Talk:Alcubierre drive/MetricArchive

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Talk:Alcubierre metric/Archive 1 (comments up to 12 Oct 2005)

Contents 1 Time travel? Yes, necessarily 2 The FTL paradox 3 RFC 4 A Layman Comments:

Time travel? Yes, necessarily

Hello, CH. I'm confident that you are correct about the metric, but my observation has nothing to do with closed timelike curves. Rather, it is based on the geometry of ordinary spacetime. Any FTL path is by definition outside the future lightcone of its originating point. It is an elementary consequence of Special Relativity that paths of this sort will, in some frames of reference, be seen to move backward in time. Since all frames of reference are equally valid, this means that the capability to travel FTL is necessarily equivalent to the capability to travel backward in time. This consequence of Special Relativity is independent of the conditions inside a hypothetical warp bubble. It pertains to the path followed by the moving system as a whole. You are correct that it does not involve closed timelike curves, but this is because a path outside the future lightcone is not timelike -- and that is the problem. I am restoring the observation, which is fundamental to understanding what claims of FTL travel mean. For discussion by a heavy-duty expert, see the comment | Grandfather Paradox by John Baez in the Physics FAQ. ---ED (still unregistered for the moment -- thanks for the note)

Hi again, 63.201.230.31, I removed the comment because I still think what you actually wrote is misleading. (Maybe I don't understand what you intended by what you wrote.) Note that "travel backward in time" can have various meanings. The key point here is that the light cone/str thing a local phenomenon which holds for any Lorentzian spacetime, but when people discuss time travel in the context of warp drives, they mean a distinct global phenomenon. Specifically, when you said any FTL path is by definition outside the future lightcone of its originating point, that is only true locally. In a way showing why this (and related statements) can fail globally is the entire point of the warp drive spacetimes as pedagogical examples of Lorentzian manifolds (not solutions to the EFE) which exhibit unusual causal structure.

I have many many pans in the fire right now, unfortunately, but I do intend to greatly revise this article when I get a chance, based on a very long review paper on warp drives which I abandoned years ago when I decided that the subject isn't really sufficiently interesting to professional physicists to warrant a review. However, I do have some nifty illustrations I could upload. Please bear with me, though, since I need to finish quite a few other things first. Again, I agree that "time travel" is an issue which has been discussed in this context, but it will require much explanation and some good illustrations to clarify what this is about.---CH (talk) 02:24, 15 October 2005 (UTC)

The future and past light cones are global phenomena, defining which events can (according to relativity) be influenced by which other events. Accordingly, everything I stated is, in fact, global. Time-like worldlines are those in which every successive point is inside the future light cone of every predecessor point (this refers to predecessor and successor points in a simple trace-the-oriented-curve sense, which is time-independent). FTL motion is not time-like and hence would enable paths that violate relativistic causal constraints. This is widely understood. I am sorry that this presents a difficulty for the scheme described in this article, but these are the facts. I have provided substantial documentation for this point. I request that you do likewise to support any contrary conclusion, and that you not delete this discussion and its documentation. KED 18:56, 15 October 2005 (UTC)

Hi, KED, you seem very sure of yourself, but you are wrong, and if you give me a chance I can tell you why.

One problem here is that the sci.physics FAQ entry you cited does not tell the whole story for warp drives, so if you understand local versus global I am puzzled why you think it is an appropriate citation here. Note that it specifically mentions "in str", which is incorporated into gtr at the level of tangent spaces, as I referred to above.

Yes, I understand local vs. global. There is no reason for the FAQ to mention local issues, because the travel in question, including time travel, isn't a local phenomenon inside a hypothetical warp bubble. It is about going somewhere far away. There is no need to consider funny business inside the bubble in examining the path of the bubble itself. All of this pertains to the path, not to the structure of the bubble.

