Standard textbooks introduce Special Relativity in this way:
- They introduce two postulates, the second being something like that
The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source [consenus definition on the english wikipedia page ]
"... light is always propagated in empty space with a definite velocity [speed] c which is independent of the state of motion of the emitting body" [A. Einstein]
- They define Einstein synchronisation which relies on the knowledge/assumption that the speed of light is everywere constant
The problem that I see is this one:
The postulate is speaking about any measure of "speed" and the meaning of (mean) "speed" is supposed to be $\Delta s/\Delta t$ (as far as the reader knows) where $\Delta t=t_1-t_2$, $t_1$ and $t_2$ being two measured times. If the times $t_1$ and $t_2$ are measured in two different positions we need to know in advance how to syncronise distant clocks but we don't know yet and we will know how to do it only afterwards: with Einstein synchronisation. But Einstein syncronisation relies on the postulate itself: it assumes that the "speed" of light is constant. This seems to produce a logical circularity: speed of light is (obviously) constant just because we define synchronisation in order to make it "artificially" constant? (*)
And what is the postulate actually telling us? We don't know what is "speed" yet since we don't know how to define time for spatially distant places. Maybe the postulate is supposed to be linked with Einstein synchronisation in order to define what is "speed"?
What actually is speed/velocity on a general (non circular) path when we drop absolute time? Before postulating anything about speed of light we need in the first place to know what speed is, and the definition shouldn't rely on the use of the notion of velocity itself that is the case with Einstein's synchronisation!
Can anyone clarify this issue?
(*) I know the M-M experiment proved that speed of light is constant when measured as an average in a closed path with mirrors but I would say it doesn't say anything about the speed of light in any non-closed interval of the path.