> I think you're missing one factor, though: the fast-but-subluminal observer. You're only considering Earth and Mars, and someone poofing between the two.

There wouldn't be anything meaningful to observe:

- An observer on Earth would see me poof out of existence and poof back into existence with a rock in my hand; a few minutes later, with a really good telescope, that observer might see me poof into existence on Mars, take a rock, and poof back out of existence.

- An observer on Mars would see me poof into existence, take a rock, and poof back out of existence; a few minutes later, with a really good telescope, that observer might see me poof out of existence on Earth and poof back into existence while holding a rock.

- An observer somewhere in between with a really good telescope might be able to see the poofing in and out of existence on Earth and/or Mars, but would only receive that light after I had already returned to Earth, and would lack the necessary information to reliably assert which happened first.

The relevance of that fast-but-subluminal observer is dependent on me actually traversing every last micron of space from Earth to Mars and back in those two seconds, but that ain't what's happening. Rather, I'm taking a shortcut, and in order for the observer to observe anything other than the endpoints said observer would need to be taking that same exact shortcut alongside me - otherwise, at worst, the observer just sees two copies of me (one on Earth, and one on Mars), and by the time the observer thinks to do anything about that I would already have handed you a Mars rock.

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The more mathy explanation of this involves the Lorentz factor, which in Lisp (because I'm on my computer and Emacs is handy) is (assuming c = 1):

(defun lorentz-factor (v) (/ 1 (sqrt (- 1 (expt v 2)))))

where v is the relative velocity between to reference frames. So, (lorentz-factor 0.1) would correspond to something moving at 0.1c, (lorentz-factor 1) would correspond to something moving at the speed of light, and (lorentz-factor 2) would correspond to something moving at twice the speed of light.

You'll notice that (lorentz-factor 1) produces a division by zero, and that anything past that produces imaginary numbers. That's the basis for the "FTL implies time travel" argument; it assumes that something is actually traveling at a faster-than-light velocity (i.e. actually moving through every last micron of the space from Earth to Mars and back within those two seconds) and thus producing a Lorentz factor which - when plugged into a full Lorentz transformation - would imply backward time travel.

However, that ain't really applicable to the "poofing" above (nor is it applicable to Alcubierre drives or wormholes, of which said "poofing" is an abstraction), because the specific premise here is that I am not actually moving at a velocity significantly above 0; instead, I'm stretching the space behind me / contracting the space in front of me (in the case of an Alcubierre drive) or punching a shortcut between two points in space (in the case of a wormhole) such that I don't have to move at a speed significantly greater than zero. Since my velocity remains basically 0, my Lorentz factor ends up being basically 1, and thereby eliminates the mathematical basis for my "poofing" having any implication of backward time travel.