Evidence for modified Newtonian dynamics from Cavendish-type gravitational constant experiments

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Abstract
Recent experimental results for the gravitational constant G from Cavendish-type experiments were analysed in the framework of modified Newtonian dynamics (MOND). MOND corrections were applied to the equation of motion of a pendulum, under the assumption that the magnitude of the horizontal time dependent gravitational acceleration determines the amount of MOND corrections. The large vertical component of the local gravitational field of the earth is fully compensated by the alignment of the torsion pendulum in accordance with Newton’s third law and therefore not considered for MOND corrections. From the analysis of the MOND corrected equation of motion of a realistic torsion pendulum with mixed gravitational and electromagnetic restoring torque simple rules for meaningful MOND corrections of measured G values determined by different operational modes of Cavendish type G experiments were derived. Based on this analysis the reported discrepancies for G determined by ‘static deflection’ and ‘electrostatic servo’ methods of the ‘BIPM’ experiment by Quinn et al and between time-of-swing and angular acceleration feedback (AAF) methods for the ‘HUST’ experiment by Li et al could be fully resolved by MOND corrections using one common MOND interpolation function, determined by a one parameter fit. The MOND corrected ‘BIPM’ and ‘HUST’ results, along with other ‘single method’ results from G experiments by Gundlach and Merkovitz, Schlamminger et al and Newman et al lead to an average G value of 6.67 422 · 10−11 m3 kg−1 s−2 with a standard deviation of 12.5 ppm only. The applied MOND correction procedure and the fitted interpolation function employed for the G experiments were found to be consistent with the most viable MOND fits to galaxy rotation curves.

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