At the end of the XIX century Poincar? had the idea that one way velocities are not measurable. To measure them one needs synchronized clocks, but to synchronize clocks one needs to know the one way velocity of some signal. It seems a perfect logical loop, impossible to overcome. Einstein essentially adopted the idea when he defined the velocity of light as constant to formulate the TSR. In 1927 the German philosopher of science Hans Reichenbach, discussed this definition concluding that even if essential for the TSR, it was “not epistemologically necessary.“
Half a century later, in the years 1977-1984, Max Jammer produced a very stimulating reconstruction of the debates about the notion of distant simultaneity. He stressed that one cannot know the simultaneity of distant events at all since simultaneity is arbitrary; and therefore we can lay down whatever definition we wish concerning it, without giving rise to any error. At this point several people must have felt that the Reichenbach-Jammer conjecture was too self-assured for a statement almost completely lacking empirical support. Researches trying to confirm/invalidate the conjecture actually started in several places.
If the coefficient of the space variable x in the Lorentz, or other, transformation of time (we call it e1) had a conventional nature it should be possible to modify it without touching the empirical predictions of the theory. Given that Einstein’s principle of relativity leads necessarily to the Lorentz transformations, and thus also to a fixed value of e1 , such a modification would imply a reformulation of the relativistic idea itself. With respect to the idealized initial picture, the concrete development of research has produced some exciting novelties. Several phenomena, in particular those taking place on accelerating systems (Sagnac effect, and all that) converge in a strong indication of the value = e1. This implies absolute simultaneity and a new type of space and time transformations, which we call "inertial". The cosmological consequences of the new structure of space and time go against the big bang model. After these results relativism, although weakened, is not dead, but survives in milder forms.