Undergrad Is the Alcubierre Warp Drive possible?

[PAllen]

The Alcubierre's warp drive spacetime does have closed timelike curves. This spacetime can be modified to produce spacetimes that do have closed timelike curves, but loads of spacetimes, including Minkowski spacetime, can be modified to produce spactimes that have closed timelike curves.

All you need to do is link up two bubbles as in the tachyonic antitelephone to create a CTC. Long ago, @bcrowell posted a paper on this.

 

[Janus]

The question is - is this a technology which can be operated at will. That would be different from the issue of whether nature might generate something like this, outside of human intentions. If I have a friend 4 light years away, and one day I've got a black box I invented which can send him a letter in what he and I both agree is 3 years, then we are in causality violation territory. Say we've been sending chess moves back and forth at the speed of light then one day I have a black box (containing Alcubierre drive with warp bubble) and I put my chess move in it and send it to him in 3 years. Then he sends the object back to me in 3 years with his move.

No, that does not involve any causality violation. For a causality violation, you would need two separate inertial frames, in relative motion with respect to each other and sending FTL messages back and forth. This is the result of the simultaneity of relativity.
So let's say that you have two spaceships traveling at 0.5c relative to the Earth, and a string of space buoys at rest with respect to the Earth strung out along its path. Space ship 1 passed Earth when its both clocks read 0. 1 year later by his clock, when he is 1/2 light year from the Earth, as he measures the distance, he sends a instantaneous message (any FTL signal will produce similar results, it's just simpler to assume instant messages) back to to spaceship 2 just as it is passing the Earth. Both spaceship 2 and Earth will agree that the Earth clock reads 0.866 yrs as spaceship 2 passes. The message is transferred to the Earth and it then sends a reply instantaneously to a space buoy that is 0.433 ly away in the same direction as spaceship 1. In the Earth frame, this buoy is right next to spaceship 1 at that moment and the reply is transferred to spaceship 1. Assuming that the clocks on the buoy and Earth are synchronized in the Earth rest frame, the buoy clock reads 0.866 years at that moment. However, according both buoy and spaceship 1, spaceship 1's clock only reads 0.75 yrs, 1/4 of a year before he sent the original message. He gets his reply before sending the message.

I'm not sure how the Alcubierre drive would work in this scenario, as you would need to use it to deliver the messages back and forth.

 

[George Jones]

The Alcubierre drive, of course, allows closed timelike loops and causality violations.

Give an explicit, mathematical demonstration the Alcubierre warp drive spacetime contains closed timelike curves.

 

[George Jones]

All you need to do is link up two bubbles as in the tachyonic antitelephone to create a CTC. Long ago, @bcrowell posted a paper on this.

This is not the Alcubierre warp drive spacetime.

 

[Dale]

loads of spacetimes, including Minkowski spacetime, can be modified to produce spactimes that have closed timelike curves.

Well, Minkowski can only be modified to have a CTC with unusual topology, like a torus. The Alcuiberre spacetime can get a CTC with standard topology.

 

[Heikki Tuuri]

https://en.wikipedia.org/wiki/Faster-than-light
The Alcubierre drive allows superluminal communication, and according to Wikipedia, that is equivalent to time travel. Then we will have all the paradoxes of time travel. And that is in an asymptotic Minkowski space - we would not need any wormhole to make a causal loop. The Alcubierre drive is enough.

 

[PeterDonis]

according to Wikipedia

Wikipedia is not a valid source. You need a textbook or peer-reviewed paper.

 

[PAllen]

This is not the Alcubierre warp drive spacetime.

True, but if more than one drive in the universe is possible, it suggests CTCs would be possible.

Here is the paper:

http://exvacuo.free.fr/div/Sciences...tt - Warp drive and causality - prd950914.pdf

 

[DrStupid]

For a causality violation, you would need two separate inertial frames, in relative motion with respect to each other and sending FTL messages back and forth.

A single message could be sufficient. With two events A and B, where one of them is the cause of the other, causality is violated if the order of the events is frame dependent. In Minkowski space this would be the case if the interaction is faster than a light signal traveling in vacuum directly between A and B. However, in the current discussion this would be only helpful if the Alcubierre warp drive can be used in a way that keeps the spacetime between A and B flat. PeterDonis sounds like this is not possible.

 

[PeterDonis]

this would be only helpful if the Alcubierre warp drive can be used in a way that keeps the spacetime between A and B flat. PeterDonis sounds like this is not possible.

Of course it's not possible. Alcubierre spacetime is not flat. If an Alcubierre drive travels between A and B, then spacetime between A and B is not flat.

 

[Heikki Tuuri]

https://arxiv.org/abs/gr-qc/9810026
The paper by Matt Visser et al. suggests that the Alcubierre drive breaks the Null Energy Condition.

The paper is not peer-reviewed. The fact that if you can do unrestricted superluminal travel then you can make causal loops, is folklore that everybody seems to know, but it is hard to find a peer-reviewed reference. The math is easy and can be found from my own blog, year 2013.

