Conformal gravity: Newton's constant is not universal

Abstract

Newton's gravitational constant $G$ has been measured to high accuracy in a number of independent experiments. For currently unresolved reasons, indicated values from different well-designed and thoroughly analyzed experiments differ by more than the sum of estimated errors. It has recently been shown that requiring both Einstein general relativity and the Higgs scalar field model to satisfy conformal symmetry (local Weyl scaling covariance) introduces gravitational effects that explain anomalous galactic rotation, currently accelerating Hubble expansion, and dark galactic halos, without invoking dark matter. This implies different values $G_n$ and $G_p$ for neutron and proton, respectively, but retains the Einstein equivalence principle for test objects accelerated by a given gravitational field. Isotopic mass defect $\mu$ per nucleon determines independent $G_m$. Thus G differs for each nuclear isotope. Several recent measurements are used here to estimate $G_n=6.60216$, $G_p=6.38926$, and $G_m=-11.60684$ in units $10^{-11}{m}^{3}k{g}^{-1}{s}^{-2}$.

4 pages, 1 figure, accepted for publication by EuroPhys.Lett

References in corpus (5)

• Precision Measurement of the Newtonian Gravitational Constant Using Cold Atoms
• The Radial Acceleration Relation in Rotationally Supported Galaxies
• Impact of a global quadratic potential on galactic rotation curves
• Fourth order Weyl gravity
• Schwarzschild limit of conformal gravity in the presence of macroscopic scalar fields