Abstract
There seems to exist a dilemma in the literature as to the correct relativistic formula for the Sagnac phase-shift. The paper addresses this issue in the light of a novel, kinematically equivalent linear Sagnac-type thought experiment, which provides a vantage point from which the effect of rotation in the usual Sagnac effect can be analyzed. The question is shown to be related to the so-called rotating disc problem known as the Ehrenfest paradox. The relativistic formula for the Sagnac phase-shift seems to depend on the way the paradox is resolved. Kinematic resolution of the Ehrenfest paradox proposed by some authors predicts the usually quoted formula for the Sagnac delay but the resolution itself is shown to be based upon some implicit assumptions regarding the behaviour of solid bodies under acceleration. In order to have a greater insight into the problem, a second version of the thought experiment involving linear motion of a “special type” of a non-rigid frame of reference is discussed. It is shown by analogy that the usually quoted special relativistic formula for the Sagnac delay follows, provided the material of the disc matches the “special type.”
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. G. Sagnac, C. R. Acad. Sci. 157, 708–710 (1913).
E. J. Post, Rev. Modern Phys. 39, 475–493 (1967).
R. Anderson, H. R. Bilger, and G. E. Stedman, Amer. J. Phys. 62, 975–985 (1994).
G. B. Malykin, Phys.-Usp. 40, 317–321 (1997).
H. Hasselbach and M. Nicklaus, Phys. Rev. A 48, 143–151 (1993).
R. Colella, A. W. Overhauser, J. L. Staudenmann, and S. A. Werner, Phys. Rev. A 21, 1419–1438 (1980).
F. Riehle, Th. Kister, A. Wittie, J. Helmcke, and Ch. J. Borde, Phys. Rev. Lett. 67, 177–180 (1991).
D. Fargion, L. Chiatti, and A. Aiello, “Quantum Mach effect by Sagnac phase shift on Cooper pair in rf-SQUID, ” preprint astro-ph/9606117 (1996), 19 pages.
S. Merhav, Aerospace Sensor Systems and Applications (Springer, New York, 1996).
D. W. Allan et al., IEEE Trans. Instrum. Meas. IM-34(2), 118–125 (1985).
N. Saburi, M. Yamamoto, and K. Harada, IEEE Trans. Instrum. Meas. IM-25, 473–477 (1976).
G. Petit and G. Wolf, Astronom. Astrophys. 286, 971–977 (1994).
J. Anandan, Phys. Rev. D. 24, 338–346 (1981).
D. Dieks and G. Nienhuis, Amer. J. Phys. 58, 650–655 (1990).
P. Langevin, C. R. Acad. Sci. (Paris) 173, 831–834, (1921).
M. Dresden and C. N. Yang, Phys. Rev. D 20, 1846–1848 (1979).
F. Selleri, Found. Phys. 26, 641–664 (1996).
F. Goy, “Non-invariant velocity of light and clock synchronization in accelerated systems, ” Proc. Physical Interpretation of Relativity Theory (V), held at Imperial College, London, pp. 129–138 (1996).
R. D. Klauber, Found. Phys. Lett. 11, 405–444 (1998).
R. D. Klauber, Amer. J. Phys. 67, 158–159 (1998).
P. Ehrenfest, Phys. Z. 10, 918(1909).
ø. Grøn, Amer. J. Phys. 43, 869–876 (1975).
T. A. Weber, Amer. J. Phys. 65, 486–487 (1997).
S. K. Ghosal and M. Sarker, “Cosmologically preferred frame, linear Sagnac effect and absolute synchrony, ” Proc. Physical Interpretation of Relativity Theory Meeting (VI) (Supplementary papers), held at Imperial College, London, pp. 52–64 (1998).
D. Dieks, Eur. J. Phys. 12, 253–259 (1991).
C. W. Sherwin, “Three theories of relative measurement, ” Paper presented at the Physical Interpretation of Relativity Theory Meeting (III), held at Imperial College, London (1992).
L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, 4th revised English edition (Pergamon, Oxford, 1975).
M. Born, Ann. Physik 30, 840(1909).
G. Cavalleri, Nuovo Cimento B 53, 415–431 (1968).
T. E. Phipps, Jr., “Experiment on relativistic rigidity of a rotating disc, ” NOLTR 73–9 (Naval Ordinance Laboratory, 1973), p. 47.
J. L. Synge, Studies in Mathematics and Mechanics: Presented to Richard von Mises by Friends, Colleagues and Pupils (New York, 1954).
J. R. Pounder, Comm. Dublin Institute for Advance Studies A 11 (1954).
Yu. I. Sokolovsky, The Special Theory of Relativity (Hindustan Publishing, Delhi, 1962).
A. S. Eddington, The Mathematical Theory of Relativity (Cambridge University Press, Cambridge, 1965).
D. H. Weinstein, Nature 232, 548(1971).
A. Tartaglia, Found. Phys. Lett. 12(1), 17–28 (1999).
C. Møller, The Theory of Relativity (Oxford University Press, Oxford, 1952).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ghosal, S.K., Raychaudhuri, B., Chowdhury, A.K. et al. Relativistic Sagnac Effect and Ehrenfest Paradox. Foundations of Physics 33, 981–1001 (2003). https://doi.org/10.1023/A:1025621628746
Issue Date:
DOI: https://doi.org/10.1023/A:1025621628746