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

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 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 6.6742210 -11 m 3 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.

Einstein’s dream to unify all forces finally materializes: a revived de Broglie’s pilot-wave theory with novel solutions

“…q q e q dq q dQ q q e q dq q dQ K K (10) As seen in section 3.2.5, force associated with Q(q) is proportional to its derivative given here in equation (10). A second integration of the latter leads to:…”

“…Thus, points (r, w) in that region are unconnected to O, and correspond to the so-called non-local phenomena (see figure 2). The physical observable is the first derivative of Q(q) given by equation (10), which is proportional to the entangled force density (see 3.2.5 and figure 3). An additional interpretation of q is as direction of time (see figure 4 in subsection 3.3.5).…”

“…The value of Newton's universal constant G. By comparison to other constants in Nature, it is quite surprising that the current value of G = 6.67408(31) E(-11) m 3 /kg.s 2 is only known up to five digits [6]. There are a variety of factors contributing to such large inaccuracy, some related to the design and operation of the equipment used to measure G [7], but some of them related to external factors as the date and epoch of the year [8], the time of day [9], and the location of laboratory on the surface of Earth [10]. The chemical and nuclear composition of materials used to determine G also play a significant role as demonstrated in the mid-1980s by Fischbach and collaborators [11][12][13][14] in their re-analysis of the classical 1890s Eötvös experiment to measure G with two different torsion balances [15].…”

Probing modified gravity with magnetically levitated resonators

“…To fully test MOND, gravitational accelerations must be utilized. Klein has recently argued that these torsion pendulum experiments are compatible with MOND [12]. Given the open debate on the universal applicability of Newton's gravitational law from the microscopic to galactic scales, i.e.…”

Shades of dark uncertainty and consensus value for the Newtonian constant of gravitation

“…Klein [33] o ers Modi ed Newtonian Dynamics (MOND) [43] as a striking and provocative explanation for why some measured values should lie as far away from the currently accepted consensus value [46] as they do, and shows how they can be "corrected. "…”