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.
> 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.
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.