Whispering Gallery Resonators and Tests of Lorentz Invariance

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.

[1]  A. Michelson,et al.  On the relative motion of the Earth and the luminiferous ether , 1887, American Journal of Science.

[2]  Wei-Tou Ni,et al.  Equivalence Principles and Electromagnetism , 1977 .

[3]  André Clairon,et al.  Tests of Lorentz invariance using a microwave resonator. , 2003, Physical review letters.

[4]  S. Reinhardt,et al.  Improved test of time dilation in special relativity. , 2003, Physical review letters.

[5]  Richard F. Gunst,et al.  Applied Regression Analysis , 1999, Technometrics.

[6]  Dale J. Fixsen,et al.  Large-Scale Anisotropy in the 2.7-K Radiation with a Balloon-Borne Maser Radiometer at 24.5 GHz , 1983 .

[7]  Electromagnetic cavities and Lorentz invariance violation , 2002, hep-ph/0212289.

[8]  Achim Peters,et al.  Modern Michelson-Morley experiment using cryogenic optical resonators. , 2003, Physical review letters.

[9]  C. Braxmaier,et al.  Tests of relativity using a cryogenic optical resonator. , 2001, Physical review letters.

[10]  Hall,et al.  Improved Kennedy-Thorndike experiment to test special relativity. , 1990, Physical review letters.

[11]  H. P. Robertson.  Postulate versus Observation in the Special Theory of Relativity , 1949 .

[12]  A. Kostelecký,et al.  $CPT$ violation and the standard model , 1997, hep-ph/9703464.

[13]  Blanchet.  A class of nonmetric couplings to gravity. , 1992, Physical review letters.

[14]  G. Smoot,et al.  3 mm Anisotropy Measurement: On the Quadrupole Component in the Cosmic Background Radiation , 1982 .

[15]  Samuel,et al.  Spontaneous breaking of Lorentz symmetry in string theory. , 1989, Physical review. D, Particles and fields.

[16]  A. Peters,et al.  OPTIS: a satellite-based test of special and general relativity , 2001, gr-qc/0104067.

[17]  P. Knobloch,et al.  A test of special relativity with stored lithium ions , 1994 .

[18]  Poulsen,et al.  Test of the isotropy of the speed of light using fast-beam laser spectroscopy. , 1988, Physical review letters.

[19]  A. Polyakov,et al.  The string dilation and a least coupling principle , 1994, hep-th/9401069.

[20]  R L Byer,et al.  High-resolution spectroscopy of whispering gallery modes in large dielectric spheres. , 1991, Optics letters.