I'd like briefly to revert to the 'thought experiment' I mentioned in my #41 above. An observer A sends an FTL message to observer B, who sends an FTL message acknowledging receipt back to A. I suggested, what I hoped was uncontroversial, that the time at which A sent his message to B would always be earlier than the time at which he received the return message from B, as recorded on A's own clock, static in A's inertial reference system. We could specify the procedure more precisely as follows:
- A's message reads: 'Dear B, I am sending you this message at time T1 as shown on my clock. Regards, A'. The time T1 could be printed automatically in the message, and simultaneously recorded as a mark on a moving tape in A's system, as in a seismograph.
- B's return message reads 'Dear A, I received your message sent at time T1 as shown on your clock, and I am sending this return message at time T2 as shown on my clock. Regards, B.'
- On receiving the return message, A would note the time T3 as shown on his clock, which could also be simultaneously recorded on A's moving tape.
Since A and B may be static in different inertial reference systems, with clocks which may be running at different rates, it is conceivable that T2 is chronologically earlier than T1, (e.g. if T1 reads as '3 p.m.' , T2 might conceivably read as '2 p.m.') But I contend that even if this is the case, T3 is still bound to be later than T1, which are times recorded in the same reference system. If the recording tape is running to the left, T3 will be recorded to the right of T1. Or we might imagine that the recording device uses a system of concentric circles, with later times recorded in circles 'further out' than earlier times. This would make the order of recorded times topologically as well as quantitatively recognisable.
If this is denied - if it is contended that T3 would be earlier than T1, and the mark recording T3 to the left of the mark recording T1, or in a circle closer to the center - then I think we are approaching physical absurdity of the 'killing one's grandparent' kind. Suppose A looks at his tape before sending his message: would he see a mark showing that he has already received a reply? Suppose he then has a heart attack (which would be understandable) and never sends the message at all? If I understand Markus's post #48 correctly, he would see this situation as a necessary result of the Lorentz transformations. If so, I would just see it as showing the inapplicability of the Lorentz transformations in this case. Moreover, if I am right that T3 must be later than T1 in A's reference system, then I think T3 must also appear later than T1 in any other reference system. According to STR, clocks may run at different rates in different inertial reference systems (as viewed from one another) but they never actually run backwards.