Pioneer acceleration and variation of light speed: experimental situation

TL;DR

This paper discusses a model where the speed of light varies with gravitational potential, potentially explaining the Pioneer anomaly through cosmological effects on light speed and proper time, consistent with current relativity tests.

Contribution

It proposes a novel explanation for the Pioneer anomaly based on light speed variation with gravitational potential and cosmological time effects, aligning with established physics.

Findings

Light speed increases with gravitational potential.

Cosmological acceleration of light explains Pioneer anomaly.

Model consistent with relativity and equivalence principle.

Abstract

The situation with respect to the experiments is presented of a recently proposed model that gives an explanation of the Pioneer anomalous acceleration $a_{\rm P}$. The model is based on an idea already discovered by Einstein in 1907: the light speed depends on the gravitational potential $\Phi$, so that it is larger the higher if $\Phi$. The potential due to all the mass and energy in the universe increases in time because of its expansion, which has the consequence that light must be slowly accelerating. Moreover it turns out that the observational effects of a universal adiabatic acceleration of light $a_\ell =a_{\rm P}$ and of an extra acceleration towards the Sun $a_{\rm P}$ of a spaceship would be the same: a blue shift increasing linearly in time, precisely what was observed. The phenomenon would be due to a cosmological acceleration of the proper time of bodies with respect to the coordinate time. It is shown that it agrees with the experimental tests of special relativity and the weak equivalence principle if the cosmological variation of the fine structure constant is zero or very small, as it seems now.