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Under what conditions would it be possible to create closed timelike curves, assuming an Alcubierre drive could exist? Would it be possible to have the latter without the former?

See here for information on the chronology protection conjecture.

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2 Answers 2

If somehow, it is only possible to create one alcubierre drive, and it can never turn around, then you won't get closed timelike curves. Otherwise, any construction is going to have them.

The reason is that you can "zoom out" far enough that the distortions to spacetime caused by the drive are no longer present, and the person flying the drive then just looks like a spacelike curve in the spacetime. At that point, you're just travelling along spacelike curves, and all the special-relativistic causality objections apply.

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We can't say much about closed timelike curves with any certainty; they are an artefact of the existence of solutions to the general relativity equations which allow them. It is possible (and quite a few physicists believe this) that a theory of quantum gravity may preclude CTC from occurring, or that CTC may occur but the information might be censored by an event horizon. It is also possible that CTC may occur but only Universes which fail to contain paradoxes exist, in which case it is unlikely that humans will ever have the ability to create CTC.

Using only Einstein's general relativity, anything that allows information to travel faster than $c$ could create a closed timelike curve and potentially the paradoxes which accompany this sort of thing. So, no, you can't have an Alcubierre drive without the ability to create closed timelike curves, even if you only travel in one direction (no offense to @JerrySchirmer but we part ways on this fact). Consider two events A and B, where in all subluminal frames of reference A barely causes B by communication at speed $c$. You're heading FTL in the opposite direction: in your frame of reference B actually precedes A. Now you can contact A after B happens as you fly by (to prevent B from ever happening). Whoops.

UPDATE

I've looked into this, and Jerry is indeed correct, at least in part: one-way FTL travel looks paradoxical to the traveler, but is otherwise paradox-free. However, I believe the drive would need to create gravity wells on the order of a black hole to function properly which means any object in its vicinity (e.g. a mass that gets clipped by the bubble as it passes) could create a closed timelike curve. So no, it can't directly cause a paradox; but you can't prevent the possibility of indirect paradoxes caused by the wake of the device.

This took me a while to figure out in part because what an Alcubierre drive would actually do is inconsistent with general relativity, and GR principles are what the device is based upon. This leaves you with an ill-defined object. The main problem is that there exists no fixed "background" to spacetime, so the only way the bubble can move something is by causing it to "fall" in one direction (a relativistic hill behind you, a gap before you, and the bubble moves with you as you fall). This means it grabs hold of you by accelerating you in one direction; and if the bubble ever goes FTL, it must lose its cargo in the process (you'll slide backwards over the hill). This implies that the only objects that can go FTL inside the bubble are objects which were already going FTL to begin with, in which case you didn't need the bubble in the first place.

(Not to mention, it breaks enough conservation laws to make Emmy Noether spin in her grave.)

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Alcubierre's original published metric is free of CTC. You can get superluminal global travel without CTC, so long as there's no turnaround -- just think of the stars beyond the cosmological horizon. Their proper distance with respect to us is greater than the speed of light, but it just doesn't matter, because there's no way to send a signal back and forth, or for them to "turn around". –  Jerry Schirmer Jul 30 at 16:41
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@JerrySchirmer It still feels like it should be breakable; I'll futz with it next week (after con) and report back should I create a rift in the spacetime continuum. :) –  Trixie Wolf Jul 30 at 21:03
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I'm somewhat uncertain about this. Assuming B is 1 light second north of A. A generates the signal. We instantly jump 1 light second south then stop. We won't see A generate the signal for 1 second and see B respond 3 seconds later. Could you go into more depth about the scenario where you effect past events (as opposed to just observing them out of order) –  Richard Tingle Jul 31 at 19:15
    
@RichardTingle It's a little complicated. I will respond when I return from my trip out of state (Monday or Tuesday). It's easy to be confused about relativity, and the most common error is in thinking it has something to do with the travel time of light. It's not the observation that changes, it's the actual order in which the events happen that changes (which allows you to detect an event and then prevent it from ever happening). When you hit c everything happens all at the same time; past this, cause and effect (in some frames) will actually reverse. –  Trixie Wolf Jul 31 at 21:27
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@JerrySchirmer I finally updated the answer. –  Trixie Wolf Aug 11 at 23:51

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