Novel Solution of Mercury Perihelion Shift

TL;DR

This paper introduces a new gravitational potential derived from a non-relativistic reduction of the Dirac equation, which explains Mercury's perihelion shift and predicts satellite frequency shifts consistent with observations.

Contribution

It proposes a novel gravitational potential from quantum mechanics that accounts for perihelion shift without free parameters and predicts GPS satellite frequency shifts.

Findings

Explains Mercury perihelion shift without free parameters.

Predicts GPS satellite frequency shift close to observed value.

Derives a new gravitational potential from the Dirac equation.

Abstract

We present a novel solution of the Mercury perihelion advance shift in the new gravity model. It is found that the non-relativistic reduction of the Dirac equation with the gravitational potential produces the new gravitational potential of $\displaystyle{V(r)=-{GMm\over r}+{G^2M^2m^2\over 2mc^2r^2}}$. This potential can explain the Mercury perihelion advance shift without any free parameters. Also, it can give rise to the $\omega-$shift of the GPS satellite where the advance shift amounts to $({\Delta \omega\over \omega})_{th} \simeq 3.4\times 10^{-10}$ which should be compared to the recent observed value of $({\Delta \omega\over \omega})_{exp} \simeq 4.5\times 10^{-10}$.