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A closed time-like curve is defined as a word-line that returns to its starting point, in the $x$, $y$, $z$, $t$ coordinates. So, for a chronology respecting observer, an object traversing a closed time-like curve would appear to violate causality. Under certain conditions (Tolman et al.), superluminal propagation of signals also appears to violate causality. Does this indicate that for a tachyonic anti-telephone situation, the worldline of a superluminal tachyon could be considered as a closed time-like curve?

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No. The world-line of a tachyon is spacelike. That's the definition of a tachyon. That means it can't be a closed timelike curve.

The existence of CTCs is a property of the spacetime, not of the particles inhabiting it. Minkowski space simply doesn't have CTCs.

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  • $\begingroup$ I see. And does the same logic apply to other methods of apparent superluminal motions, like wormholes? $\endgroup$ – CuriousDroid Sep 10 at 21:56
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    $\begingroup$ @CuriousDroid: No, in a traversable wormhole, there really can be CTCs. That is a different property of that spacetime. $\endgroup$ – Ben Crowell Sep 10 at 22:38
  • $\begingroup$ I see. So a wormhole that allows for superluminal motion relative to an outside observer, but that does not have a relative time shift between the mouths, that would NOT produce a CTC, but still allow for an apparent causality violation? $\endgroup$ – CuriousDroid Sep 11 at 0:07

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