General Relativity and Gravitation

, Volume 36, Issue 10, pp 2351–2372 | Cite as

Whispering Gallery Resonators and Tests of Lorentz Invariance

  • Peter Wolf
  • Michael E. Tobar
  • Sébastien Bize
  • André Clairon
  • André N. Luiten
  • Giorgio Santarelli

Abstract

The frequencies of a cryogenic sapphire oscillator and a hydrogen maser are compared to set new constraints on a possible violation of Lorentz invariance. We give a detailed description of microwave resonators operating in Whispering Gallery modes and then apply it to derive explicit models for Lorentz violating effects in our experiment. Models are calculated in the theoretical framework of Robertson, Mansouri and Sexl (RMS) and in the standard model extension (SME) of Kostelecky and co-workers. We constrain the parameters of the RMS test theory to 1/2 − βMS + δMS = (1.2 ± 2.2) × 10−9 and βMS − αMS − 1 = (1.6 ± 3.0) × 10−7 which is of the same order as the best results from other experiments for the former and represents a 70 fold improvement for the latter. These results correspond to an improvement of our previously published limits [Wolf P. et al., Phys. Rev. Lett.90, 6, 060402, (2003)] by about a factor 2.

Violation of Lorentz invariance equivalence principle 

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REFERENCES

  1. [1]
    Will, C. M. (1993). Theory and Experiment in Gravitational Physics, Revised edition, Cambridge University Press.Google Scholar
  2. [2]
    Kostelecky, V. A., and Samuel, S. (1989). Phys. Rev. D 39, 683.Google Scholar
  3. [3]
    Damour, T. (1997). gr-qc/9711060.Google Scholar
  4. [4]
    Damour, T., and Polyakov, A. M. (1994). Nucl.Phys. B 423, 532.Google Scholar
  5. [5]
    Colladay, D., and Kostelecky, V. A. (1997). Phys. Rev. D 55, 6760; Colladay, D., and Kostelecky, V. A. (1998). Phys.Rev. D58, 116002.Google Scholar
  6. [6]
    Bluhm R., Kostelecký , V. A., Lane, C. D., and Russell, N. (2002). Phys. Rev. Lett. 88 (9)}, 090801, (2002).2372 Wol f et al.Google Scholar
  7. [7]
    Robertson, H. P. (1949). Rev. Mod. Phys. 21, 378.Google Scholar
  8. [8]
    Mansouri, R., and Sexl, R. U. (1977). Gen. Relat. Grav. 8, 497, 515, 809.Google Scholar
  9. [9]
    Lightman, A. P., and Lee, D. L. (1973). Phys. Rev. D 8, 2, 364.Google Scholar
  10. [10]
    Blanchet, L. (1992). Phys. Rev. Lett. 69, 4, 559.Google Scholar
  11. [11]
    Ni, W.-T. (1977). Phys. Rev. Lett. 38, 301.Google Scholar
  12. [12]
    Kostelecky, A. V., and Mewes, M. (2002). Phys. Rev. D D66, 056005.Google Scholar
  13. [13]
    Wolf, P., Bize, S., Clairon, A., Luiten, A. N., Santarelli, G., Tobar, M. E. (2003). Phys. Rev. Lett. 90, 6, 060402.Google Scholar
  14. [14]
    M¨ uller, H., Herrmann, S., Braxmaier, C., Schiller, S., and Peters, A. (2003). Phys. Rev. Lett. 91, 2, 020401.Google Scholar
  15. [15]
    Braxmaier, C., M¨ uller, H., Pradl, O., Mlynek, J., Peters, A., and Schiller, S. (2002). Phys. Rev. Lett. 88, 1, 010401.Google Scholar
  16. [16]
    Tobar, M. E., and Mann, A. G. (1991). IEEE Tran. Microw. Theor. Tech. 39, 2077Google Scholar
  17. [17]
    Cros, D., and Guillon, P. (1990). IEEE Trans. Microw. Theor. Tech. 38, 1667.Google Scholar
  18. [18]
    Guillon, P., and Jiao, X. (1987). Proc. IEE, H. 134.Google Scholar
  19. [19]
    Krupka, J., Cros, D., Aubourg, M., and Guillon, P. (1994). IEEE Trans. Microw. Theor. Tech. 41, 56.Google Scholar
  20. [20]
    Schiller, S., and Beyer, R. L. (1991). Opt. Lett. 16, 1138.Google Scholar
