Precision measurement of the Newtonian gravitational constant

The Scale Invariant Vacuum Paradigm: Main Results and Current Progress

We present a summary of the main results within the Scale Invariant Vacuum (SIV) paradigm as related to the Weyl Integrable Geometry (WIG) as an extension to the standard Einstein General Relativity (EGR). After a brief review of the mathematical framework, we will highlight the main results related to inflation within the SIV, the growth of the density fluctuations, and the application of the SIV to scale-invariant dynamics of galaxies, MOND, dark matter, and the dwarf spheroidals. The possible connection between the weak-field SIV equations and the notion of un-proper time parametrization within the reparametrization paradigm is also discussed.

Additional Solar System Gravitational Anomalies

This article is motivated by uncertainty in experimental determinations of the gravitational constant, G, and numerous anomalies of up to 0.5 percent in Newtonian gravitational force on bodies within the solar system. The analysis sheds new light through six natural experiments within the solar system, which draw on published reports and astrophysical databases, and involve laboratory determinations of G, orbital dynamics of the planets and the moons of Earth and Mars, and non-gravitational acceleration (NGA) of ‘Oumuamua and comets. In each case, values are known for all variables in Newton’s Law F=G·M·mR2, except for the gravitational constant, G. Analyses determine the gravitational constant’s observed value, G^, which—across the six settings—varies with the mass of the smaller, moving body, m, so that G^=G×0.998+0.00016×lnm. While further work is required, this examination shows a scale-related Newtonian gravity effect at scales from benchtop to Solar System, which contributes to the understanding of symmetry in gravity and has possible implications for Newton’s Laws, dark matter, and formation of structure in the universe.

An Analytical Approach to the Universal Wave Function and Its Gravitational Effect

Based on quantum origin of the universe, in this article we find that the universal wave function can be far richer than the superposition of many classical worlds studied by Everett. By analyzing the more general universal wave function and its unitary evolutions, we find that on small scale we can obtain Newton’s law of universal gravity, while on the scale of galaxies we naturally derive gravitational effects corresponding to dark matter, without modifying any physical principles or hypothesizing the existence of new elementary particles. We find that an auxiliary function having formal symmetry is very useful to predict the evolution of the classical information in the universal wave function.