Now, you are quite right that at least for globally hyperbolic spacetimes such as we have here, there is a global notion of past and future light cone (unfortunately people tend to use the same words for light cones at the level of tangent spaces and globally, which can lead to confusion, which may have happened here). However, the whole point of these warp drive spacetimes is that observers inside the warp bubble achieve effectively superluminal travel without their world lines ever becoming non-timelike. Moreover, there are no closed timelike or closed null curves.

There is no need to consider observers inside a warp bubble. The path of the bubble is clear with respect to observers outside. It goes where and when they observe it going. If it is moving faster than light then, by definition, it is following a non-timelike path. This is fundamental to relativity. If you disagree with this, please point to some reputable source that supports your position.

You said

Any form of faster-than-light travel would (by definition) follow a path outside the future light cone of its point of origin in spacetime. The light cone defines the absolute future, hence these paths are not time-like or subject to causal constraints. Faster-than-light travel therefore would necessarily enable travelers to reach points in spacetime that fall in their past lightcones, that is to say, in their past (See Grandfather Paradox). This does not involve closed time-like paths, but is instead a consequence of the fundamental Minkowsky geometry of spacetime.

The bubble velocity is defined as the velocity, as seen from the point of view of a flat space observer, of any matter contained within the curved space created by the faster-than-light drive.

I have removed these because I believe they are misleading or even wrong in this context. The alleged flat background mentioned in the second paragraph and implied in the first is ill-defined. In particular, when you say observers inside the warp bubble can reach points outside their (global?) light cone, if you mean in the curved spacetime, this is false by definition; if you mean, in some flat background, this appears to be ill-defined.---CH (talk) 02:47, 16 October 2005 (UTC)

Allow me to try to clarify what I mean by the flat background, which is not at all ill-defined:

Imagine an interstellar flight using your warp bubble. (1) The bubble is presumably small compared to the distance to be traveled. (2) Therefore, we can define a sphere around it such that almost all of the warp, whatever that may be, is inside, and almost all of the distance to be traveled is outside. (3) The space outside is essentially flat. (4) The vehicle-plus-warp-bubble is traveling through that flat space. (4) The path of the vehicle in the flat space between the stars is the path of the bubble. (5) Because the path is through a flat space, special relativity can describe its properties. (6) The properties are as I have said. Is this clear? If I seem very confident, it is because I know what I am talking about, and the facts are very clear and simple.

I am becoming interested in procedures for adjudicating irreconcilable disagreements in Wikipedia. I am restoring my edit. Please leave it in place, or provide some evidence that it is wrong. Your arguments to date suggest that you do not understand special relativity. This is, however, a prerequisite for understanding general relativity, and thus for understanding the subject of this article. KED 08:03, 18 October 2005 (UTC)

One more tidbit: the #1 Google entry for <"faster than light" "time travel" minkowski >, by a physicist, notes that "since there is no absolute reference frame separating the regions of superluminal past and future, faster-than-light motion in Minkowski space-time implies the possibility of time travel". OK? I can pile this references higher, if you like. Here's one in Wikipedia: Faster-than-light#Possibility_of_FTL. If you still think that what I wrote is misleading, I submit that the absence of any statement of this sort is far more misleading. If you don't agree, please edit the "Faster than light" entry to explain your position, which is incompatible with what is there. KED 08:31, 18 October 2005 (UTC)

KED, you keep citing irrelevant FAQ pages (incidently, Phil Gibbs, not John Baez, wrote the page on grandfather paradox). I already said that I have read the arXiv literature on warp drives (not all these papers are equally correct, but that is another question). More to the point, I have constructed my own simplified warp drive spacetimes and analyzed them in detail. Indeed, I have used bump functions with compact support to construct simple examples which are very similar to the Alcubierre example, but with the warp bubble completely confined to some compact region. If you do this, and plot light cones (with two spatial dimensions suppressed), you will see that the bubble achieves effectively superluminal motion without any world lines ever becoming null or spacelike.