If you restrict the superluminal travel, then you can prevent causal loops. One may, for example allow a superluminal trip on Earth as long as it takes you forward in the UTC time coordinate. Causal loops cannot happen because the UTC time always advances on every trip.

 

[DrStupid]

If an Alcubierre drive travels between A and B, then spacetime between A and B is not flat.

My question was not limited to this special case. The ship can also go a long way around, running the warp drive only far away from A and B and flying the rest with conventional engines.

 

[George Jones]

https://arxiv.org/abs/gr-qc/9810026
The paper by Matt Visser et al. suggests that the Alcubierre drive breaks the Null Energy Condition.

I am not disputing the fact that Alcubierre warp drive spacetime violates one or more energy conditions, but violation of an energy condition is not a (mathematically) sufficient condition for closed timelike curves.

The paper is not peer-reviewed. The fact that if you can do unrestricted superluminal travel then you can make causal loops, is folklore that everybody seems to know

What does "superluminal travel" mean? If it means "woldline outside a local lightcone", then I agree. Alcubierre warp drive spacetime, however, does not have this property. Folks (e.g., @bobob , @PeterDonis ) have noted this in this thread.

The math is easy and can be found from my own blog, year 2013.

This statement is not true.

http://meta-phys-thoughts.blogspot.com/2013/
This bolgpost most certainly does not demonstrate mathematically (i.e., using actual GR spacetimes) that, specifically, Alcubierre warp drive spacetime contains closed timelike curves.

 

[1977ub]

Of course it's not possible. Alcubierre spacetime is not flat. If an Alcubierre drive travels between A and B, then spacetime between A and B is not flat.

A small kernel of heavily warped spacetime in a large ocean of flat-ish spacetime such as between here and alpha centauri. This is why i described the vehicle to be within a black box. At the quantum level, spacetime may be heavily warped but that doesn't enable FTL communication or travel at the macroscopic scale.

Adherents of the drive accept that it will allow me to send messages to my friend 4 ly away in what he and I both agree to be 3 years. This is a causality violation, as agreed by Alcubierre and others.

 

[PeterDonis]

The ship can also go a long way around, running the warp drive only far away from A and B and flying the rest with conventional engines.

A and B are points in spacetime, not space. You are stipulating that a light ray not going through the warp bubble could not reach B from A. That means the warp bubble has to affect the spacetime geometry between those events.

 

[PeterDonis]

A small kernel of heavily warped spacetime in a large ocean of flat-ish spacetime such as between here and alpha centauri.

See my response to @DrStupid just now.

 

[PeterDonis]

The math is easy and can be found from my own blog

Your blog is not a valid reference. Please do not reference it again. If you do you will receive a warning.

 

[PeterDonis]

Adherents of the drive accept that it will allow me to send messages to my friend 4 ly away in what he and I both agree to be 3 years.

A lot of complexities that you are blithely ignoring are lurking underneath your simple-looking statement "in what he and I both agree to be 3 years". As has already been pointed out multiple times, nothing moves outside the light cones in Alcubierre spacetime. You cannot just wave your hands and ignore the spacetime curvature involved.

 

[DrStupid]

You are stipulating that a light ray not going through the warp bubble could not reach B from A.

No, I'm stipulating, that a light ray could reach B from A, not going throuth the warp bubble. There may also be light rays, reaching B from A, going through the warp bubble. But I'm not interested in them because I'm currently checking causality in the flat parts of the space-time.

 

[Ibix]

Alcubierre's 1994 paper notes that his spacetime is globally hyperbolic and therefore does not contain any causal loops.

Everett's paper (linked upthread) points out that Alcubierre's solution can be written as $\eta_{\mu\nu}+h_{\mu\nu}$ and that $h$ is very small except near the bubble. So you can have two warp bubbles traveling in opposite directions essentially as a linear superposition of two Alcubierre spacetimes - i.e. $\eta_{\mu\nu}+h_{\mu\nu}+h'_{\mu\nu}$ where the two $h$s are warp bubbles moving in $\pm x$ directions and offset by some distance in the $y$ direction so that they do not interfere with each other. Furthermore, he argues that there's no reason that the two warp bubbles have to share a notion of "at rest" and both can arrive at their destinations in arbitrarily short coordinate times for their rest frames. Thus he says you can build a tachyonic anti-telephone with two warp drives, although you can't do it with one.

I don't know whether or not Everett's analysis is correct. It seems plausible on the face of it, but if I understand correctly Alcubierre's paper assumes a spacetime in which CTC's are impossible before showing that the warp drive is a solution. So it's not completely clear to me that simply adding two warp bubbles can work quite as Everett claims - he seems to have ended up with a spacetime that isn't consistent with the one Alcubierre used.

I may be wrong - this is just my impression from reading the papers this morning.

 

[PeterDonis]

I'm stipulating, that a light ray could reach B from A, not going throuth the warp bubble.

