MacM: You say the Earth is at rest every time you talk about your silly 0.433c "launch point" of A and B, which you say has to be used to calculate the relative time dilation of A and B (non-existent, according to you). The fact that you don't recognise this shows just how far off the rails you really are. I only ever use the correct "relavistic" (sic) mathematics. I understand that the ECI frame is not a "common, local, preffered rest frame" (sic). L and E are the same frame. Are you getting confused again? Or trying to confuse? Can't you tell when something has been addressed? I've addressed it too many times to count. Wake up. A and B never record a "mutual" time dilation, because A and B are in different reference frames. Nothing they do is "mutual". I've already explained that to you very carefully above. Re-read it.