You keep referring to a background metric, but this doesn't make sense in the context of Lorentzian manifolds. If you do the exercise I suggested (plot the light cones in a simplified example) you should see what is wrong with your claim. When you have convinced yourself, please remove the paragraph you added. TIA---CH (talk) 15:36, 18 October 2005 (UTC)

Once again, rephrasing: nothing pertaining to the interior of the "warp bubble" has anything whatsoever to do with the issue at hand, which is about paths through the ordinary spacetime of interstellar space, regardless of what it is that follows a path. Ordinary spacetime has entirely uncontroversial properties in this regard. Accordingly, your repeated return to the properties of the "warp bubble" in this context is inappropriate. You have failed to provide any support for your view, much less for repeatedly removing a statement of the standard view. I think that this clearly violates NPOV. KED 02:10, 30 October 2005 (UTC)

The FTL paradox

Hi CH, I read through the debate, and it is an interesting one. Here's the problem as I see it: KED is echoing a viewpoint that is commonly taught in introductory GR courses: that superluminal travel implies time travel. Thus, there is an obvious, appearant paradox that the Albacurrie drive somehow avoids. I don't quite know how it avoids this, but simply stating that "the worldline of the observer has no loops", while appearantly true, doesn't help most readers resolve the paradox. Take me, for example: I know enough GR to both mostly understand the article and to be familiar with the basis of KED's complaints. I do not know enough to be able to guess the correct resolution for the paradox (yes, the "no loops" is a good clue, but still leave me hanging a bit). Thus, I fully expect other educated readers to also stumble over this, and protest in a fashion not unlike KED. It would be best if the article tried to deal with this issue in as direct a way as possible, and (among other things) acknowledge that there is a real paradox (which has a real resolution, if somewhat subtle.) linas 00:20, 18 October 2005 (UTC)

The whole discussion is rather futile. What will happen, if we can distort the space-time, despite the need for negative energy densities, and a lot of other unphysical pre-conditions is like discussing the physics of the philosopher's stone. Anyway, while A. metric doesn't have CTC, the question of CTCs and trime travel in other but related metrics has been discussed, see e.g. gr-qc/9702049. --Pjacobi 08:40, 18 October 2005 (UTC)

Thanks, Pjacobi, but

• I know that paper (I already said I read the literature some years ago!),
• this article is about the Alcubierre spacetime, not the Krasnikov example.

The whole point is that KED is arguing that X must always happen, but that's wrong, as analysis of the Alcubierre example (or my simplified examples) shows.---CH (talk) 15:45, 18 October 2005 (UTC)

Below is the text which is misleading. KED or whomever, if you want to put this someplace, can you create an article on the Krasnikov tube and put it there? Please don't just add it back to this article, because it doesn't apply to the Alcubierre warp drive spacetimes. TIA---CH (talk) 20:14, 24 October 2005 (UTC)

However, any form of faster-than-light travel would by definition follow a path outside the future light cone of its point of origin in spacetime, whether or not a vehicle is wrapped in a locally distorted metric. Because the interior of the future light cone defines the absolute future, these flight paths would not be time-like or subject to causal constraints. Faster-than-light travel therefore would necessarily enable travelers to reach points in spacetime that are within their past lightcones, that is to say, in their past (See Grandfather Paradox). This fact is a consequence not of closed time-like paths, but of the fundamental Minkowsky geometry of the essentially flat spacetime of interstellar space.

As I reiterate above, this is not an issue of General Relativity, since the motion in question is through (effectively) flat spacetime. This is an issue of Special Relativity. The view that I am presenting is noncontroversial. Your recourse to General Relativity indicates that you do not understand the issue. I have no idea what the relevance of a "Krasnikov tube" is, or why it would address the issue at hand for me to create a page on it. You have offered no relevant response. I have reverted the page. KED 02:13, 30 October 2005 (UTC)

I reverted back to the last good version. KED, change your tone of voice and start disscussing please. Questions, rather than asertations of being correct would be apropreate here. DV8 2XL 03:07, 30 October 2005 (UTC)

I have a rather large collection of relevant papers, of which I only listed a handful in the references section (combination of not wishing to take the time plus not wanting to overwhelm readers). But anyone interested can search the arXiv like this (also try other keywords such as "quantum inequalities"). In addition, of course, you can do a conventional literature search, but I think pretty much the entire literature on warp drives is present in eprint form on the arXiv. Probably I need not point out that there are some controversies in this literature, and also a handful of questionable preprints which other authors seem to ignore. Par for the course.---CH (talk) 23:46, 30 October 2005 (UTC)

RFC

KED, ironically enough, I have been considering submitting this content dispute for an RFC, but apparently you have already done this. I hope this means you are now willing to discuss the issue here reasonably.

