I thought the "closed" part of closed timelike curves takes care of that. Like in a Feynman diagram where a photon splits and recombines into an electron/positron pair, isn't that equivalent to an electron looping through time and annihilating itself? You could argue it's just a formalism, but mathematically it still seems like (trivial) time travel.
Why can't you extend that from a single particle to a system of particles? Where's the math break down?
No, in a closed timeline curve, the closed portion means "You can arrive where you started, eventually, if you turn around or whatever." The timelike means that you have, effectively, gone into the past.
Wherein you can shoot yourself before you step into your FTL ship.
though, I still don't see how FTL has to cause paradoxes. What if a wormhole connects you to your destination's past, specifically the 4.3 years ago? There's no causality paradox because both points are in each other's light cones. Earthicans can watch you live by telescope.
...oh. that would imply that you'd see Earth 4.3 years in the future by telescope, while stepping back into the wormhole would either take you into the future (not closed timelike) or to the past (where a Centaurian could shoot themself.) I see.
Why can't you extend that from a single particle to a system of particles? Where's the math break down?