The Pioneer anomaly as an effect of the dynamics of time

TL;DR

This paper proposes that the Pioneer anomaly results from the acceleration of cosmological proper time relative to coordinate time, causing an apparent acceleration of light and a blue shift, rather than actual spacecraft motion.

Contribution

It introduces a novel explanation for the Pioneer anomaly based on the dynamics of time and the background gravitational potential of the universe.

Findings

The anomaly can be explained by the acceleration of light due to time dynamics.

The observed blue shift is an effect of time acceleration, not spacecraft acceleration.

The model links the Pioneer anomaly to the interplay between proper and coordinate time.

Abstract

A model is presented in which the Pioneer anomaly is not related to the motion of the spaceship, but is a consequence of the acceleration of the cosmological proper time $\tau$ with respect to the coordinate parametric time $t$, what is an effect of the background gravitational potential of the entire universe. The light speed, while being constant if defined with respect to $\tau$ ({\it i. e.} as ${\rm d}\ell /{\rm d} \tau$), would suffer an adiabatic secular acceleration, $a_\ell={\rm d}c/{\rm d}t >0$, if defined in terms of $t$ ({\it i. e.} as ${\rm d}\ell /{\rm d} t$). Such an adiabatic acceleration of light, and a small acceleration of the Pioneer towards the Sun $a_{\rm P}$ could be mistaken the one for the other, because they do have the same fingerprint: a blue shift. However, this shift would be quite unrelated to any anomalous motion of the Pioneer, being just an observational effect of the acceleration of light with respect to time $t$. The Pioneer anomaly turns out then to be an interesting case of the dynamics of time, its explanation involving the interplay between the two times $\tau$ and $t$.