You have declined to discuss your background, so I don't know how much you know about various relevant issues concerning curved Lorentzian manifolds, such as the distinction between various levels of structure (e.g. tangent space vs. local neighborhood vs. global structure, or conformal versus topological structure). Nor is it yet clear to me how well you understand the distinction between various different notions of "FTL" and "time travel", not all of which are relevant here. You have also failed to clearly state whether you have read the dozen or so preprints available on the arXiv which deal with various aspects of so-called warp-drive spacetimes, which I have done.

I have also studied in great detail simplified versions of the Alcubierre spacetime, using smooth bump functions to construct a soda-can shaped warp bubble in an axisymmetric spacetime which is exactly locally flat outside the warp bubble, in distinction to the tanh function employed by Alcubierre to construct a spherical bubble in a spacetime which is approximately locally flat outside the bubble. In this variant warp-drive spacetime, the metric has the ADM form

where F,G,V are appropriate smooth functions.

Therefore, I consider myself intimately familiar with the mathematical construction, analysis, and physical interpretation of warp-drive spacetimes. In particular, I know that the light cones look like in my own warp-drive spacetime, which is good enough to understand the relevant qualitative features in the original Alcubierre warp-drive. I hope that the relevance of the appearance of the light cones is not in dispute.

As anyone who has studied the literature knows, other warp-drive spacetimes have been proposed, but this article is about the Alcubierre warp drive. My own warp-drive spacetime is only a minor variant of Alcubierre's construction, but some of the other proposals are significantly different. In particular, some of the constructions which have been mentioned on this talk page are significantly different globally from my construction and the original Alcubierre construction discussed in this article. I don't dispute that more general discussions in the published literature (mostly in CQG) or alternative constructions are in some cases notable, but these should probably go into a new article which I have been planning to write when I find the time. (This has not been a very hot area recently, so filling other gaps in current Wikipedia coverage have, in my opinion, higher priority.)

Earlier, you cited Phil Gibb's "grandfather paradox" article in the sci.physics FAQ (of which I am another coauthor, by the way), but you didn't quote this bit which tends to support my contention that there are several possible notions of "FTL" and "time travel", not all of which are applicable here.

You also wrote:

Any form of faster-than-light travel would (by definition) follow a path outside the future light cone of its point of origin in spacetime. The light cone defines the absolute future, hence these paths are not time-like or subject to causal constraints. Faster-than-light travel therefore would necessarily enable travelers to reach points in spacetime that fall in their past lightcones, that is to say, in their past (See Grandfather Paradox). This does not involve closed time-like paths, but is instead a consequence of the fundamental Minkowsky geometry of spacetime.

The bubble velocity is defined as the velocity, as seen from the point of view of a flat space observer, of any matter contained within the curved space created by the faster-than-light drive.

This suggests you are trying to appeal to some kind of flat spacetime background metric, but in a curved spacetime such a background metric will usually not support an unambigious physical interpretation, at least not in a metric theory of gravitation like general relativity. There are some bimetric theories, but these are not nearly as well-studied as general relativity, and most of the literature on warp drives attempts to study the question of whether or not the putative energy-momentum tensor in warp-drive spacetimes makes sense physically if interpreted in the context of general relativity. That is, we compute the Einstein tensor, which we can do for any Lorentzian manifold whatever, divide by 8π, and attempt to interpret the result as the energy-momentum tensor generated by some possibly "strange" matter plus possibly "exotic" nongravitational fields.

