[bitdizzy]

So the thing that paper does is it assumes you can make warp bubbles in any reference frame. The original paper makes one warp bubble and this doesn't lead to anything paradoxical.

But if I can make two warp bubbles in two different frames, I can make a round trip that arrives before it starts.

So you need to violate special relativity in a global way to avoid these issues. You have to have a spacetime where only certain warp geometries are possible.

I apologize for being a bit impatient before, these issues are subtle. The only real way to get it is to bear with the math onesself.

[yellowapple]

> I apologize for being a bit impatient before, these issues are subtle.

No worries, and thanks again :)

> But if I can make two warp bubbles in two different frames, I can make a round trip that arrives before it starts.

Even for the metric as Alcubierre describes? Or for one that's modified per Everett? Now that I'm rereading the Everett paper, I'm not really sure where he's getting his "Lorentz boost"; if there's technically no actual "motion" (because everything's locally at rest and the warp bubble is outright expanding/contracting space around it), then I'm having a hard time figuring out what there would be to "boost", since the relevant Lorentz transformations should be no-ops if everything's locally at rest. Is Everett moving the ship itself at relativistic speeds within the bubble? Is an observer moving at relativistic speeds outside the bubble?

> So you need to violate special relativity in a global way to avoid these issues.

Which the universe kinda already does, no? The mechanism here (from what I understand) is the same as the one driving universal expansion (the difference being that there's no corresponding contraction in the universal case - right?). If that expansion were to be reversed somehow, would that, too, result in causality violations?

And further, doesn't special relativity already only hold in cases with low gravitational potential - so i.e. not in a gravitational field?

Sorry if these are kinda dumb questions.

[bitdizzy]

A lorentz boost is just a change of perspective. Let's say you have a bubble that is at rest with respect to your reference frame. Well, someone flying by your solar system has just as valid a reference frame as you and they see the bubble moving with respect to them. The relation between their point of view and yours is described by a lorentz boost. Same physical situation, different perspective.

Now, if special relativity holds in the large then there is no reason why they can't also construct a warp bubble. Relative to you and your bubble that bubble is in motion. Since this is allowed, we can construct a closed timelike curve with two judiciously chosen bubbles.

> Which the universe kinda already does, no?

The expansion of the universe does violate special relativity but not in a way that protects warp geometry from creating paradoxes. The kind of violation you would need would distinguish between frames of reference that SR says are equivalent.

> And further, doesn't special relativity already only hold in cases with low gravitational potential - so i.e. not in a gravitational field?

Special relativity holds well enough in most situations that the same argument applies even if you accounted for general relativity except near extreme situations like black holes

Warp drives are not permitted by any deviation from special relativity. You need specific contrived geometries of the entire universe that don't match up with what we know about it.

[SideburnsOfDoom]

> The expansion of the universe does violate special relativity

I am curious as to how?

If, we take as axiomatic that there is no such thing as "an object in motion", only "an object in motion with respect to another object", i.e. motion is not a property of an object, but a relation between two objects.

And that since it's 4.3 light-years to Alpha Centauri, therefor a cause (e.g. a radio wave) sent from Earth today cannot have an effect (e.g. an Astronomer writes a paper about it) at Alpha Centauri for 4.3 years, and vice versa. There is 4.3 years of "Absolute elsewhere" to get through first where there is no possible cause-and-effect relation between events. At the other side of our galaxy it's around 100 000 years. And further out, objects are not just far, but receding from us (or us from them, equivalently)

Assuming an unbounded and expanding universe, for very distant parts of the universe receding from us at lightspeed (or speeds faster than light?) and us from them, equivalently. So lightspeed signals from there never reach us, by definition? That part is is utterly unobservable, permanently Absolute elsewhere. The universe's observable edge is a slowed-down red-shift that trails off into the unobservable. In other words, the at no time in the future will those signals have an effect on Earth, or us on them. So, they can't have an effect in our future, let alone our past. No impact to causality at all?

[bitdizzy]

> I am curious as to how?

Special relativity describes a flat lorentzian manifold. The uniform expansion of the universe implies that the curvature of spacetime is slightly negative.

Special relativity is not simply a theory of causality but specifically of the geometry of spacetime. From this theory you can derive predictions about specific phenomena, like causality.

But that doesn't mean other spacetime geometries don't share properties with flat minkowski spacetime. Just not all properties. For example there is no cosmological horizon in minkowksi spacetime but there is for our universe.

[SideburnsOfDoom]

> Cosmological horizon

https://en.wikipedia.org/wiki/Cosmological_horizon

Oh, that's the term that I was groping for. Thanks!