A proposal that explains the Pioneer anomaly
  We propose here an explanation of the Pioneer anomaly which is not in conflict with the cartography of the solar system. In our model, the spaceship does not suffer any extra acceleration but follows the trajectory predicted by standard gravitational theory. The observed acceleration is not real but apparent and has the same observational footprint as a deceleration of astronomical time with respect to atomic time. The details can be summarized as follows: i) as we argued in a recent paper, there is an unavoidable coupling between the background gravitation that pervades the universe and the quantum vacuum because of the long range and universality of gravity; ii) via the fourth Heisenberg relation, we show that this coupling causes a progressive desynchronization of the astronomical and atomic clock-times, in such a way that the former decelerates adiabatically with respect to the latter; and iii) since gravitational theory uses astronomical time and the observers use atomic time (they are using devices based on quantum physics), this desynchronization necessarily causes a discrepancy between theory and observation, so that the observed velocity of the spaceship is smaller than the predicted one, in such a way that the Pioneer seems to lag behind its expected position. The discoverers of the anomaly suggested "the possibility that the origin of the anomalous signal is new physics" although they added "the most likely cause of the effect is an unknown systematics," but also that "In the unlikely event that there is new physics, one does not want to miss it because one had the wrong mind set." 
Antonio F. Ranada and Alfredo Tiemblo