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Register a new userTesting Lorentz violation by the comparison of atomic clocks
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A more complete theoretical model of testing Lorentz violation by the comparison of atomic clocks is developed in the Robertson-Mansouri-Sexl kinematic framework. As this frame postulates the deviation of the coordinate transformation from the Lorentz transformation, from the viewpoint of the transformation violations on time and space, the LI violating effect in the atomic clock comparison can be explained as two parts: time-delay effect $alpha frac {v^2}{c^2}$ and structure effect $-frac {beta+2delta}{3} frac {v^2}{c^2}$. Standard model extension is a widely used dynamic frame to characterize the Lorentz violation, in which a space-orientation dependence violating background field is regarded as the essential reason for the Lorentz violation effect. Compared with the RMS frame which only indicates the kinematic properties with the coordinate transformation, this dynamic frame provides a more complete and clear description for the Lorentz violation effect.
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For the purpose of searching for Lorentz-invariance violation in the minimal Standard-Model Extension, we perfom a reanalysis of data obtained from the $^{133}text{Cs}$ fountain clock operating at SYRTE. The previous study led to new limits on eight components of the $tilde{c}_{mu u}$ tensor, which quantifies the anisotropy of the proton kinetic energy. We recently derived an advanced model for the frequency shift of hyperfine Zeeman transition due to Lorentz violation and became able to constrain the ninth component, the isotropic coefficient $tilde{c}_{TT}$, which is the least well-constrained coefficient of $tilde{c}_{mu u}$. This model is based on a second-order boost Lorentz transformation from the laboratory frame to the Sun-centered frame, and it gives rise to an improvement of five orders of magnitude on $tilde{c}_{TT}$ compared to the state of the art.
Sagnac gyroscopes with increased sensitivity are being developed and operated with a variety of goals including the measurement of General-Relativistic effects. We show that such systems can be used to search for Lorentz violation within the field-theoretic framework of the Standard-Model Extension, and that competitive sensitivities can be achieved. Special deviations from the inverse square law of gravity are among the phenomena that can be effectively sought with these systems. We present the necessary equations to obtain sensitivities to Lorentz violation in relevant experiments.
The cryogenic sapphire oscillator (CSO) at the Paris Observatory has been continuously compared to various Hydrogen Masers since 2001. The early data sets were used to test Local Lorentz Invariance in the Robertson-Mansouri-Sexl (RMS) framework by searching for sidereal modulations with respect to the Cosmic Microwave Background, and represent the best Kennedy-Thorndike experiment to date. In this work we present continuous operation over a period of greater than six years from September 2002 to December 2008 and present a more precise way to analyze the data by searching the time derivative of the comparison frequency. Due to the long-term operation we are able to search both sidereal and annual modulations. The results gives P_{KT} = beta_{RMS}-alpha_{RMS}-1 = -1.7(4.0) times 10^{-8} for the sidereal and -23(10) times 10^{-8} for the annual term, with a weighted mean of -4.8(3.7) times 10^{-8}, a factor of 8 better than previous. Also, we analyze the data with respect to a change in gravitational potential for both diurnal and annual variations. The result gives beta_{H-Maser} - beta_{CSO} = -2.7(1.4) times 10^{-4} for the annual and -6.9(4.0) times 10^{-4} for the diurnal terms, with a weighted mean of -3.2(1.3) times 10^{-4}. This result is two orders of magnitude better than other tests that use electromagnetic resonators. With respect to fundamental constants a limit can be provided on the variation with ambient gravitational potential and boost of a combination of the fine structure constant (alpha), the normalized quark mass (m_q), and the electron to proton mass ratio (m_e/m_p), setting the first limit on boost dependence of order 10^{-10}.
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The Newton limit of gravity is studied in the presence of Lorentz-violating gravitational operators of arbitrary mass dimension. The linearized modified Einstein equations are obtained and the perturbative solutions are constructed and characterized. We develop a formalism for data analysis in laboratory experiments testing gravity at short range and demonstrate that these tests provide unique sensitivity to deviations from local Lorentz invariance.
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