For whatever reason, this post is causing me to be accused of being someone I am not etc. However, in different forums a correct answer was not given to this problem. Also, I am not sure if this forum allows questions like this to be asked. If not, just remove it and this is fine.
Anyway here it is.
This is a modification to the train-embankment experiment. I am hoping someone can solve this problem. Assume when M and M' are co-located, lightning strikes their common location. There is also an observer B' in the negative direction of M’. After some time elapses in each frame, B' and M become co-located. Considering only the negative and positive x directions, the goal is to determine all of the special relativity truths for the lightning light beams at the instant M and B' are co-located. 1) The light beams are equidistant from M in the M frame. So, label these locations as (d,0,0) and (-d,0,0). 2) The light beams are equidistant from M’ in the M’ frame. So, label these as (d’,0,0) and (-d’,0,0) To make it simple, label the common frame event of B’ and M being co-located as P. So, P is true if and only if B’ and M are co-located. Below are additional truths. 3) If P is true in M, then P is true in M’. 4) If P is true in M’, then P is true in M. 5) Therefore, if P is false in M’ then P is false in M. 6) Also, if P is false in M then P is false in M’. Do the lorentz transforms work consistently under these assumptions?