Assuming the default gtr context, in a spacetime like my own which is locally flat outside the bubble, the geometry in those regions is indeed Minkowskian, but a key point is that this doesn't mean that you can extend the flat spacetime metric inside the bubble, as you appear to want to do. It is true that some authors have used a flat spacetime background metric in the context of spacetimes with small curvature, but the Alcubierre warp-drive spacetimes (and minor variants like my own construction) do not fit this bill, at least for bubbles which actually go "effectively superluminal" at some point during their history. See for example gr-qc/0412065, where the point is to study Alcubierre-like warp-bubbles with small curvature (which means they don't move very fast) in order to argue that certain objectional features of the their energy-momentum tensor are generic features of the basic Alcubierre construction. The point is, this weak-field approximation is a valid tool for studying tensor fields (e.g. the metric perturbations does behave mathematically like a tensor field in flat spacetime, but it would be incorrect to naively assume that the background metric is physically observable or can be used to define some kind of velocity. To do that you need to explain how to correlate events in two spacetimes (e.g. a globally hyperbolic warp-drive spacetime, outside the bubble, versus Minkowski spacetime); one of the benefits of my own variant of the Alcubierre spacetime, incidently, is that because my spacetime is locally flat outside the bubble, it is much easier to see potential pitfalls in attempting to make such a correlation.

I have already stated that much of what I am saying here will only become clear if I rewrite the article to include some material such as a plot of the light cones in my own variant of the Alcubierre spacetime (where the soda-can shape of the warp bubble makes it a bit easier to study the putative flow of energy-momentum around the bubble and also the to take dimensional reductions to more easily visualize the light cones, since my variant is axially symmetric while Alcubierre's warp drive spacetime is not truly spherically symmetric). I hope that you would have no objection to my doing that when I get a chance, but this might not occur for some time.

However, in the mean time I can propose a compromise. I think our content dispute basically boils down to my judgement that you keep editing the article to make statements which I think are misleading, simplistic, and too strong or too general. However, a weaker statement or one which is suitably qualified might be acceptable. For example, judging from your past edits, you want to claim that FTL implies time travel. My basic objection to this is that "FTL" is ambiguous (tachyons and warp bubbles are quite different in how they achieve "superluminal motion" and indeed, this refers to two quite different senses of the geometrical meaning of "superluminal motion"), and "time travel" is also ambiguous (there are various distinct notions, not all of which apply to the Alcubierrre warp-drives and minor variants such as my own construction). But instead, you could say that some of the literature on warp-drive constructions in general discusses the relationship between warp drives and certain notions of time-travel. Would that be acceptable to you? If so, I hope you will permit me to find an appropriate place to insert such a statement which won't break up the flow of ideas in the existing article.---CH (talk) 20:53, 30 October 2005 (UTC)

Well I think CH is offering a good compromise here. Although I would like to see some of the literature get referenced. I dislike the phrase as often I see it as a Trojan Horse to introduce some very marginal ideas into science articles in Wikipedia. DV8 2XL 21:57, 30 October 2005 (UTC)

Thanks! As for literature, I have a rather large collection of relevant papers, of which I only listed a handful in the references section (combination of not wishing to take the time plus not wanting to overwhelm readers). But anyone interested can search the arXiv like this (also try other keywords such as "quantum inequalities"). In addition, of course, you can do a conventional literature search, but I think pretty much the entire literature on warp drives is present in eprint form on the arXiv. Probably I need not point out that there are some controversies in this literature, and also a handful of questionable preprints which other authors seem to ignore. Par for the course.---CH (talk) 23:46, 30 October 2005 (UTC)

