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 $10^{-11}m^3kg^{-1}s^{-2}$.