LIGO: The hypothesis of photons with non-zero rest mass

This study is done under the following assumptions: A) The results presented in the two relativistic works of Henri Poincaré "Sur la dynamique de l'électron" [1,2] are true. B) the "second principle" of Einstein, the constancy of the velocity of light, in "Zür Elektrodynamik der bewegten Körper" [4)], is not necessarily true and the photons can have an extremely small but non-zero rest mass m_o. Of course all photons will be considered as identical, an already common assumption for electrons, for protons and for all particles. In these conditions are analyzed the small modifications of the aberration of stars, of the Doppler-Fizeau effect, of the Maxwell equations for the propagation of electromagnetic fields, etc. Some test observations and experiments are proposed. The photon-photon interaction is analyzed. It may have very large consequences in astronomy and cosmology. (paper)