Could a warp drive work as a time machine?

[bcrowell]

Time travel is normally taken as being able to construct a CTC - that is, you leave e1 on some time like world line and return to e0 that is earlier on that world line. With tachyons, for example, this requires the additional assumption that tachyons obey the POR (as opposed to picking out a preferred frame; if you allow POR violation, then the tachyon anti-telephone and all similar constructions need not occur).

These seem like two different definitions of time travel to me. In general, I would define causality by saying that (1) the spacetime is time-orientable and (2) uniqueness and existence hold for solutions of the wave equations that describe the matter fields. (#1 is necessary because you can't define the initial data for a Cauchy problem otherwise.) In a spacetime with CTCs, we expect 2 to fail because of the geometry of the spacetime. In a model with tachyons, we expect 2 to fail because that's the behavior of the wave equations for tachyons (even in a flat spacetime, where there are no CTCs).

IMO dauto's #4 is correct: any mechanism for FTL should be expected to violate casuality, for the reasons s/he gives. I'm not claiming that this is a rigorously well-defined claim, or that I have a rigorous proof, but the physical argument is very strong, and I'm not aware of any counterexamples.

 

[yuiop]

You missed my point. Certainly, within the bubble, the world-line of the ship is time-like. In fact, since the ship does not experience proper acceleration, we can pick an inertial coordinate system in which the ship is always at rest. That's as time-like as it gets.

But consider the ship's trajectory from outside the bubble. The space-time is asymptotically flat at any point along the path before the warp bubble reaches it and after it passes. This means that from perspective of outside observer, propagation of the bubble and the ship is equivalent to an object following a space-like curve in flat space-time.

I agree with your position. Externally, the motion is spacelike no matter how it is dressed up. In fact the paper linked to earlier states as much. Once that is accepted then the analysis is no different to the analysis of tachyons.

 

[PAllen]

These seem like two different definitions of time travel to me. In general, I would define causality by saying that (1) the spacetime is time-orientable and (2) uniqueness and existence hold for solutions of the wave equations that describe the matter fields. In a spacetime with CTCs, we expect 2 to fail because of the geometry of the spacetime. In a model with tachyons, we expect 2 to fail because that's the behavior of the wave equations for tachyons (even in a flat spacetime, where there are no CTCs).

IMO dauto's #4 is correct: any mechanism for FTL should be expected to violate casuality, for the reasons s/he gives. I'm not claiming that this is a rigorously well-defined claim, or that I have a rigorous proof, but the physical argument is very strong, and I'm not aware of any counterexamples.

In a later post I gave what I think is a more precise definition: the ability for a message or test body to leave some event e1 and reach some event in the causal past of e1.

I disagree with your conclusion about FTL and causality and gave a specific example for tachyons. If you say tachyons pick out a preferred frame such that in this preferred frame all tachyon trajectories move forward in coordinate time, then there are no causality violations (anti-telephone) in any frame. Other frames will see tachyon trajectories going back in coordinate time, but never e1 sending a message to e2 in its causal past. In fact, you could detect your motion relative to the preferred frame by anisotropy of observable tachyon trajectories. Only in the preferred frame do you have isotropy of tachyon behavior.

Such a construction need not violate any known physics because you postulate that all other phenomena other than tachyons behave consistent with SR (which, of course, can be made consistent with an unobservable preferred frame; which now becomes observable with tachyons).

I only point this out because there is a line of research in the literature that argues these points - that FTL + SR do not necessarily lead to causality violations. You need at least the assumption that tachyon phenomenology observes the POR.

 

[Dale]

I agree with your position. Externally, the motion is spacelike no matter how it is dressed up. In fact the paper linked to earlier states as much. Once that is accepted then the analysis is no different to the analysis of tachyons.

No. The the ship's worldline is everywhere timelike, and the paper was very careful to state that: "The spaceship beats the light signal to S2 not because its motion is spacelike but because, in effect, the bubble acts like a wormhole and provides a shortcut from S1 to S2." This is a discussion about closed timelike curves in GR, not spacelike curves in SR.

 

[yuiop]

Instead of just guessing, the paper bcrowell provided gives a precise construction to achieve time travel with alcubierre drive. It does it in the way I proposed #13 before seeing the paper, solving what I thought was the possible sticking point.

