Foundations of Physics

, Volume 42, Issue 4, pp 488–511 | Cite as

Vectorial Form of the Successive Lorentz Transformations. Application: Thomas Rotation

  • Riad ChamseddineEmail author


A complete treatment of the Thomas rotation involves algebraic manipulations of overwhelming complexity. In this paper, we show that a choice of convenient vectorial forms for the relativistic addition law of velocities and the successive Lorentz transformations allows us to obtain straightforwardly the Thomas rotation angle by three new methods: (a) direct computation as the angle between the composite vectors of the non-collinear velocities, (b) vectorial approach, and (c) matrix approach. The new expression of the Thomas rotation angle permits us to simply obtain the Thomas precession. Original diagrams are given for the first time.


Successive Lorentz transformations Relativistic addition law of velocities Thomas rotation Thomas precession 



I would like to thank the referees for their very helpful comments which have led to improvement of this paper.


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Physics, Faculty of Sciences-ILebanese UniversityBeirutLebanon

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