Pioneer Effect: An Interesting Numerical Coincidence

Abstract

We note that if we construct from the observed anomalous acceleration \(a_P=(8.74\pm1.33)\times 10^{-10}m/s^2\) of the spacecrafts Pioneer 10 and 11 towards the Sun, the proton mass \(m_p\) and Newton's gravitational constant \(G\) a quantity \(\ell_P:=(Gm_p/a_P)^{1/2}\), which has the same dimension as length, then \(\ell_P\) is roughly of the same order of magnitude as is the Compton wave length of a proton. We formulate a simple quantum mechanical hypothesis, which aims to provide an explanation to this interesting numerical coincidence.