Partly I was trying to give a simplification of the paper which even you agreed was a little convoluted and I quote:

The paper posted shows a way to achieve CTCs with a pair of Alcubierre bubbles, but the key parts of the derivation are not what I would call obvious.

Your example proposed in #13:

... An example of a minimal derivation of time travel with alcubierre or similar warp drive would be to show you can have two drives set up in an analagous way as the tachyon anti-telephoned, such that they approach close to each other at one event, and you have a way to send a message or payload from the inside of one warp bubble to the inside of another. ...

is certainly simply but does sort of assumes that the velocity of the drive is greater than infinite and backwards in time, without clarifying how that can come about. For example if a rocket travels from A to B and back to A and always traveling at 2c, it does not arrive back at A before it left. The point is to illustrate that if the speed of light can be exceeded by even a small amount in any reference frame, then it possible to construct a scenario in which travel to the past light cone is possible (or alternatively transmission of information to the past light cone.)

My scenario was also a response to these challenges by K^2:

No. You cannot get this in any inertial frame. To do what you suggest, your frame of reference need to accelerate, and then you can no longer use Special Relativity to describe what's going on. So in flat-space time you still cannot get the practical time travel you are looking for.

...
As PAllen pointed out, the requirement here is that you can move information into past cone of an event. Alcubierre drive let's you go backwards in time, but only outside of the past light cone. That means that you cannot construct a frame of reference where the loop is closed..

... to find a scenario in flat spacetime where time travel back to a past light cone is possible:

My first example used a circular track that avoided the need to keep switching reference frames, but perhaps circular motion introduces additional complications. Here is an example with only linear motion.

Again we have two stars A and B. We also have two Alcubierre tracks. One moves with constant velocity from A to B at say 0.8c. The other moves with constant velocity in the opposite direction e.g -0.8c. Assume the bubble can move at a fixed superluminal speed in either direction relative to a given track. The speed only has to be marginally superluminal, eg 1.3c.

The trick is to send the bubble in the opposite direction to the motion of the track as measured in the rest frame of the two stars. On the outward leg, the velocity of the bubble using relativistic velocity addition is (-0.8 + 1.3)/(1 +(-0.8*1.3)) = -12.5c. This is negative because it is going in the positive x direction but backwards in time. On the return journey (assuming the bubble or its contents or its information can switch tracks) the velocity is (0.8 +(-1.3))/(1 + 0.8*-1.3) = +12.5c. This is positive because it is going in the negative x direction and going in the negative time direction. The end result is the bubble arriving back at A before it left. This scenario is analysed completely in flat spacetime where the localised curvature around the warp bubble is ignored and where near instantaneous acceleration is assumed in order to simplify things.

Counter-intuitively, if the bubble is sent in the same direction as the motion of the track, it takes longer to get from A to B than when the track is stationary with respect to A and B and the backwards in time effect is lost.

 

[Dale]

You missed my point. Certainly, within the bubble, the world-line of the ship is time-like. In fact, since the ship does not experience proper acceleration, we can pick an inertial coordinate system in which the ship is always at rest. That's as time-like as it gets.

But consider the ship's trajectory from outside the bubble. The space-time is asymptotically flat at any point along the path before the warp bubble reaches it and after it passes. This means that from perspective of outside observer, propagation of the bubble and the ship is equivalent to an object following a space-like curve in flat space-time.

Coordinate systems used by outside observers are irrelevant to the timelike or spacelike nature of the ship's worldline. The tangent vector (and its norm) is a local quantity on the ship's worldline. The spacetime is curved, even if it is asymptotically flat, so you cannot just use flat spacetime concepts and assert that the path is spacelike simply because there is another path nearby which is spacelike.

The bubble doesn't disappear when the ship stops. Ship stops when the bubble disappears.

OK

 

[yuiop]

No. The the ship's worldline is everywhere timelike, and the paper was very careful to state that: "The spaceship beats the light signal to S2 not because its motion is spacelike but because, in effect, the bubble acts like a wormhole and provides a shortcut from S1 to S2." This is a discussion about closed timelike curves in GR, not spacelike curves in SR.

The very next sentence is: "Since a four-vector with components (T,0,0,D) is spacelike, the temporal order of the spaceship's arrival and departure is not well defined; ... we introduce a new set of primed coordinates .."

