N ov 2 00 4 The Pioneer anomaly as an effect of the dynamics of time Antonio

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 τ with respect to the coordinate parametric time t, i. e. of the value of d2τ/dt2 (> 0). Assuming flat spatial sections and that all the matter and energy is uniformly distributed throughout the universe, it is shown that this inequality is an effect of the background gravitational potential of the entire universe. According to this model, the light speed, while being constant if defined with respect to τ (i. e. as dl/dτ) as is required in general relativity, would suffer an adiabatic secular acceleration, al = dc/dt > 0, if defined in terms of t (i. e. as dl/dt). It turns out that such an adiabatic acceleration of light (according to the second definition), and a small acceleration of the Pioneer towards the Sun aP 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, in such a way that aP = al/2. A simple estimation predicts aP ≃ 5.2 × 10−10 m/s, just about 40% smaller than the so-called Pioneer acceleration, which would correspond to the blueshift. 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 τ and t. The view presented here is the relativistic version of a previous Newtonian model.