The purpose of this paper is twofold: (1) to discuss the basis of the Lorentz transformations showing that the invariance of the velocity of light has in them a role even more important than usually believed, and (2) to find the complete set of theories empirically equivalent to the special theory of relativity (STR) under the assumption that the one-way velocity of light is not measurable.
In particular it will be shown that any modification of the coefficients of the Lorentz transformation, however small, gives rise to an ether theory, in the sense that the modified theory necessarily predicts the existence of a privileged frame that in principle can be detected experimentally, Therefore all the theories equivalent to STR but based on different transformation laws, must necessarily negate the validity of the relativity principle. We will come thus to the surprising conclusion that if the one-way velocity of light is not measurable, the content of the relativity principle is entirely conventional, since it can be affirmed or negated without any practical change in the predictive power of the theory.
