The pioneer anomaly is a rather well established phenomena wichs is still lacking a satisfactory explanation.
The Spanish physicist Antonio F. Rañada, well known in his country by his textbook about classic dynamics, and also by a semi divulgative book of introduction to physics (I would add that his theory of topological treatment of electromagnetism, elaborated in collaboration with Jose Luis Trueba is very estimable) in collaboration with Alfredo Tiemblo (sorry Alfredo, I don´t know anything about your work to cite it)have just written this paper that offers a possible explanation.
The idea goes as follows. The pioneer anomaly consist of an apparent excess of slowing down of the spacecraft, in his way out of the solar system, respect to the one predicted by general relativity. The most obvious interpretation of this anomaly would be a modification to the behaviour of gravity, in MOND (modified newton dynamics) like theories. A second possible interpretation, proposed by Anderson, is that the anomaly is apparent and not real. It comes from the way in the measurement of the effect. It involves the measurement of time by two methods, one depending in an atomic clock and the other depending on astrophysical inputs. Anderson introduces and ad-hoc difference in this two times as a possible explanation of the effect, but he gives no glimpse on how this desynchronization could arise.
Precisely that is the point of the Rañeda paper, they argue that the well know indeterminacy of energy and time, E.t=hbar, (which is referred by them as the fourth heisenberg indeterminacy) is affected by the averaged dimensionless
gravitational potential, i. e. the potential of all the mass-energy in the entire universe assuming that it is uniformly distributed. That leads to an increase of the lifetime of virtual pairs of electrons-positrons and , consequently, to a modification of the behaviour of atomic clocks (the details are actually a little more involved and go through the use of the optical density of vacuum, see the paper to re3ad about them.The order of magnitude of the effect agrees with the one needed to explain the Pioneer anomaly.
The latter part of the article explains how this effect is good because it explains the anomaly without conflicting general relativity. Also they explain that the nature of the effect makes that it is very hard to detect for other natural bodies in the solar system (mainly planets) so that it avoids conflicts with other observations.
Well, I am not at all expert in the pioneer anomaly so I cant judge how good this theory fits incorporation with other proposals. About the somewhat "quantum gravity" related effect that is behind his explanation the authors refers to other papers where they go into further details that I haven't read. With this limitations my judgement can´t be considered authoritative but my impression is that the paper looks very elegant and I hope that it will go in the right direction.
I will end this entry with an apology. I had begun(and almost has finished) to write a post about the recent claim by Craig Hogan about a possible observation of a quantum gravity related effect in the measurements of the geo 600 interferometer related to a theory developed by Hogan named "holographic noise". That theory is, basically, an implementation of the holographic principle of -hooft and susskind by a different mechanism to the already proposed (mainly the AdS/CFT correspondence). I had read two of the relevant arxiv papers and had outlooked the other and I explained briefly the ideas. Unfortunately my computer hanged before submitting the post and because of some unknown reason blogspot didn't conserve any draft copy. I hate to write things twice so I refer to the interested reader to press releases, like this one or to an blog entry on the subject in the bog "dynamics of cats".