The Light Speed and the Interplay of the Quantum Vacuum, the Gravitation of all the Universe and the Fourth Heisenberg Relation

A recently proposed model which accounts for the observed time dependence of the fine structure constant is summarized. The model is based on the combined effect of the fourth Heisenberg relation and the gravitation of all the expanding universe on the quantum vacuum. As is shown here, it predicts that the light must have now an acceleration close to H₀c≃6.9×10^-10 m/s². This suggests an explanation of the anomalous acceleration a_P≃8.5×10^-10 m/s² found in the Pioneer 10 spacecraft, because an acceleration of light has the same radio observational signature as an acceleration of the ship.