Could a warp drive work as a time machine?

[KeplerJunior]

I'm sure you've heard of the warp/Alcubierre drive that would work by expanding space behind it and contracting it in front to achieve faster than light travel. I was thinking about this the other day and was wondering if this concept could be applied to time as well to allow time travel. Would this be possible or would times one-dimensional nature not allow it?

 

[berkeman]

Thread closed for Moderation...

 

[Dale]

We have re-opened the thread. Be sure to keep responses factual.

Personally, I am not aware of time travel directly with an Alcuiberre spacetime, but I would not be surprised to learn that someone has worked it out mathematically.

 

[dauto]

Even with trying to find a direct solution for the field equations that leads to time travel (That would be hard to do), it is clearly possible to travel back in time using any means of FTL travel because of the relativity of simultaneity. A FTL travel connects to points whose distance is space-like, and there is always a boost that reverts the order of two events connected by a space-like distance due to relativity of simultaneity. That is how we know that FTL is not possible and Warp-drive is a pipe dream.

 

[PAllen]

Even with trying to find a direct solution for the field equations that leads to time travel (That would be hard to do), it is clearly possible to travel back in time using any means of FTL travel because of the relativity of simultaneity. A FTL travel connects to points whose distance is space-like, and there is always a boost that reverts the order of two events connected by a space-like distance due to relativity of simultaneity. That is how we know that FTL is not possible and Warp-drive is a pipe dream.

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).

With wormholes, it has been shown with sufficient exotic matter you can arrange a traversible one that allows CTCs.

For alcubierre drive, it is not at all obvious that the construction can be used to construct a CTC because it is normally not possible to escape and enter the warp bubble (a slight practical problem with such a 'drive' )

My knowledge is consistent with Dalespam - I've never seen a time travel construction using warp drive, nor have I seen an argument that it is impossible, and would not be surprised if some variation could allow it.

 

[dauto]

The problem is this idea is threefold.

*Getting rid of POR is just wishful thinking.
*Sufficiently exotic matter doesn't exist.
*Wormholes probably do not exist either.

 

[PAllen]

The problem is this idea is threefold.

*Getting rid of POR is just wishful thinking.
*Sufficiently exotic matter doesn't exist.
*Wormholes probably do not exist either.

I'm not saying they do. I'm saying the statement that FTL = travel back in time (as normally understood - getting back to an event that is in your causal past) is not a formally correct statement. Without violating any currently known physics, it is possible, in principle, to add FTL phenomenology without producing time travel. I agree the laws you would have to propose for it are 'ugly', and there is not the slightest reason to expect it to be possible.

However, the OP asked specifically about alcubierre drive. I have read many papers on this and related spacetimes, and none that I have seen suggest the possibility of time travel. This is in contrast to Kip Thorne's wormhole constructions which definitely produce it. However, like Dalespam, I would not be very surprised if someone produced such a construction because there are many constructions allowing time travel in GR if you allow sufficient exotic matter.

These statements are factual. An opinion of mine (in, I think, agreement with you) is none of this is likely possible in our universe. However, I think it is important to distinguish what mathematical GR (or SR for known physics plus contrived FTL) allows, versus opinions on what is likely true.

 

[Dale]

Well said, PAllen.

 

[K^2]

Of course Alcubierre Drive allows for time travel in some limited sense. Forget about the warp field itself. Look at the statement of the problem from perspective of nearly-flat space-time away from the ship. You have something that travels from event A to event B. The two events are space-like separated. That's the whole point of FTL travel. Now, order of any two space-like separated events is frame dependent. So if you have a ship under Alcubierre Drive depart at event A and arrive at event B in one frame, there is a frame of reference in which it departs from B and arrives at A.

That's time travel.

Granted, it's not what most people think of when they talk about time travel. There are some very strict limitations on this, and yet you can have an observer watch information carried drom a "future" event to a "past" event breaking causal relationship.

This is not directly useful to anyone at departure or arrival locations, of course, because in their frame of reference no "time travel" takes place. What would be interesting is to have a closed loop, and that requires you to do something creative with space-time. Where Alcubierre Drive can make a difference is that it's very difficult to organize a closed time-like loop under anything like reasonable conditions. If, however, you have a ship that can follow a space-like trajectory, you have opportunity for time travel in its fullest sense.

