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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}.
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 Lorent
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.
The frequencies of three separate Cs fountain clocks and one Rb fountain clock have been compared to various hydrogen masers to search for periodic changes correlated with the changing solar gravitational potential at the Earth and boost with respect
General relativity with fermions has two independent symmetries: general coordinate invariance and local Lorentz invariance. General coordinate invariance is implemented by the Levi-Civita connection and by Cartans tetrads both of which have as their
The idea that the vacuum energy density $rho_{Lambda}$ could be time dependent is a most reasonable one in the expanding Universe; in fact, much more reasonable than just a rigid cosmological constant for the entire cosmic history. Being $rho_{Lambda