev Yakovlevich Strum and the hypothesis of the existence of tachyons” 55 1134–1139 (2012)
  3. A. Sommerfeld “On the addition of velocities in the theory of relativity” 53 929–931 (2010)
  4. G.B. Malykin “Earlier studies of the Sagnac effect” 40 317–321 (1997)
  5. V.P. Vizgin “On the discovery of the gravitational field equations by Einstein and Hilbert: new materials” 44 1283–1298 (2001)
  6. F. Dyson “Birds and frogs in mathematics and physics” 53 825–834 (2010)
  7. D.E. Burlankov “Gravity and absolute space. The works of Niels Bjern (1865-1909)” 47 833–844 (2004)
  8. V.P. Vizgin “The nuclear shield in the ’thirty-year war’ of physicists against ignorant criticism of modern physical theories” 42 1259–1283 (1999)
  9. K. Barley, J. Vega-Guzmán et al “Discovery of the relativistic Schrödinger equation” 65 90–103 (2022)
  10. I.L. Fabelinskii “Seventy years of combination (Raman) scattering” 41 1229–1247 (1998)
  11. B.B. Kadomtsev, V.I. Kogan et al “On the fiftieth anniversary of the paper by M. A. Leontovich and L. I. Mandel’shtam (’On the theory of the Schrödinger equation’)” 21 272–273 (1978)
  12. I.Yu. Kobzarev “Henri Poincaré’s St. Louis lecture, and theoretical physics on the eve of the theory of relativity” 17 584–592 (1975)
  13. E.G. Maksimov “About Ginzburg — Landau, and a bit about others” 53 1185–1190 (2010)
  14. Yu.Ya. Stavissky “Nuclear energy for space missions” 50 1179–1187 (2007)
  15. V.P. Milant’ev “Creation and development of Bohr’s theory (on the 90th anniversary of the Bohr theory of the atom)” 47 197–203 (2004)
  16. K.N. Mukhin, A.F. Sustavov, V.N. Tikhonov “On the centenary of the Nobel Prize: Russian laureates in physics” 46 493–547 (2003)
  17. V.D. Shafranov, B.D. Bondarenko et al “On the history of the research into controlled thermonuclear fusion” 44 835–843 (2001)
  18. E.P. Likhtman “Supersymmetry — 30 years ago” 44 973–979 (2001)
  19. G.E. Volovik “Fifty years of research at the Landau Institute for Theoretical Physics (on the 100th anniversary of the birth of I.M. Khalatnikov)” 62 1031–1045 (2019)
  20. V.I. Kogan “The discovery of the Planck constant: ’roentgenoscopy’ of the scientific situation (1900). Missed opportunities in the choice of the Second Step (on the centenary of the First Step of quantum theory)” 43 1253–1259 (2000)

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