Earlier they said "Inertial observers at rest outside the bubble on S1 and S2 will see the motion of the bubble with the spaceship at its centre as superluminal, since it covers a distance D in a time interval T<D". That by definition is spacelike.

While I concede that the spaceship itself in its bubble has timelike motion, it does not change the fact that matter or information is transmitted from A to B superluminally, thus violating at least one the basic tenets of relativity and allowing the construction of CTCs.

 

[Dale]

The very next sentence is: "Since a four-vector with components (T,0,0,D) is spacelike, the temporal order of the spaceship's arrival and departure is not well defined; ... we introduce a new set of primed coordinates .."

Sure, but that four-vector is not the path of the ship nor a tangent vector to the path of the ship.

Earlier they said "Inertial observers at rest outside the bubble on S1 and S2 will see the motion of the bubble with the spaceship at its centre as superluminal, since it covers a distance D in a time interval T<D". That by definition is spacelike.

Only in flat spacetimes, which this isn't. In curved spacetimes superluminal means faster than light, which may not be spacelike since the light and the ship must travel on different paths.

Look, this is just a matter of definitions. The tangent to the ship's worldline is at all points timelike, therefore the ship's path is timelike. Because the space is curved you can have both closed timelike curves and superluminal timelike curves. Neither of those facts make the ship's path spacelike, and the paper was very clear on that point. The flat background, and distant observer's coordinates are irrelevant.

Here are some other quotes from the paper: "The theory in MA differs, however, from one with tachyons in that the world lines of all objects are timelike", "a spaceship with position given by r(t)= r0(t) is in free fall, moving along a timelike geodesic", "the spaceship moves at all times within its forward light cone".

While I concede that the spaceship itself in its bubble has timelike motion, it does not change the fact that matter or information is transmitted from A to B superluminally, thus violating at least one the basic tenets of relativity and allowing the construction of CTCs.

Yes. The spacetime is curved, so it does indeed violate some of the basic tenents of SPECIAL relativity.

 

[OCR]

Could a warp drive work as a time machine?

I wondered about the same thing...

So I talked to me yesterday, and said I had already read this complete thread, tomorrow...

So, I now agree with me... the answer is... NO!

People initially thought of tachyons as particles traveling faster than the speed of light...But we now know that a tachyon indicates an instability in a theory that contains it. Regrettably for science fiction fans, tachyons are not real physical particles that appear in nature.

http://en.wikipedia.org/wiki/Tachyon

http://en.wikipedia.org/wiki/Alcubierre_drive

http://ntrs.nasa.gov/search.jsp?R=20130011213

http://en.wikipedia.org/wiki/Warp-field_experiments

http://en.wikipedia.org/wiki/Harold_G._White_(NASA)

http://en.wikipedia.org/wiki/Closed_timelike_curve

http://en.wikipedia.org/wiki/Quantum_mechanics_of_time_travel

the answer is... NO!

And last week, I will bet you anything you want... I was, I am, and, I will still be... Right.



OCR

 

[bcrowell]

I disagree with your conclusion about FTL and causality and gave a specific example for tachyons. If you say tachyons pick out a preferred frame such that in this preferred frame all tachyon trajectories move forward in coordinate time, then there are no causality violations (anti-telephone) in any frame.

Could you point me to the post where you described this in more detail?

I only intended to discuss this in the context of standard relativity, not in some other theory with preferred frames.

As a side note, if your preferred frame is a frame in which the tachyons are at rest, then your example doesn't work in 3+1 dimensions. There is a no-go theorem (Gorini 1971) that shows that you can't extend the Lorentz group in this way in m+n dimensions unless m=n.

The definition I've given is very similar to the notion of global hyperbolicity (Hawking and Ellis, p. 206). There is a theorem (Geroch 1970) that says that global hyperbolicity gives uniqueness and existence of solutions to Cauchy problems. I don't have access to the Geroch paper, but this characterization is given in Penrose 1973. Global hyperbolicity also includes a prohibition on naked singularities.

