Empirical evidences in favor of a varying-speed-of-light

Abstract: The empirical evidences in favor of the hypothesis that the speed of light decreases by a few centimeters per second each year are examined. Lunar laser ranging data are found to be consistent with this hypothesis, which also provides a straightforward explanation for the so-called Pioneer anomaly, that is, a time-dependent blue-shift observed when analyzing radio tracking data from distant spacecrafts, as well as an alternative explanation for both the apparent time-dilation of remote events and the apparent acceleration of the Universe. The main argument against this hypothesis, namely, the constancy of fine-structure and Rydberg constants, is discussed. Both of them being combinations of several physical constants, their constancy imply that, if the speed of light is indeed time-dependent, then at least two other "fundamental constants" have to vary as well. This defines strong constraints which will have to be fulfilled by future varying-speed-of-light theories.