Now, if we start talking about consequences of something like this, that's where physics as we know it breaks down. Time travel is entirely fine in General Relativity. Whether solutions that allow it are plausible remains to be seen, but there is no problem with framework of Relativity itself.

Similarly, we can build a particle field theory in any plausible space-time. Including a space-time that has closed time-like loops. Id est, allow time travel. There could be serious problems with renormalization in such a theory, and I don't know if anyone has done the math on this in earnest, but we at least have an idea of how to approach the problem.

But the moment we acknowledge the fact that space-time geometry is a consequence of matter field configurations in that space-time, we no longer have a theory we can actually make a use of. So we cannot possibly do a complete description of what's going to happen if we use a warp field to guide a ship along a closed time loop.

 

[yuiop]

If the Alcubierre drive predicts FTL travel then it appears that it also predicts reverse time travel. For example if the drive gets from A to B faster than light in one reference frame, then there is another reference frame where the drive can return to location A before it departed. Thus it seems that the drive violates causality. This is only avoidable if the POR is violated which in effect means that an absolute or preferred reference frame exists. If the POR is violated then one of the postulates of relativity is invalidated.

 

[bcrowell]

I have read many papers on this and related spacetimes, and none that I have seen suggest the possibility of time travel.

How about this?

Everett, Allen E. (15 June 1996). "Warp drive and causality". Physical Review D 53 (12): 7365–7368. Available online here: http://exvacuo.free.fr/div/Sciences...tt - Warp drive and causality - prd950914.pdf

Alcubierre recently exhibited a spacetime which, within the framework of general relativity, allows travel at
superluminal speeds if matter with a negative energy density can exist, and conjectured that it should be
possible to use similar techniques to construct a theory containing closed causal loops and, thus, travel
backwards in time. We verify this conjecture by exhibiting a simple modification of Alcubierre’s model,
requiring no additional assumptions, in which causal loops are possible.

 

[Dale]

While I wouldn't be surprised to find CTC's with the Alcubierre drive, I don't think it is that obvious.

First, simply going backwards in time in some frame does not lead to a CTC. You have to turn around and go back to where you started along a second spacelike trajectory. I am not sure if the Alcubierre drive can turn.

Second, the interior of the bubble is causally disconnected from the bubble itself. So it isn't clear to me that the interior of the bubble forms a CTC even if you can get the bubble back to the same event.

Those two things make it unclear to me. I am sure that someone has worked out the math, but I haven't seen it and I don't know what the conclusion is. Neither conclusion would surprise me.

EDIT: Thanks bcrowell, you posted while I was writing this. That is exactly what was needed!

 

[PAllen]

Of course Alcubierre Drive allows for time travel in some limited sense. Forget about the warp field itself. Look at the statement of the problem from perspective of nearly-flat space-time away from the ship. You have something that travels from event A to event B. The two events are space-like separated. That's the whole point of FTL travel. Now, order of any two space-like separated events is frame dependent. So if you have a ship under Alcubierre Drive depart at event A and arrive at event B in one frame, there is a frame of reference in which it departs from B and arrives at A.

That's time travel.

That isn't time travel according common usage in the literature. Time travel is taken to be a way to get from some event e1 to some event in the causal past of e1 (possibly just sending a message - but there is little difference since the message must be made of something). In the case of tachyons, it is well accepted that you don't get time travel without the assumption that the physics of tachyons is the same in all frames. If, instead, you allow tachyons to pick a preferred frame (while all other physics follows the POR), you can prevent all forms time travel using tachyons. All you need is to posit there exists at least one privileged frame in which all tachyon paths move forward in coordinate time.

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. I would not be shocked to see such a thing established, but it is also not at all obvious - there are problems getting anything into or out of a warp bubble in the constructions I've seen.

 

[PAllen]

How about this?

Everett, Allen E. (15 June 1996). "Warp drive and causality". Physical Review D 53 (12): 7365–7368. Available online here: http://exvacuo.free.fr/div/Sciences...tt - Warp drive and causality - prd950914.pdf

Great, I never saw this one. As advertised, I am not surprised either. In particular, they address the issue of getting from one bubble to another, addressing the issue I was unsure about.

 

[K^2]

If the Alcubierre drive predicts FTL travel then it appears that it also predicts reverse time travel. For example if the drive gets from A to B faster than light in one reference frame, then there is another reference frame where the drive can return to location A before it departed.