Geroch, J Math Phys 11 (1970) 437

V. Gorini, "Linear Kinematical Groups," Commun Math Phys 21 (1971) 150; open access via project euclid: http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cmp/1103857292

Penrose, Gravitational radiation and gravitational collapse; Proceedings of the Symposium, Warsaw, 1973. Dordrecht, D. Reidel Publishing Co. pp. 82-91, free online at http://adsabs.harvard.edu/full/1974IAUS...64...82P , p. 85

 

[PAllen]

Could you point me to the post where you described this in more detail?

#5, #13. I thought (mistakenly?) that the idea of tachyons (only) violating POR via a preferred frame was sufficiently clear not to require further elaboration.

I only intended to discuss this in the context of standard relativity, not in some other theory with preferred frames.

I agree that if we require all laws (including for tachyons) to be Lorentz invariant, and that there is no physical construct (e.g. CMB radiation) that is taken to somehow influence tachyon behavior, then FTL->time travel.

As a side note, if your preferred frame is a frame in which the tachyons are at rest, then your example doesn't work in 3+1 dimensions. There is a no-go theorem (Gorini 1971) that shows that you can't extend the Lorentz group in this way in m+n dimensions unless m=n.

Who said at rest? I said trajectory moves forward in time. That is, in the preferred frame, the set of all possible tachyon trajectories is all spacelike paths where coordinate time is strictly increasing. For any other frame, the set of allowed tachyon trajectories is the Lorentz transform of such paths. These will be mixes of backward and forward in (coordinate) time paths, but no causality violations will be possible.

 

[PAllen]

The definition I've given is very similar to the notion of global hyperbolicity (Hawking and Ellis, p. 206). There is a theorem (Geroch 1970) that says that global hyperbolicity gives uniqueness and existence of solutions to Cauchy problems. I don't have access to the Geroch paper, but this characterization is given in Penrose 1973. Global hyperbolicity also includes a prohibition on naked singularities.

I'm aware of this, but I was using a slightly more general definition that allowed for tachyons in SR with various phenomenology. One that captured the minimal essence of time travel in an invariant way: event e1, by any conceivable means, sending an influence to an event in its causal past.

 

[bcrowell]

Who said at rest? I said trajectory moves forward in time. That is, in the preferred frame, the set of all possible tachyon trajectories is all spacelike paths where coordinate time is strictly increasing. For any other frame, the set of allowed tachyon trajectories is the Lorentz transform of such paths. These will be mixes of backward and forward in (coordinate) time paths, but no causality violations will be possible.

OK. I don't see the motivation for considering this particular Lorentz-violating theory. Has it ever been discussed in the literature?

 

[PAllen]

OK. I don't see the motivation for considering this particular Lorentz-violating theory. Has it ever been discussed in the literature?

I don't know if this particular formulation has been discussed in the literature. However, the general idea that if tachyons need not follow the POR, then they need not produce causality problems, has. The particular scheme I proposed is simply one with the virtue that it is easy to explain and trivial to demonstrate that all causality problems are removed. Discussions I've seen in the literature often don't give any examples - they just demonstrate the derivation of causality violation from FTL is relying on tachyons following the POR.

 

[yuiop]

OK. I don't see the motivation for considering this particular Lorentz-violating theory. ...

I guess the motivation is that if tachyons exist, then having a preferred reference frame is a lesser evil than causality violation. The relevance to this thread is that if there is a preferred frame for warp drives, then they need not violate causality. The problem with causality violation is that it raises all sorts of genuine paradoxes/ logical contradictions. This is why Hawking proposed the chronological protection conjecture.

 

[yuiop]

The flat background, and distant observer's coordinates are irrelevant. ...

I don't think they are entirely irrelevant. While the motion of the ship inside the bubble is timelike, the motion of the bubble itself is spacelike according to the observers in the flat background is spacelike. Since the curvature at the edge of the bubble is extreme (but localised) the outside observers will be be able to detect the tidal effects of a passing bubble and so will be able to use warp bubbles to send information faster than light and if the POR holds they can be used to send information into a past light cone. Since CTCs already exist in GR solutions such as the Kerr metric, I guess that is not a problem as far as GR is concerned.

I wonder why it is that we readily accept that infinitely rigid extended bodies are not compatible with relativity because they allow FTL transmission of information, but we do not readily conclude that exotic matter with negative energy density (that allows warp drives and worm holes) is not compatible with relativity for the same reason?