  21. [21]
    Tobar, M. E., Anstie, J. D., and Hartnett, J. G. (2003). IEEE Trans. UFFC. 50, 11, 1407.Google Scholar
  22. [22]
    Aubourg, M., and Guillon, P. (1991). J. Electromagn. Waves Appl. 45, 71.Google Scholar
  23. [23]
    Brillet, A., and Hall, J. L., Phys. Rev. Lett. 42, 9, 549.Google Scholar
  24. [24]
    Hils, D., and Hall, J. L. (1990). Phys. Rev. Lett. 64, 15, 1697.Google Scholar
  25. [25]
    Riis, E., Andersen, L. A., Bjerre, N., Poulsen, O., Lee S. A., and Hall, J. L. (1998). Phys. Rev. Lett. 60, 81.Google Scholar
  26. [26]
    Wolf, P., and Petit, G. (1997). Phys.Rev. A56, 6, 4405.Google Scholar
  27. [27]
    Fixsen, D. J., Cheng, E. S., and Wilkinson, D. T., (1983). Phys. Rev. Lett. 50, 620.Google Scholar
  28. [28]
    Lubin, P. M., Epstein, G. L., and Smoot, G. F. (1983). Phys. Rev. Lett. 50, 616.Google Scholar
  29. [29]
    Michelson, A. A., and Morley, E. W. (1887). Am.J.Sci. 34, 333.Google Scholar
  30. [30]
    Kennedy, R. J., and Thorndike, E. M. (1932). Phys.Rev. B42, 400.Google Scholar
  31. [31]
    Grieser, R., Klein, R., Huber, G., Dickopfl, S., Klaft, I., Knobloch, P., Merz, P., Albrecht, F., Grieser, M., Habs, D., Schwalm, D., and Kuhl, T. (1994). Appl. Phys. B 59, 127.Google Scholar
  32. [32]
    Saathoff, G., Karpuk, S., Eisenbarth, U., Huber, G., Krohn, S., Muñoz Horta, R., Reinhardt, S., Schwalm, D., Wolf, A., and Gwinner, G. (2003). Phys. Rev. Lett. 91, 19, 190403.Google Scholar
  33. [33]
    Bauch, A., and Weyers, S. (2002). Phys.Rev. D65, 081101.Google Scholar
  34. [34]
    Tobar, M. E., Hartnett, J. G., and Anstie, J. D. (2002). Phys. Lett. A300, 33.Google Scholar
  35. [35]
    Krupka, J., Derzakowski, K., Abramowicz, A., Tobar, M. E., and Geyer, R. G. (1999). IEEE Trans. MTT, 47, 6, 752.Google Scholar
  36. [36]
    M¨ uller, H., Braxmaier, C., Herrmann, S., Peters, A., and L¨ ammerzahl, C. (2003). Phys. Rev. D 67, 056006.Google Scholar
  37. [37]
    Kostelecky, V. A., and Lane, C. D. (1999). Phys.Rev. D60, 116010.Google Scholar
  38. [38]
    Bize, S., Sortais, Y., Abgrall, M., Zhang, S., Calonico, D., Mandache, C., Lemonde, P., Laurent, P., Santarelli, G., Salomon, C., Clairon, A., Luiten, A., and Tobar, M. (2002). Proceeding of the 6th Symporium on Frequency Standards and Metrology. World Scientific, Singapore.Google Scholar
  39. [39]
    Schmidt, L. S. Metrologia 40, 3, S305-S311.Google Scholar
  40. [40]
    Draper, N. R., and Smith, H. (1966). Applied Regression Analysis,Wiley, New York.Google Scholar
  41. [41]
    Salomon, Ch., Dimarcq, N., Abgrall, M., Clairon, A., Laurent, P., Lemonde, P., Santarelli, G., Uhrich, P., Bernier, L. G., Busca, G., Jornod, A., Thomann, P., Samain, E., Wolf, P., Gonzalez, F., Guillemot, Ph., Leon, S., Nouel, F., Sirmain, Ch., Feltham, S. (2001). C. R. Acad. Sci. Paris. 2, 4, 1313.Google Scholar
  42. [42]
    L¨ ammerzahl, C., Dittus, H., Peters, A., and Schiller, S. (2001). Class. Quant. Grav., 18, 2499.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2004

Authors and Affiliations

  • Peter Wolf
    • 1
    • 2
  • Michael E. Tobar
    • 3
  • Sébastien Bize
    • 1
  • André Clairon
    • 1
  • André N. Luiten
    • 3
  • Giorgio Santarelli
    • 1
  1. 1.BNM-SYRTEObservatoire de ParisParisFrance
  2. 2.Bureau International des Poids et MesuresCedexFrance
  3. 3.School of PhysicsUniversity of Western AustraliaNedlandsAustralia

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