# I Is the Alcubierre Warp Drive possible?

#### 1977ub

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.

#### hmmm27

The question is - is this a technology which can be operated at will.
Since it isn't a technology, and the mathematics that it is make no overt references to "will" or not . . .

#### Heikki Tuuri

If you are allowed to choose the metric freely, you can make a patch of space to travel faster than light. That is clear.

Then you can use the Einstein field equation to calculate the stress-energy tensor T which would produce such a metric.

The Alcubierre drive, of course, allows closed timelike loops and causality violations. It breaks the principles of special relativity since we would have a spaceship which travels faster than light. The energy of such an object in special relativity is imaginary. These contradictions strongly suggest that the stress-energy tensor T is impossible to realize.

The stress-energy tensor T for the drive is very weird: there should be something which makes space to contract in front of the rocket and stretch behind it. I think matter with a negative energy density does not accomplish this. Ordinary matter has stretched the radial dimension r around it, and negative energy matter has contracted r. But it is static - there is no dynamic stretching or contracting around such matter.

One may imagine that the rocket would move inside a solid rod where a lever mechanism keeps negative pressure in front of the rocket and positive pressure behind it. One problem is how a rocket can fly inside a solid rod? Maybe we should instead of a rocket use a neutrino which can fly trough solid rock.

The negative pressure has to be huge to win the positive gravity of the material in the rod. Such material does not exist in nature. Can it exist theoretically? I think such material would allow faster-than-light travel for the neutrino. Since faster-than-light travel involves the causality violations, that strongly suggests that the required material for the rod cannot exist, even in theory.

#### PeterDonis

Mentor
Even with Novikov, CTCs allow the possibility of e.g. a play or symphony that has no author. I think many, if not most, physicists would consider this a form of causality violation.
But that is a different usage of the term "causality" than the standard one, which is that nothing moves outside the light cones. IMO it would be better to just say "closed timelike curves".

#### PeterDonis

Mentor
It breaks the principles of special relativity since we would have a spaceship which travels faster than light.
First, SR is inapplicable since we are talking about a curved spacetime.

Second, as I've repeatedly said in this thread, nothing moves "faster than light" in this spacetime. Nothing moves outside the light cones.

The energy of such an object in special relativity is imaginary.
SR is inapplicable; see above. What makes the stuff that produces the Alcubierre warp bubble "exotic matter" is that its pressure is greater than its energy density in the rest frame of the bubble. There is no imaginary energy anywhere. (There are frames where the energy density is negative, but none in which it is imaginary.)

Don't "think". Do the math and see. The properties of the Alcubierre spacetime are well understood.

One may imagine
Don't "imagine". Do the math.

The negative pressure has to be huge to win the positive gravity of the material in the rod. Such material does not exist in nature. Can it exist theoretically?
As multiple posters have already said in this thread, most physicists think the answer to this is no.

I think such material would allow faster-than-light travel for the neutrino.
Please review the PF rules on personal speculation.

#### 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

Staff Emeritus
Gold Member
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 space ship 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 space ship 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

Staff Emeritus
Gold Member
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

Staff Emeritus
Gold Member
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

Mentor
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

Mentor
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:

#### 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 travelling 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

Mentor
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

Staff Emeritus
Gold Member
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.

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

Mentor
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

Mentor
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

Mentor
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

Mentor
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 travelling 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.

"Is the Alcubierre Warp Drive possible?"

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