Eckard
"A and B are merely assumed to increase their distance. It did not matter if they possibly traveled in the same direction. Only their relative motion matters"
No, it is the distance which matters. If the distance is altering then the rate at which successive lights are received alters, and hence the perceived rate of change varies from the actual rate of change. This can be an outcome of both travelling at the same constant speed, in straight lines, but in different directions, or they are travelling at different speeds in the same direction, or any combination thereof. Put the other way round, the actual and perceived rate of change only remains the same if both are travelling at the same speed in the same direction, ie despite movement the distance remains constant over time, so the delay (duration) whilst light travels remains constant. So the frequency of receipt remains constant and the same as reality. Indeed, both could accelerate/decelerate, so long as they do that simultaneously. Einstein's 'hangup' with inertia was because of his concern about supposed length alteration at different speeds. He was not thinking of actual/perceived rate of change effects.
Re the Poincaré quote you picked up on. The point here is that he is talking about getting timing devices synchronised with a specific event, given that they are in spatially different locations. In other words, eliminating the effect of the spatial difference. So a timing device has to be set backwards if it is to tell the time of occurrence of a 'distant' event, in order to compensate for the duration incurred whilst the signal travels from that event. This is not how timing works. All timing devices are set to the same point in time and alter at the same rate. So they provide a common reference. Then, obviously, determining when an event occurred depends on calibrating distances and times of receipt of light. There was only one event, it cannot occur at different times. The two points have to be stationary, ie no alteration in distance over time, because of the way he is going about 'synchronising' these devices. Any given event (reality) occurred at a time. Any given other event may or may not have occurred at that same time. That's it, the occurrence of reality has nothing whatsoever to do with observation (ie the receipt of light).
Einstein picked this up and was meant to be applying it to observation, ie the signal becomes observational light. But he failed, because he had no observational light.
Re you translation, I seem to be confusing you. In the Introduction, the postulates are defined (as of second sentence second paragraph). The 1923 translation reads:
"They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the "Principle of Relativity") to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely..." What did he actually write?
Paul
