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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.)
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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
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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
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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. ---
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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.
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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
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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.
1107:. 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
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1165:(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.---
738:(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.---
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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.
1459:. Please be aware that this could easily be interpreted as a statement that you are hoaxing the Knowledge or otherwise gaming the system to make some point which is obscure (and possibly uninteresting) to the general Knowledge community of readers/editors. I did you see that you disavowed such a purpose, but you didn't really explain what you
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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.
1388:. 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.
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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,
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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.
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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
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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
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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
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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
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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.
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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,
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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
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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
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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
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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
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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?)
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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I am becoming interested in procedures for adjudicating irreconcilable disagreements in Knowledge. 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
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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.
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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
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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
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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
1240:(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 Knowledge. We shall see what develops, I guess.---
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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.
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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.
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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
438:. 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.
668:, 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
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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
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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."
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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."
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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
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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.
1209:. 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.---
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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
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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.
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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
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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
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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.
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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
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planning to write when I find the time. (This has not been a very hot area recently, so filling other gaps in current Knowledge coverage have, in my opinion, higher priority.)
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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.
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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.---
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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.
290:, 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
1201:. 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
1086:, and attempt to interpret the result as the energy-momentum tensor generated by some possibly "strange" matter plus possibly "exotic" nongravitational fields.
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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.---
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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
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By the way, I am not an author or coauthor of a preprint in this area. My chief interest is to see whether Knowledge is as self-correcting as I had hoped.
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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
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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
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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.---
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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 Knowledge.
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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.
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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
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some of the literature on warp-drive constructions in general discusses the relationship between warp drives and certain notions of time-travel
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some of the literature on warp-drive constructions in general discusses the relationship between warp drives and certain notions of time-travel
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which tends to support my contention that there are several possible notions of "FTL" and "time travel", not all of which are applicable here.
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572:. 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.
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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
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features in the original Alcubierre warp-drive. I hope that the relevance of the appearance of the light cones is not in dispute.
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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:
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observers inside the warp bubble achieve effectively superluminal travel without their world lines ever becoming non-timelike
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consequences of FTL for the passage of time. Accordingly, I am restoring the statement and hope that this is satisfactory.
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Sorry to interject my static in the middle of your comment (usually not a good practice), but KED, please ask yourself how
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to find an appropriate place to insert such a statement which won't break up the flow of ideas in the existing article.---
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bubble in examining the path of the bubble itself. All of this pertains to the path, not to the structure of the bubble.
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Everybody else's position seems to be, more or less: "KED, would you please actually read what you just wrote?"
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particular, some of the constructions which have been mentioned on this talk page are significantly different
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nothing pertaining to the interior of the "warp bubble" has anything whatsoever to do with the issue at hand,
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KED, ironically enough, I have been considering submitting this content dispute for an RFC, but apparently
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prerequisite for understanding general relativity, and thus for understanding the subject of this article.
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Hi, KED, you seem very sure of yourself, but you are wrong, and if you give me a chance I can tell you why.
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That is, we compute the Einstein tensor, which we can do for any Lorentzian manifold whatever, divide by
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985:{\displaystyle ds^{2}=-dt^{2}+\left(dz+V(t)\,(1-F(z)\,G(r))\,dt\right)^{2}+dr^{2}+r^{2}\,d\theta ^{2}}
1349:. Some papers in the literature conclude that this does not hold for some warp-drive constructions.
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locally flat outside the bubble. In this variant warp-drive spacetime, the metric has the ADM form
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qualified might be acceptable. For example, judging from your past edits, you want to claim that
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I have also studied in great detail simplified versions of the Alcubierre spacetime, using smooth
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by John Baez in the Physics FAQ. ---ED (still unregistered for the moment -- thanks for the note)
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Allow me to try to clarify what I mean by the flat background, which is not at all ill-defined:
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One more tidbit: the #1 Google entry for <"faster than light" "time travel" minkowski : -->
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If you disagree with this, please point to some reputable source that supports your position.