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.

Time travel is taken to be a way to get from some event e1 to some event in the causal past of e1

Fair enough. If we define it that way, Alcubierre Drive does not allow for time travel in the otherwise flat space-time.

While I wouldn't be surprised to find CTC's with the Alcubierre drive, I don't think it is that obvious.

Why? Take any known closed space-time curve with space-like regions. Send a FTL ship along it. From perspective of the crew, they've traversed a CTC. QED.Honestly, you don't need to make Alcubierre Drive more complicated than it is. If we fiat ability to build a warp drive, form there on all you have to consider is a ship that can traverse along space-like world lines. You no longer have to think about the specific geometry of the space-time near the ship. We can make the ship and the warp field small enough to fit through whatever neighborhood of the world line that's practically available. In theory. Practically, things might be very different.

 

[yuiop]

First, simply going backwards in time in some frame does not lead to a CTC. You have to turn around and go back to where you started along a second spacelike trajectory. I am not sure if the Alcubierre drive can turn.

Second, the interior of the bubble is causally disconnected from the bubble itself. So it isn't clear to me that the interior of the bubble forms a CTC even if you can get the bubble back to the same event.

I am curious.
Can an Alcubierre drive stop or be turned off once started? If not then it is not much use for transporting material or passengers from A to B.
Can an Alcubierre drive be detected perhaps by the warping of space that makes it work? If the drive can be detected by any means at all, then it can be used to transmit information from A to B faster than light. If it is completely undetectable and causally disconnected (i.e. can not collide with objects in this universe) then it effectively does not exist in this universe.

We do not need the Alcubierre drive to stop or turn around at B, to send material or information back to A in the causal past. All we need is to send a second Alcubierre drive from B in the opposite direction when the first drive arrives at B. If there is any way to detect a drive in this universe, then the only way to forbid information being transmitted FTL or into the causal past is to specify that the drive must always be traveling FTL. This means an Alcubierre drive can not be invented or constructed, but must have always existed.

 

[PAllen]

Why? Take any known closed space-time curve with space-like regions. Send a FTL ship along it. From perspective of the crew, they've traversed a CTC. QED.


Honestly, you don't need to make Alcubierre Drive more complicated than it is. If we fiat ability to build a warp drive, form there on all you have to consider is a ship that can traverse along space-like world lines. You no longer have to think about the specific geometry of the space-time near the ship. We can make the ship and the warp field small enough to fit through whatever neighborhood of the world line that's practically available. In theory. Practically, things might be very different.

To me, showing you can have closed loop Alcubierre trajectory in asymptotically flat spacetime is a significant result beyond the the main papers on this and related metrics. 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.

 

[George Jones]

Why? Take any known closed space-time curve with space-like regions. Send a FTL ship along it. From perspective of the crew, they've traversed a CTC. QED.

I don't think I know what you mean. Are you saying that ships can move along curves that have spacelike tangent vectors?!

 

[yuiop]

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.

It is fairly well established in this forum, that as soon as you can transmit matter or information FTL, then it follows that you can violate causality or you violate the POR. As I am sure you are aware, if we preserve the POR, then transmission of information FTL allows us to construct causality violating situations such as the tachyonic anti-telephone.

We do not need to accelerate to a different reference frame to get the practical time travel. All we have to do is show that there exists in principle, an inertial reference frame where the FTL travel will be seen as travel back in time. The second reference frame is only there to illustrate the situation and is not actually required for practical time travel. All we need is an FTL drive and we can violate just about anything we like about relativity. As mentioned before an FTL drive that does not violate relativity would have to be so disconnected from this universe that it would it would be completely undetectable and unable to interact with anything in this universe and so effectively does not exist, like the aether.

 

[K^2]

To me, showing you can have closed loop Alcubierre trajectory in asymptotically flat spacetime is a significant result beyond the the main papers on this and related metrics. 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.

Define asymptotically flat. If you mean with respect to Alcubierre metric itself, then no, it's impossible and I've stated that already. You need source of significant curvature outside of the warp bubble. That curvature can be asymptotically flat itself and such solutions are known.

I don't think I know what you mean. Are you saying that ships can move along curves that have spacelike tangent vectors?!

A FTL ship, yes. Of course.

