Conformal gravity: Newton's constant is not universal

TL;DR

This paper explores how conformal gravity theories imply that Newton's gravitational constant G is not universal but varies for different particles and isotopes, challenging the traditional notion of a single G value.

Contribution

It introduces a conformal gravity framework that explains galactic phenomena without dark matter and shows G varies for neutrons, protons, and isotopes based on recent measurements.

Findings

G varies for neutrons, protons, and isotopes

Conformal gravity explains galactic effects without dark matter

Measured G values differ for different particles

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