So you mean that in the original Einstein's example when it is said "Just when the flashes of lightning occur, the point M' coincides with the point M...", it is meant that when the points coincide the flashes occur but only for the observer on the embankment - so the whole example is described...
That is exactly what I want you to imagine - that they are aware of the experiment. Because the flashes of lightning occur just when points M and M' coincide, therefore both observers can experience that moment equally well, and will know that two beans of light are traveling(from point A and B...
In special relativity the relativity of simultaneity is explained with the following example.
We have one frame of reference - a train moving from left to right with constant speed v relatively to the embankment, and second frame of reference - the embankment itself. On the embankment there are...