Is the special theory of relativity (STR) a “simple” or “tricky” theory? They who think that it is a simple theory say (i) that its postulates are simple, that Nature is such, (ii) that the mathematics of STR is perfect, and (iii) that experiments support it.
I consider its two postulates to be very true, whereas the mathematics of the STR has a shortcoming, and, as for the experiments, the question must be posed: which theory do they support best? The problem for STR lies in the transition from its postulates to its basic equations, i.e., Lorentz
transformation and the velocity addition formula. The passage from the principle of relativity and the constancy of the speed of light to the basic equations of the STR is affected by four fundamental errors—three physical and one mathematical. Continuous attempts to reconcile these
latent mistakes have made STR increasingly tricky. As a result, it is in a similar situation to Ptolemy's geocentric model after “improvements” thereto by Tycho Brahe. However, the “Copernican solution” for relative motion—offered by extended Galilean relativity—is
very simple and effective.
Time Dilation and the Equivalence of Inertial Frames