The Pioneer anomaly as an effect of the dynamics of 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 $\mathrm{d}\ell /\mathrm{d}\tau$), would suffer an adiabatic secular acceleration, $a_{\ell }=\mathrm{d}c/\mathrm{d}t>0$, if defined in terms of $t$ ({\it i. e.} as $\mathrm{d}\ell /\mathrm{d}t$). Such an adiabatic acceleration of light, and a small acceleration of the Pioneer towards the Sun $a_{\mathrm{P}}$ 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 $t$.

25 pages,2 figures. New text and new figures in this version