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But this isn't really time travel, because if you tried to send a message back to Sol telling yourself not to set out, it would always arrive after you left (due to the fact that the backward-propagating effects always go slower than their rated speed in the preferred frame).
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I don't quite understand. Does this impose a speed limit on the FTL? Suppose you have a path in the preferred frame that gives you negative displacement in time. I can see that going back by the same route moves you back forward. But what about a return path not in the privileged frame? That is, you FTL to Alpha Centauri, pick up -5 years, then radio a message back through normal space. That takes four years, but would arrive before you left. If the latter is forbidden, then it must be that you can't get -5 years on that particular trip.