[yellowapple]

This explanation, like previous explanations for "FTL implies time travel" I've read, presupposes that the signal is actually moving at superluminal speeds, i.e. actually covering a distance greater than 299,792,458 meters in a single second from the signal's perspective. This would not be relevant for Alcubierre drives or wormholes or anything else that warps spacetime, since the whole point of such things is to stretch/contract space such that the thing is traveling a much shorter distance per second.

In short, if I were to instantaneously poof out of existence here on Earth, poof into existence on Mars a second later, grab a rock, poof out of existence again, and poof back into existence back on Earth again another second later and hand you that rock, it doesn't seem reasonable to assert that I traveled backward in time when I clearly traveled forward by two seconds. The whole lecture on that external observer is irrelevant, since there's nothing to observe unless the observer happens to be in my bubble/wormhole/whatever - and even then, one'd only be observing subluminal actions/signals within that region of spacetime.

[xenadu02]

The problem is that if FTL travel exists then our existing theories about spacetime are wrong in some way (despite making lots of great predictions) or time paradoxes are possible in which case we have no idea what the consequences could be.

Your example assumes there is some underlying rate at which time advances for the universe (or at least Earth and Mars) and that spacetime as we know it (including relativity and time dilation) are just some kind of modifier on top.

But theory and experiment so far point to that not being the case. There is no "pop out of existence here and pop in over there" without time travel (as best as we can tell). The whole light cone / worldline explanations are more formal explanations of that.

Now you can magic this problem away by proposing any number of schemes... like saying the entire universe's worldline is exists within a metaworldline and time travel actually resets the state of the universe as it was in the past then re-runs the universe... but all of that always proceeds forward in the metaworldline. In other words all past histories existed in a causal order, changing the past just adds "new commits" to the universe but history is never really rewritten. Bam! Our magic theory solves all paradox problems without requiring billions of parallel universes and allows time travel! But it's not a theory we can test or make predictions with so it isn't a useful scientific theory. It might as well be literal magic.

Similarly you could propose that GR is wrong... but your new theory is gonna need to match GR's predictions that have proven true while making some new ones we can test, while also avoiding or explaining causality and paradoxes.

[yellowapple]

> Your example assumes there is some underlying rate at which time advances for the universe (or at least Earth and Mars) and that spacetime as we know it (including relativity and time dilation) are just some kind of modifier on top.

Not necessarily; only that time is advancing in a forward direction. Whether 1 second on Earth is 1 second or 10 seconds or 0.1 seconds or what have you on Mars doesn't change the underlying premise: something disappeared from one place and appeared some positive amount of time later in another place. The only way I see that implying backward time travel is if time on Earth or Mars is already advancing backward, and if that's the case then the effects of Alcubierre drives on causality are probably the least of our worries.

And on that note...

> There is no "pop out of existence here and pop in over there" without time travel (as best as we can tell). The whole light cone / worldline explanations are more formal explanations of that.

The whole concept of a "light cone" seems to assume that spacetime is uniform (or at least doesn't have bubbles or holes in it). If spacetime is lumpy / Swiss cheesy (as Alcubierre drives or wormholes would cause, respectively), then that would result in similar lumpiness or holeyness in the light cone. In other words: why assume that it's "cone" shaped in situations that would in all likelihood dramatically deform that cone? In other other words: the light cone / worldline explanations don't really address cases where spacetime is outright deformed to shorten the distance something has to travel in order to go from point A to point B.

Further, the "light cone" argument (as presented in the article) seems to hinge on when observers find out about events... but just because an observer observed something to happen in a given order doesn't mean it actually happened in that order. If the light from Mars blowing up reaches us one second before the light from Pluto blowing up reaches us, does that mean that Mars blew up one second before Pluto did? It doesn't seem like observations are absolute truths, and I'm failing to understand why we're treating them as such.

[kelnos]

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.

The issue is that if you have a subluminal (but moving at a significant fraction of the speed of light) observer outside the reference frames of Earth and Mars, there are conditions where they could see you appear on Mars, and then communicate back to Earth -- before you left -- to tell you not to poof to Mars in the first place.

This doesn't have anything to do with the idea of physically moving through space at some rate (that is, "touching" every point between Earth and Mars during your journey there); poofing from one place to another would have the same effect. And I don't think it matters how much time you spend on Mars, whether it's 1 second or 1 day, before poofing back to Earth.

Also, this explanation does not suggest that the poofer has time-traveled to the past (as you argue against); it's the fast-but-subluminal observer who has done so.

At least that's how I understand it; I'm no physicist.

[yellowapple]

> 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.

----

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.