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It's very unlikely. If Dave has Carol diary, then Carol made the trip already, so Carol will notice empty fuel tanks and big holes in the shield. She will may have problems with memory, but she is not stupid.

No she didn't. X is the point in spacetime where Carol begins her trip. From her perspective, Dave came from the future.

The only reason that this cannot happen is that X and Y are so far away in space, and close in time, that it is impossible to travel between them.

Sorry, I cannot follow you here. Maybe it's well known thought experiment, but I'm unable to find it.

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