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On the relation of Thomas rotation and angular velocity of reference frames

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Abstract

In the extensive literature dealing with the relativistic phenomenon of Thomas rotation several methods have been developed for calculating the Thomas rotation angle of a gyroscope along a circular world line. One of the most appealing concepts, introduced in Rindler and Perlick (Gen Rel Grav 22:1067, 1990), is to consider a rotating reference frame co-moving with the gyroscope, and relate the precession of the gyroscope to the angular velocity of the reference frame. A recent paper (Herrera and di Prisco in Found Phys Lett 15:373, 2002), however, applies this principle to three different co-moving rotating reference frames and arrives at three different Thomas rotation angles. The reason for this apparent paradox is that the principle of Rindler and Perlick (Gen Rel Grav 22:1067, 1990) is used for a situation to which it does not apply. In this paper we rigorously examine the theoretical background and limitations of applicability of the principle of Rindler and Perlick (Gen Rel Grav 22:1067, 1990). Along the way we also establish some general properties of rotating reference frames, which may be of independent interest.

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Authors and Affiliations

  1. Department of Applied Analysis, Eötvös University, Pázmány P. sétány 1C., 1117, Budapest, Hungary

    Tamás Matolcsi

  2. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda utca 13–15., 1053, Budapest, Hungary

    Máté Matolcsi

  3. Department of Solid State Physics, Eötvös University, Pázmány P. sétány 1A., 1117, Budapest, Hungary

    Tamás Tasnádi

Authors
  1. Tamás Matolcsi
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  2. Máté Matolcsi
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  3. Tamás Tasnádi
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Correspondence to Máté Matolcsi.

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Matolcsi, T., Matolcsi, M. & Tasnádi, T. On the relation of Thomas rotation and angular velocity of reference frames. Gen Relativ Gravit 39, 413–426 (2007). https://doi.org/10.1007/s10714-007-0399-1

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  • DOI: https://doi.org/10.1007/s10714-007-0399-1

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