Then there is no "violation of causality" even in the (mistaken) sense you are using the term, since events A and B can be connected by light rays in the absence of any warp bubble, so even "causality in the flat parts of the spacetime" is not violated (that would require events A and B to not be connected by any timelike or null paths that do not go through the warp bubble).

 

[PeterDonis]

it's not completely clear to me that simply adding two warp bubbles can work quite as Everett claims

Since the EFE is nonlinear, we should not expect simply adding together two solutions to give a solution. So it's quite possible that the scenario Everett describes is not in fact a solution of the EFE.

 

[martinbn]

Since the EFE is nonlinear, we should not expect simply adding together two solutions to give a solution. So it's quite possible that the scenario Everett describes is not in fact a solution of the EFE.

It will be a solution with a different stress energy tensor. As long as the sum is still a Lorentzian metric, which it need not be in general. The paper is very sketchy, I am not sure that he achieves what he claims.

 

[PeterDonis]

It will be a solution with a different stress energy tensor. As long as the sum is still a Lorentzian metric

Yes, it's true that you can take any Lorentzian metric and call it a "solution" by simply computing its Einstein tensor and dividing it by $8 \pi$ and calling that the "stress-energy tensor".

 

[Ibix]

Since the EFE is nonlinear, we should not expect simply adding together two solutions to give a solution. So it's quite possible that the scenario Everett describes is not in fact a solution of the EFE.

That's kind of my point. Everett points out that the disturbances are small except near the warp bubble, and hence that the superposition ought to be near a solution (even if not actually a solution) as long as the warp bubbles don't get too close. However, "the components of a tensor are small" is not a coordinate independent statement and I don't think Everett shows that the components of one disturbance are small in the coordinate system in which the components of the other are small. So I don't think it's completely clear that adding the solutions is necessarily "nearly right" for a spacetime containing two warp drives. At least, not from that paper.

 

[DrStupid]

Then there is no "violation of causality" even in the (mistaken) sense you are using the term

Do you have a reference for the sense you are using the term?

that would require events A and B to not be connected by any timelike or null paths that do not go through the warp bubble

I am talking about events A (e.g. departure of the spaceship) and B (e.g. arrival of the spaceship at the destination) that cannot be connected by any timelike or null paths that do not go through the warp bubble.

 

[PeterDonis]

Do you have a reference for the sense you are using the term?

Do you?

I am talking about events A (e.g. departure of the spaceship) and B (e.g. arrival of the spaceship at the destination) that cannot be connected by any timelike or null paths that do not go through the warp bubble.

Then you are contradicting yourself, since you said:

I'm stipulating, that a light ray could reach B from A, not going throuth the warp bubble.

If a light ray could reach B from A, not going through the warp bubble, then that light ray's worldline is a null path connecting A and B.

 

[Ibix]

I am talking about events A (e.g. departure of the spaceship) and B (e.g. arrival of the spaceship at the destination) that cannot be connected by any timelike or null paths that do not go through the warp bubble.

Alcubierre's solution has a globally applicable notion of "forward in time", picked out by his initial choice of foliation. So it cannot include causal paradoxes.

Everett, as far as I understand it, points out that the choice of foliation is not unique. Thus causal paradoxes become possible in a more general spacetime that includes multiple warp bubbles. However I am not convinced by his argument because it does not appear clear to me that you can combine two Alcubierre solutions in the way he does (or, at least, that it must necessarily have the properties he ascribes to such a combination). I could, of course, be missing something.

 

[PeterDonis]

Alcubierre's solution has a globally applicable notion of "forward in time", picked out by his initial choice of foliation.

The particular notion of "forward in time" that he describes might be foliation dependent, but as you pointed out in a previous post, the key property for the absence of causal loops is that the spacetime is globally hyperbolic, and that property is not foliation dependent; it's an invariant geometric property.

 

[PAllen]

Alcubierre's solution has a globally applicable notion of "forward in time", picked out by his initial choice of foliation. So it cannot include causal paradoxes.

Everett, as far as I understand it, points out that the choice of foliation is not unique. Thus causal paradoxes become possible in a more general spacetime that includes multiple warp bubbles. However I am not convinced by his argument because it does not appear clear to me that you can combine two Alcubierre solutions in the way he does (or, at least, that it must necessarily have the properties he ascribes to such a combination). I could, of course, be missing something.

It seems to me the only thing missing from Everett's paper is a more explicit demonstration that the combined metric tensor he constructs is a valid metric tensor. It would not be expected to preserve the global hyperbolicity of the one bubble metric. I would find it totally convincing if there were an argument that the candidate metric he writes in equation (10) [ confusingly using upper case G for something that is clearly meant as a metric] has the same signature everywhere. Everything else would hang together, IMO, if this were demonstrated. Continuity and such are already demonstrated (and G being symmetric is also obvious), and there are very minimal requirements to simply declaring some tensor on a manifold be treated as the fundamental tensor. Unchanging signature is the only nontrivial requirement that would not obviously hold in this case.