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Relativity in Rotating Frames pp 179–220Cite as

The Relativistic Sagnac Effect: Two Derivations

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Part of the Fundamental Theories of Physics book series (FTPH,volume 135)

Abstract

The phase shift due to the Sagnac Effect, for relativistic matter and electromag-netic beams, counter-propagating in a rotating interferometer, is deduced using two different approaches. From one hand, we show that the relativistic law of velocity addition leads to the well known Sagnac time difference, which is the same independently of the physical nature of the interfering beams, evidencing in this way the universality of the effect. Another derivation is based on a formal analogy with the phase shift induced by the magnetic potential for charged particles travelling in a region where a constant vector potential is present: this is the so called Aharonov-Bohm effect. Both derivations are carried out in a fully relativistic context, using a suitable 1+3 splitting that allows us to recognize and define the space where electromagnetic and matter waves propagate: this is an extended 3-space, which we callrelative space. It is recognized as the only space having an actual physical meaning from an operational point of view, and it is identified as the ’physical space of the rotating platform’: the geometry of this space turns out to be non Euclidean, according to Einstein’s early intuition.

Keywords

  • Inertial Frame
  • Relativistic Context
  • Relative Space
  • Matter Wave
  • Space Tensor

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Author information

Authors and Affiliations

  1. Dipartimento di Fisica, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129, Torino, Italy

    Guido Rizzi & Matteo Luca Ruggiero

  2. Sezione di Torino, INFN, Via Pietro Giuria 1, I-10125, Torino, Italy

    Guido Rizzi & Matteo Luca Ruggiero

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  1. Guido Rizzi
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  2. Matteo Luca Ruggiero
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Editors and Affiliations

  1. Politecnico di Torino and Istituto Nazionale di Fisica Nucleare, Torino, Italy

    Guido Rizzi & Matteo Luca Ruggiero & 

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Rizzi, G., Ruggiero, M.L. (2004). The Relativistic Sagnac Effect: Two Derivations. In: Rizzi, G., Ruggiero, M.L. (eds) Relativity in Rotating Frames. Fundamental Theories of Physics, vol 135. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0528-8_12

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  • DOI: https://doi.org/10.1007/978-94-017-0528-8_12

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