All we have to do is show that there exists in principle, an inertial reference frame where the FTL travel will be seen as travel back in time.

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.

I can draw you a diagram if you like.

 

[George Jones]

I don't think I know what you mean. Are you saying that ships can move along curves that have spacelike tangent vectors?!

A FTL ship, yes. Of course.

How could a ship move on a spacelike curve?

This is not what is usually meant by "time machine". See, for example, definitions 17 and 18 on page 206 of "Lorentzian Wormholes" by Visser. These standard definitions involve closed timelike and lightlike curves, i.e., non-spacelike curves.

 

[K^2]

How could a ship move on a spacelike curve?

That's what faster-than-light means. You cover distance in less time than it would take light. Id est, the separation between start and finish is space-like. Somewhere in between, world-line of the ship has to be space-like.

This is not what is usually meant by "time machine". See, for example, definitions 17 and 18 on page 206 of "Lorentzian Wormholes" by Visser. These standard definitions involve closed timelike and lightlike curves, i.e., non-spacelike curves.

FTL is what let's you drop this restriction and make use of space-like curves for time travel.

We really need some concrete examples here. I'll see if I can dig up a simple metric that let's us build closed curves traversable with FTL ship. Kerr metric might do, actually. I'll have to think about it for a bit.

 

[George Jones]

That's what faster-than-light means. You cover distance in less time than it would take light. Id est, the separation between start and finish is space-like. Somewhere in between, world-line of the ship has to be space-like.


FTL is what let's you drop this restriction and make use of space-like curves for time travel.

How can a ship move from a timelike curve to a spacelike curve?

We really need some concrete examples here. I'll see if I can dig up a simple metric that let's us build closed curves traversable with FTL ship. Kerr metric might do, actually. I'll have to think about it for a bit.

Kerr spacetime nicely illustrates a time machine as standardly defined, i.e., it has closed timelike curves.

Let me elaborate a bit on what Chris said.

O'Neill, in his book The Geometry of Kerr Black Holes, proves:

there is a closed timelike curve through any event inside the inner (Cauchy) horizon, i.e., through any event for which r < r-.

Carroll gives the following simple example. Consider a curve for which \phi varies, and for which t, r, \theta are held constant. Because of periodicity with respect to \phi, any such curve is closed.

Now, the timelike part.

Take r &lt; 0 with |r| small, and \theta = \pi/2. Note r is a coordinate, not a radial distance, and negative r is part of (extended) Kerr. Because 0 = dt = dr = d \theta, the line element along the curve is

<br /> ds^2 = \left( r^2 + a^2 + \frac{2Mr a^2}{r^2} \right) d\phi^2<br />

For r negative and small. the last term, whcih is negative, dominates, and thus ds^2 is the line element for a timilike curve.

 

[K^2]

Sure. Bellow the event horizon. Considering the fact that the interior Kerr solution is known to be unstable, and even if it was stable, making use of something located below the event horizon is problematic, this is absolutely useless. What you want are closed curves that pass through an arbitrary point in asymptotically flat space, and you do not get such CTCs with Kerr metric or any other metric known to be stable.

But yes, this is why my first thought was to Kerr metric. Taking the r² slightly greater than zero allows for a closed space-like curve with all the same properties. So a FTL ship should be capable to keep station at constant t above Cauchy surface. Again, assuming the interior region is stable.

Now, the question is how far we can raise r and still have a closed curve that's traversable by FTL. After all, there are limits to how far we can push Alcubierre Drive. In flat space-time, I can still take a t = constant curve which will have positive ds². But you can't follow that with Alcubierre Drive. You can only push it so far past null curve with finite energy.

I have a feeling event horizon might still end up being a hard cutoff for that and I'd have to come up with something more creative, but I really should just bite the bullet and work this out properly.

How can a ship move from a timelike curve to a spacelike curve?

By changing parameters in the Alcubierre Metric, presumably via adjusting energy densities required to generate such metric. Assuming we are still talking about an Alcubierre Drive, of course. If you have some other FTL method in mind, you'd have to tell me how it's done. But in either case, if we are saying that a FTL ship is possible, ability to move from a time-like trajectory to a space-like one is part of what it has to be capable of.P.S. Yeah, for r >> r_s Kerr looks like rotating Schwarzschild, so there is definitely nothing to gain there. If there is going to be anything interesting about FTL near a Kerr black hole, it's going to be in the Ergosphere.

