The experimental verification of certain formulas of the theory of relativity concerning Einstein's ideas about relative time and space cannot be called into question. But it is otherwise with respect to assert the validity of the interpretation of Einstein. Although proper time and length are as essential in the theory of general relativity as the isotropic law and the constancy of the speed of light in the Galilean systems of special relativity, this does not preclude to stress three antinomies that bring contradictions, scratch the invariances and cast a harsh light on the shortcomings of Einstein's theory: the Allais effect that seems to make vary the gravitational potential and therefore the proper time; the Pioneer effect indicating that the energy decreases with distance; the apparent superluminal neutrino which takes a shorter path than the photon, what we term "neutrino’s temporal oscillations". Several physicists deny the existence of these anomalies, others attribute them to technical failures or to experiment errors. We treat these three cases with the formulas of relativity with necessarily different points of views than Einstein, without, however, questioning the constant nature of the speed of light.