Afterthought: KED, in the above metric for an axially symmetric warp-drive spacetime, F,G are more or less arbitrary bump functions (one in the interior of the warp bubble, zero outside it, and taking intermediate values in the "walls" of the warp bubble, which is where the curvature and other weird stuff happens; the interior and exterior regions are both locally flat) and V controls the motion of the warp bubble. If you take F,G to be zero everywhere, the obvious timelike congruence shows that V is velocity like. But when you take nontrivial bump functions, it is not so easy to give a purely geometric or physically meaningful defintion of "velocity". For example, you could try to examine the motion of the locus where the bump functions become nonzero. Mathematically that is well defined, but in a sufficiently small neighborhood of the "outer margin" of the walls of the warp bubble, the curvature is always neglible. In my paper I pointed out that one can use optical effects like blue shift to define a velocity, but this is always subluminal. This measureable velocity is related, for this class of spacetimes, to what you want to call, I think, "bubble velocity", but that formula is only valid if you know the spacetime has the given form! Which of course means such a definition should probbably be regarded as physically dubious. Perhaps this gives a better sense of what I mean when I say that you cannot simply continue the background metric inside the walls of the warp bubble to try to define a bubble velocity in a naive way.---CH (talk) 00:13, 31 October 2005 (UTC)

Oops, another afterthought: DV8 2XL, I entirely share your concern that some parties might use this RFC discussion as a "Trojan Horse" to give certain poor quality arXiv eprints greater weight than they deserve, although I don't know if we have the same parties in mind. That would of course amount to gaming the system (particularly if KED happens to be coauthor of one of these preprints--- by the way, KED, this is one reason why I think it would be helpful it you would divulge your identity) and in my view would be unacceptable behavior in the Wikipedia. We shall see what develops, I guess.---CH (talk) 00:21, 31 October 2005 (UTC)

• Oh, the usual suspects....DV8 2XL 01:00, 31 October 2005 (UTC)

I am puzzled by the the responses that CH has offered, which seem off-topic. I had stated in a revision of the article that:

Any form of faster-than-light travel would (by definition) follow a path outside the future light cone of its point of origin in spacetime....The bubble velocity is defined as the velocity, as seen from the point of view of a flat space observer, of any matter contained within the curved space created by the faster-than-light drive.

Sorry to interject my static in the middle of your comment (usually not a good practice), but KED, please ask yourself how precisely you intend to define the "velocity" of the bubble. Please think about this carefully. Are you looking at the "edges" of the bubble, where the spacetime becomes perfectly flat? (In my version which is locally flat outside the warp walls.) Or are you trying to extend the flat spacetime metric inside the bubble, as some kind of background in a curved spacetime? Or are you trying to obtain a physical definition, perhaps using the formula I mentioned relating blueshift of stars immediately ahead of the bubble, as seen by an observer within the bubble? Note that my V(t) above presumably corresponds to what you want to call bubble velocity. But while this is defined in this model, is this really physically well-defined? Hope this helps, but if you still don't see what I mean, I think this can't be settled except at the whiteboard, unfortunately. ---CH (talk) 02:59, 8 November 2005 (UTC) and now back to KED's comment:

In this Talk page, I earlier stated that "nothing pertaining to the interior of the "warp bubble" has anything whatsoever to do with the issue at hand, which is about paths through the ordinary spacetime of interstellar space, regardless of what it is that follows a path....Accordingly, your repeated return to the properties of the "warp bubble" in this context is inappropriate."

In short: the bubble interior is beside the point. Only the bubble's path matters when considering where the bubble itself goes in spacetime, for example, backward in time. Yet CH's discussion above is entirely about the bubble interior and concludes with the statement: "I say that you cannot simply continue the background metric inside the walls of the warp bubble to try to define a bubble velocity in a naive way." No physics background is needed to see that this response is not relevant to the issue. By discussing the interior, it addresses the opposite of the point that I made. Please excuse my frustrated tone. In light of the above, I hope that it is understandable and perhaps even forgivable.

Regarding a compromise, a statement that some of the literature on warp-drive constructions in general discusses the relationship between warp drives and certain notions of time-travel strikes me as extremely vague. Perhaps Faster-than-light paths through flat spacetime are spacelike rather than timelike, and hence enable travel backward in time. Some papers in the literature conclude that this does not hold for some warp-drive constructions. Since a statement regarding time dilation currently appears at the beginning of the article, it seems that a statement on this time-related issue should appear there as well. If this would disrupt the present flow of the article, then I would suggest that the present flow is obscuring a key issue, and should be altered.

