A rotating Michelson interferometer from the co-rotating point of view

Research Article


The phase shift induced by a uniform rotation in a Michelson interferometer is re-derived in the geometrical framework of the coordinate-free formalism of general relativity from the co-rotating point of view. The effect is second order in the ratio of the interferometer’s speed to the speed of light and further suppressed by the ratio of the length of the interferometer’s arms to the radius of rotation. The relation of the effect to gravitational time dilation is discussed.


Michelson interferometry Speed of light in non-inertial frame of reference Gravitational time dilation Equivalence principle Rotation sensing 



I would like to thank V.I. Ritus for pointing out the analogy between the phase shifts induced by terrestrial gravity and by a uniform rotation in a Michelson interferometer. I am also indebted to G.B. Malykin for having stimulated the re-derivation of the phase shift formula from the co-rotating point of view and to J.-P. Zendri for carefully reading the manuscript and related comments.


  1. 1.
    Schrödinger, E.: Expanding Universe. Cambridge University Press, Cambridge (1956)MATHGoogle Scholar
  2. 2.
    Bażański, S.L.: The split and propagation of light rays in relativity. In: Harvey, A. (ed.) On Einstein’s Path: Essays in Honor of Engelbert Schucking, p. 81. Springer, New York (1999)Google Scholar
  3. 3.
    Bażański, S.L.: Some properties of light propagation in relativity. In: Rembielinski, J. (ed.) Particels, fields and gravitation. AIP Conference Proceeding, vol. 453, p. 421 (1998)Google Scholar
  4. 4.
    Mattingly, D.: Modern tests of lorentz invariance. Living Rev. Relativ. 8, pp. 5 (2005). http://www.livingreviews.org/lrr-2005-5. Accessed 3 Jan 2016
  5. 5.
    Ashtekar, A., Magnon, A.: The sagnac effect in general relativity. J. Math. Phys. 16, 341 (1975)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    Stedman, E., Schreiber, K.U., Bilger, H.R.: On the detectability of the Lense-Thirring field from rotating laboratory masses using ring laser gyroscope interferometers. Class. Quantum Gravity 20, 2527 (2003)ADSCrossRefMATHGoogle Scholar
  7. 7.
    Bosi, F., et al.: Measuring gravito-magnetic effects by multi ring-laser gyroscope. Phys. Rev. D. 84, 122002 (2011)ADSCrossRefGoogle Scholar
  8. 8.
    Freise, A., Strain, K.: Interferometer techniques for gravitational-wave detection. Living Rev. Relativ. 13, pp. 5 (2010). http://www.livingreviews.org/lrr-2010-1. Accessed 3 Jan 2016
  9. 9.
    Pitkin, M., Reid, S., Rowan, S., Hough, J.: Gravitational wave detection by interferometry (Ground and Space). Living Rev. Relativ. 14, pp. 5 (2011). http://www.livingreviews.org/lrr-2011-5. Accessed 3 Jan 2016
  10. 10.
    LIGO Laboratory Home Page, project homepage California Institute of Technology. http://www.ligo.caltech.edu. Accessed 3 January 2016
  11. 11.
    VIRGO, project homepage, INFN; http://www.virgo.infn.it. Accessed 3 Jan 2016
  12. 12.
    Maraner, P., Zendri, J.-P.: General relativistic sagnac formula revised. Gen. Relativ. Gravit. 44, 1713 (2012)ADSMathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Maraner, P.: The effect of rotations on Michelson interferometers. Ann. Phys. 350, 95 (2014)ADSCrossRefGoogle Scholar
  14. 14.
    Landau, L.D., Lifshitz, E.M.: Classical Theory of Fields. Addison-Wesley, Massachussets (1996)MATHGoogle Scholar
  15. 15.
    Rindler, W.: Relativity: Special General and Cosmological. Oxford University Press, Oxford (2009)MATHGoogle Scholar
  16. 16.
    Rizzi, G., Ruggiero, M.L.: Space geometry of rotating platforms: an operational approach. Found. Phys. 32, 1525 (2002)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Michelson, A.A., Morley, E.W.: Am. J. Sci. 34, 333 (1887)CrossRefGoogle Scholar

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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.School of Economics and ManagementFree University of Bozen-BolzanoBolzano-BozenItaly

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