Here is something else I am pondering on. Given an observer at a given event in flat spacetime, we can define the future and past light cones. We claim the future light cone is the set off all possible events that the observer can be at in the future and the past light cone is the set of all events that the observer could possibly have been at in the past. Now we switch on a warp drive and transport the observer for a while and switch it off again. When the spacetime settles down, the observer is now outside his old future light cone and his new past light cone does not include all of his past worldline. It seems that we can jump out of the light cone at will (or redefine it) by dynamically curving the spacetime. That is something I had not realized before.

 

[PAllen]

I wonder why it is that we readily accept that infinitely rigid extended bodies are not compatible with relativity because they allow FTL transmission of information, but we do not readily conclude that exotic matter with negative energy density (that allows warp drives and worm holes) is not compatible with relativity for the same reason?

Plenty of people (including me) would say that they believe that is close enough to true that such things will never exist in accessible spacetime regions. What makes it not so obvious is that classical analogs of perfectly reasonable quantum fields violate the energy conditions. I believe that to rule out all all forms to causality violation in non-singular regions (you can't rule it out in singular regions, e.g. the inside of Kerr BH), it is necessary to assume the dominant energy condition (which is one of the stronger ones). (I recently saw a paper that showed that Gralla-Wald type limiting argument for showing a test body follows a geodesic as a consequence of the EFE, when done with matter allowed to violate only the dominant energy condition can lead to spacelike trajectories for the test body).

 

[Dale]

I wonder why it is that we readily accept that infinitely rigid extended bodies are not compatible with relativity because they allow FTL transmission of information, but we do not readily conclude that exotic matter with negative energy density (that allows warp drives and worm holes) is not compatible with relativity for the same reason?

Well, my objection to infinitely rigid bodies is different from that. My objection (which I think is the usual objection) is given in the FAQ: https://www.physicsforums.com/showthread.php?t=536289

However, I suspect that most physicists (myself included) do doubt the existence of exotic matter. It violates the energy conditions, which are not specifically required by the EFE, but are used specifically to check the plausibility of a given solution. I don't think that Albicurre warp drives are possible precisely because they violate the energy conditions, but I could be wrong about that without GR being wrong also.

 

[WannabeNewton]

(I recently saw a paper that showed that Gralla-Wald type limiting argument for showing a test body follows a geodesic as a consequence of the EFE, when done with matter allowed to violate only the dominant energy condition can lead to spacelike trajectories for the test body).

Was it something along the lines of what is shown starting on page 9 of the following: http://philsci-archive.pitt.edu/4908/1/GeodesicLaw.pdf ?

 

[PAllen]

Was it something along the lines of what is shown starting on page 9 of the following: http://philsci-archive.pitt.edu/4908/1/GeodesicLaw.pdf ?

Similar, but it referred to Malament, and produced a more remarkable result: that that a spacelike curve can satisfy if the dominant energy condition is dropped. I'll post it if I find it again.

 

[PAllen]

Was it something along the lines of what is shown starting on page 9 of the following: http://philsci-archive.pitt.edu/4908/1/GeodesicLaw.pdf ?

Similar, but it referred to Malament, and produced a more remarkable result: that that a spacelike curve can satisfy if the dominant energy condition is dropped. I'll post it if I find it again.

At some point I had seen one based on the Gralla-Wald technique, but I can't seem to find it now. However, here is one showing that using the older Geroch technique, the WEC is not enough to prevent spacelike trajectories. This paper builds on Malament's work to which you refer:

http://arxiv.org/abs/1106.2336

In effect, these types of results suggest to me that admitting generally available matter violating energy conditions is equivalent to admitting tachyonic bodies, without recourse to warp bubbles or wormholes. I personally doubt such will ever be observed.

 

[WannabeNewton]

At some point I had seen one based on the Gralla-Wald technique, but I can't seem to find it now. However, here is one showing that using the older Geroch technique, the WEC is not enough to prevent spacelike trajectories. This paper builds on Malament's work to which you refer:

http://arxiv.org/abs/1106.2336

In effect, these types of results suggest to me that admitting generally available matter violating energy conditions is equivalent to admitting tachyonic bodies, without recourse to warp bubbles or wormholes. I personally doubt such will ever be observed.

I agree, and thank you for the link! I'll read through it right after my exam tonight