 

[Dale]

they address the issue of getting from one bubble to another, addressing the issue I was unsure about.

Yes, they mentioned the key for me which was that the bubble disappears when v=0. For some reason, that had never clicked with me previously.

 

[Dale]

That's what faster-than-light means. You cover distance in less time than it would take light. Id est, the separation between start and finish is space-like. Somewhere in between, world-line of the ship has to be space-like.

No, the worldline of the ship in the Alcuiberre metric is always timelike. We are not talking about spacelike trajectories, we are trying to find out if the Alcubierre metric allows closed timelike curves (which it does according to the paper).

 

[Dale]

Can an Alcubierre drive stop or be turned off once started? If not then it is not much use for transporting material or passengers from A to B.

I was unsure about this. The ship inside the warp bubble cannot control the bubble, but it turns out that the bubble simply disappears when it stops. It would have to be pre-set to stop somehow, but once it stops the passengers can leave.

 

[yuiop]

I was unsure about this. The ship inside the warp bubble cannot control the bubble, but it turns out that the bubble simply disappears when it stops.

OK, it appears that the Alcubiere drive requires a sort of track to be constructed in advance. The drive is started and stopped by turning the track on or off. Now there are some other issues. It appears that this drive requires negative mass which is quite difficult to obtain. It also requires that the space time wave that drives the bubble has to propagate faster than light and this outside the bubble.

Putting all the reality issues aside and assuming we can actually build such a drive, here is how we can travel back in time. First, let us assume the top speed of the drive is defined relative to its track. A and B are two locations in flat space that are at rest with respect to each other. A track is built in a circle such that A and B are at opposite points on the perimeter of the circular track. Now if the top speed of the bubble is 2c relative to the circular track, then the bubble arrives back at A after it left (as measured by an observer that remains at A) and no time travel is observed. Now let us say the track is rotated to a relativistic speed (Say 0.8c) in a clockwise direction. Now an Alcubierre bubble traveling at 2c relative to the track, in an anti-clockwise direction will arrive back at A before it left.

 

[PAllen]

OK, it appears that the Alcubiere drive requires a sort of track to be constructed in advance. The drive is started and stopped by turning the track on or off. Now there are some other issues. It appears that this drive requires negative mass which is quite difficult to obtain. It also requires that the space time wave that drives the bubble has to propagate faster than light and this outside the bubble.

Putting all the reality issues aside and assuming we can actually build such a drive, here is how we can travel back in time. First, let us assume the top speed of the drive is defined relative to its track. A and B are two locations in flat space that are at rest with respect to each other. A track is built in a circle such that A and B are at opposite points on the perimeter of the circular track. Now if the top speed of the bubble is 2c relative to the circular track, then the bubble arrives back at A after it left (as measured by an observer that remains at A) and no time travel is observed. Now let us say the track is rotated to a relativistic speed (Say 0.8c) in a clockwise direction. Now an Alcubierre bubble traveling at 2c relative to the track, in an anti-clockwise direction will arrive back at A before it left.

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.

 

[K^2]

No, the worldline of the ship in the Alcuiberre metric is always timelike. We are not talking about spacelike trajectories, we are trying to find out if the Alcubierre metric allows closed timelike curves (which it does according to the paper).

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.

So long as space-time around the warp bubble is sufficiently flat on the scale of the warp bubble's size, you can forget about the warp bubble, and simply think about what would happen if you had a ship following a space-like curve. This way, you don't have to solve for metric of the warp field in the neighborhood of a star or a black hole. So long as you don't get too close to event horizon, you can just take the corresponding metric of the gravitational source and consider a ship that's not restricted to time-like curves in this metric.

In fact, if you actually read the way Alcubierre Metric is defined, it is defined in terms of the space-time curve the bubble follows. And that curve is allowed to be space-like.

I was unsure about this. The ship inside the warp bubble cannot control the bubble, but it turns out that the bubble simply disappears when it stops.

The bubble doesn't disappear when the ship stops. Ship stops when the bubble disappears. In fact, ship never moves. It's the bubble that moves along a predefined curve from source to destination.

It's all in the definition of the metric. It's worth reading through the definition and figuring out what all of the individual components mean.

 

[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.