Search for Lorentz invariance violation through tests of the gravitational inverse square law at short-ranges

A search for sidereal variations in the non-Newtonian force between two tungsten plates separated at millimeter ranges sets experimental limits on Lorentz invariance violation involving quadratic couplings of Riemann curvature. We show that the Lorentz invariance violation force between two finite flat plates is dominated by the edge effects, which includes a suppression effect leading to lower limits than previous rough estimates. From this search, we determine the current best constraints of the Lorentz invariance violating coefficients at a level of $10^{-8}$ m$^{2}$.

Testing local position and fundamental constant invariance due to periodic gravitation and boost using long-term comparison of the SYRTE atomic fountains and H-masers

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 to the Cosmic Microwave Background (CMB) rest frame. The data sets span over more than eight years. The main sources of long-term noise in such experiments are the offsets and linear drifts associated with the various H-masers. The drift can vary from nearly immeasurable to as high as 1.3*10^-15 per day. To circumvent these effects we apply a numerical derivative to the data, which significantly reduces the standard error when searching for periodic signals. We determine a standard error for the putative Local Position Invariance (LPI) coefficient with respect to gravity for a Cs-Fountain H-maser comparison of 4.8*10^-6 and 10^-5 for a Rb-Fountain H-maser comparison. From the same data the putative boost LPI coefficients were measured to a precision of up to parts in 10^11 with respect to the CMB rest frame. By combining these boost invariance experiments to a Cryogenic Sapphire Oscillator versus H-maser comparison, independent limits on all nine coefficients of the boost violation vector with respect to fundamental constant invariance (fine structure constant, electron mass and quark mass respectively), were determined to a precision of parts up to 10^10.

Testing Local Lorentz and Position Invariance and Variation of Fundamental Constants by searching the Derivative of the Comparison Frequency Between a Cryogenic Sapphire Oscillator and Hydrogen Maser

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}.