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Any form of faster-than-light travel would (by definition) follow a path outside the future
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Hi again, 63.201.230.31, I removed the comment because I still think what you actually
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have happened here). However, the whole point of these warp drive spacetimes is that
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you cannot simply continue the background metric inside the walls of the warp bubble
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any FTL path is by definition outside the future lightcone of its originating point
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my chief interest is to see whether Knowledge is as self-correcting as I had hoped
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Well I think CH is offering a good compromise here. Although I would like to see
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to construct a soda-can shaped warp bubble in an axisymmetric spacetime which is
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If you wish to start a new discussion or revive an old one, please do so on the
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If you wish to start a new discussion or revive an old one, please do so on the
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phenomenon which holds for any Lorentzian spacetime, but when people discuss
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This topic of yours has absolutly nothing to do with the Alcubierre metric;
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Am I interpreting all this correctly? Or am I misunderstanding something?
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this article is about the Alcubierre spacetime, not the Krasnikov example.
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I know that paper (I already said I read the literature some years ago!),
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Which of course means such a definition should probbably be regarded as
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that fall in their past lightcones, that is to say, in their past (See
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are very similar to the Alcubierre example, but with the warp bubble
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geometry of the essentially flat spacetime of interstellar space.
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of its point of origin in spacetime. The light cone defines the
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above, which is locally flat outside the walls of the bubble).
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travel would by definition follow a path outside the future
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you have not recived a consensus to re-insert this passage
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Like DV8 2XL, I am alarmed my your statement above that
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Note that this page is the talk page from the merged
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and the superluminal paths in question are actually
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in the context of warp drives, they mean a distinct
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984:
302:, but is instead a consequence of the fundamental
1408:drive" perhaps be reconsidered as a description.
1345:are spacelike rather than timelike, and hence
1386:Don't disrupt Knowledge to illustrate a point
994:where F,G,V are appropriate smooth functions.
783:which deal with various aspects of so-called
8:
1315:In this Talk page, I earlier stated that "
1203:you know the spacetime has the given form!
199:of tangent spaces, as I referred to above.
1335:Regarding a compromise, a statement that
1068:
976:
961:
948:
932:
843:
824:
815:
1339:strikes me as extremely vague. Perhaps
1279:created by the faster-than-light drive.
967:
919:
902:
879:
564:The whole discussion is rather futile.
1534:Do not edit the contents of this page.
44:Do not edit the contents of this page.
672:). This fact is a consequence not of
7:
1494:you all are actually arguing about.
436:Faster-than-light#Possibility_of_FTL
1367:KED- is is considered poor form to
1463:mean by this disturbing statement.
570:physics of the philosopher's stone
24:
1519:
1341:Faster-than-light paths through
29:
1194:sufficiently small neighborhood
129:. Specifically, when you said
1347:enable travel backward in time
1305:and now back to KED's comment:
916:
913:
907:
899:
893:
881:
876:
870:
430:, by a physicist, notes that "
96:Time travel? Yes, necessarily
1:
1481:02:59, 8 November 2005 (UTC)
1437:20:48, 5 November 2005 (UTC)
1423:20:30, 5 November 2005 (UTC)
1413:07:39, 31 October 2005 (UTC)
1393:20:30, 5 November 2005 (UTC)
1376:00:54, 1 November 2005 (UTC)
1360:07:31, 31 October 2005 (UTC)
1303:02:59, 8 November 2005 (UTC)
1259:01:00, 31 October 2005 (UTC)
1248:00:21, 31 October 2005 (UTC)
1217:00:13, 31 October 2005 (UTC)
1173:23:46, 30 October 2005 (UTC)
1144:21:57, 30 October 2005 (UTC)
1123:20:53, 30 October 2005 (UTC)
746:23:46, 30 October 2005 (UTC)
721:03:07, 30 October 2005 (UTC)
700:02:13, 30 October 2005 (UTC)
641:20:14, 24 October 2005 (UTC)
622:15:45, 18 October 2005 (UTC)
581:08:40, 18 October 2005 (UTC)
559:00:20, 18 October 2005 (UTC)
533:02:10, 30 October 2005 (UTC)
503:15:36, 18 October 2005 (UTC)
495:paragraph you added. TIA---
443:08:31, 18 October 2005 (UTC)
411:08:03, 18 October 2005 (UTC)
354:02:47, 16 October 2005 (UTC)
173:18:56, 15 October 2005 (UTC)
159:02:24, 15 October 2005 (UTC)
1380:DV8 2XL- Your reference on
1585:
1254:Oh, the usual suspects....