By the way, I am not an author or coauthor of a preprint in this area. My chief interest is to see whether Wikipedia is as self-correcting as I had hoped. KED 07:31, 31 October 2005 (UTC)

• • KED- is is considered poor form to experiment in this way. DV8 2XL 00:54, 1 November 2005 (UTC)
    • DV8 2XL- Your reference on experiment is to a page titled Don't disrupt Wikipedia to illustrate a point. I plead innocent: I am not experimenting in any sense discussed on that page. I agree with the norms expressed there. I am trying to work within the system as best I understand it correct a scientific article to make a simple, true, and highly relevant point. I do hope to learn something from the process. KED 20:30, 5 November 2005 (UTC)

On reflection, I realize that I have been making the assumption that the circumference of a warp bubble would be small compared to the distance that it might travel, and that the speed of the bubble itself (rather than only that of its contents) is supposed to be superluminal. If this is not correct, and the superluminal paths in question are actually within a bubble that itself follows a subluminal path, please accept my apologies for my distracting misunderstanding. If this is the case, however, I would argue that the vast size of the warp bubble (or alternatively, the short distance traveled) be stated early and explicitly, and that the term "warp drive" perhaps be reconsidered as a description. KED 07:39, 31 October 2005 (UTC)

No criticism of the fact regarding time travel that I have stated has been offered, since the response (as I document in the paragraphs above) addressed a different and unrelated question. This fact is as or more important than the statement that it follows, and is on the same topic -- the consequences of FTL for the passage of time. Accordingly, I am restoring the statement and hope that this is satisfactory. KED 20:30, 5 November 2005 (UTC)

• This topic of yours has absolutly nothing to do with the Alcubierre metric; you have not recived a consensus to re-insert this passage; it is unsourced. I am going to ask that you remove it until you recive such a consensus. DV8 2XL 20:48, 5 November 2005 (UTC)

KED, if it helps, I too am thinking of a "small" bubble. Part of my objection is that I don't think your bubble velocity is well-defined (please see above and consider thoughtfully my questions, hopefully drawing careful pictures of the light cones in examples of the simpler warp spacetime I gave above, which is locally flat outside the walls of the bubble).

Like DV8 2XL, I am alarmed my your statement above that my chief interest is to see whether Wikipedia is as self-correcting as I had hoped. Please be aware that this could easily be interpreted as a statement that you are hoaxing the Wikipedia or otherwise gaming the system to make some point which is obscure (and possibly uninteresting) to the general Wikipedia community of readers/editors. I did you see that you disavowed such a purpose, but you didn't really explain what you did mean by this disturbing statement.

KED, I also ask that you voluntarily excise your claims until we can settle this dispute here. You did say that you are interested in learning, so despite my frustration in trying to explain my points, if neccessary I might be willing to try to prepare and upload some figures or something.---CH (talk) 02:59, 8 November 2005 (UTC)

A Layman Comments:

I don't know very much about relativity, special or general; I'm only looking at this page as a result of my interests in science fiction. I must say, though, that this is an impressively heated intellectual discussion, and I have read through nearly all of it and am still very confused about what you all are actually arguing about.

KED's position, as best I can tell, is more or less: "In theory, the Alcubierre Metric would allow an object to travel faster than the speed of light without violating Einstein's Theory of Relativity. But everybody knows that Einstein's Theory of Relativity shows that it is impossible to travel faster than the speed of light; Therefore the Alcubierre Metric violates Einstein's Theory of Relativity, and so a disclaimer must be put into this article to the effect that the Alcubierre Metric is self-contradictory and false."

Everybody else's position seems to be, more or less: "KED, would you please actually read what you just wrote?"

Am I interpreting all this correctly? Or am I misunderstanding something?

--Robin Moshe 22:37, 18 June 2006 (UTC)