660:of its point of origin in
1512:22:37, 18 June 2006 (UTC)
676:, but of the fundamental
298:). This does not involve
1352:and should be altered.
1105:FTL implies time travel
568:is like discussing the
1137:some of the literature
1080:
986:
674:closed time-like paths
306:geometry of spacetime.
300:closed time-like paths
1532:of past discussions.
1081:
1079:{\displaystyle 8\pi }
987:
785:warp-drive spacetimes
652:However, any form of
103:| Grandfather Paradox
42:of past discussions.
18:Talk:Alcubierre drive
1384:is to a page titled
1067:
814:
787:, which I have done.
589:Thanks, Pjacobi, but
133:, that is only true
670:Grandfather Paradox
296:Grandfather Paradox
1489:A Layman Comments:
1207:physically dubious
1076:
982:
968:
920:
903:
880:
1572:
1571:
1544:
1543:
1538:current talk page
1238:gaming the system
654:faster-than-light
127:global phenomenon
88:Alcubierre metric
82:
81:
54:
53:
48:current talk page
1576:
1558:
1546:
1545:
1523:
1522:
1516:
1085:
1083:
1082:
1077:
1041:You also wrote:
991:
989:
988:
983:
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980:
966:
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937:
936:
931:
927:
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26:
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1491:
1065:
1064:
972:
957:
944:
857:
853:
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839:
820:
812:
811:
756:
666:absolute future
551:
549:The FTL paradox
327:bubble velocity
288:absolute future
98:
64:
30:
22:
21:
20:
12:
11:
5:
1582:
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1371:in this way.
1343:flat spacetime
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1092:mathematically
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798:bump functions
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1473:something.---
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830:
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821:
817:
810:
807:
806:approximately
803:
799:
795:
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792:
786:
782:
777:
776:
775:
774:
768:
765:have already
764:
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574:gr-qc/9702049
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37:
1526:This is an
1509:Robin Moshe
123:time travel
36:This is an
1382:experiment
1369:experiment
1199:subluminal
658:light cone
473:spacelike.
470:completely
284:light cone
1567:ArchiveĀ 4
1562:ArchiveĀ 3
1556:ArchiveĀ 2
1550:ArchiveĀ 1
1292:precisely
1163:like this
767:done this
736:like this
678:Minkowsky
662:spacetime
304:Minkowsky
292:spacetime
77:ArchiveĀ 4
72:ArchiveĀ 3
66:ArchiveĀ 2
60:ArchiveĀ 1
1330:opposite
1060:bimetric
1030:this bit
1016:globally
266:You said
139:globally
115:intended
1529:archive
1434:DV8 2XL
1373:DV8 2XL
1256:DV8 2XL
1141:DV8 2XL
802:exactly
718:DV8 2XL
578:Pjacobi
135:locally
90:article
39:archive
1478:(talk)
1405:within
1300:(talk)
1245:(talk)
1214:(talk)
1170:(talk)
1120:(talk)
743:(talk)
638:(talk)
633:TIA---
619:(talk)
500:(talk)
351:(talk)
156:(talk)
781:arXiv
556:linas
465:arXiv
149:agree
119:local
111:wrote
16:<
576:. --
325:The
1475:CH
1461:did
1420:KED
1410:KED
1390:KED
1357:KED
1297:CH
1242:CH
1236:to
1211:CH
1167:CH
1117:CH
763:you
754:RFC
740:CH
697:KED
635:CH
616:CH
530:KED
497:CH
440:KED
408:KED
348:CH
170:KED
153:CH
1507:--
1113:me
1074:Ļ
974:Īø
888:ā
834:ā
1540:.
1071:8
978:2
970:d
963:2
959:r
955:+
950:2
946:r
942:d
939:+
934:2
929:)
925:t
922:d
917:)
914:)
911:r
908:(
905:G
900:)
897:z
894:(
891:F
885:1
882:(
877:)
874:t
871:(
868:V
865:+
862:z
859:d
855:(
850:+
845:2
841:t
837:d
831:=
826:2
822:s
818:d
50:.
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