The warp drive: hyper-fast travel within general relativity

NASA, which even includes pretty slides that your galaxy brain can understand: https://ntrs.nasa.gov/api/citations/20110015936/downloads/20... Now, I tried to be civil, and even went so far as to recognize when I stopped being civil, apologized for it, and tried again. Yet you still insist on being an asshole about it. Well guess what: > There's no math here, just waffle. Yep, "just waffle" is all you've contributed to this discussion, and by the looks of it all you intended to contribute. Gotta flex your intellectual superiority, right? Too bad you're - like me - just another guy on the Internet, so any such superiority you think you might have is illusory, at best. > and I don't mind being a Jerk now You clearly didn't mind being a jerk from the get-go. Probably because that's all you can contribute, but here I was hoping that maybe you'd contribute something else. Oh well. Have a good one, I guess. Maybe next time we run into each other it'll be on more civil terms.

theory permits the existence ofregions with negative energy densities in some special circumstances (as, for example, inthe Casimir effect [4]). The need of exotic matter therefore doesn’t necessarily eliminate the possibility of using a spacetime distortion like the one described above for hyper-fast interstellar travel. https://arxiv.org/pdf/gr-qc/0009013.pdf The excitement here is partly due to the fact that this is both a trekkie thing and one that was previously not even supposed to numerically make sense. It's likely this "not requiring any specific fringe-physics thing" is what is causing the idea to catch on and continue to be ellaborated, because having specificed this mechanics well enough, then maybe and only maybe it might be possible to cause at least an analogue of it to exist and that'd be awesome.

kicker: "we would then insist that the final field configuration is, not what the observer wills it to be, but rather what follows, evolving these data via [dynamical equations]" Notably, this is backwards from the Alcubierre drive's formulation, which starts with a desired final field configuration, and is trapped by having no "before the bubble existed" initial values surface. The Alcubierre solution is eternal, and offers no way to be stitched into our apparently non-eternal universe (it sure seems to have a beginning, or at least an early hot/dense boundary close to which the presence of an Alcubierre bubble seems even less physically plausible than today). Although it is safe to describe really fantastical configurations of matter very near that early boundary, one has to settle things down in far less than seconds, in order to match several different lines of evidence of about the distribution of the first free-streaming photons (and the earlier free-streaming neutrinos, when we figure out how to build observatories to study them in detail). You could put Alcubierre bubbles everywhere during Cosmic Inflation, for instance, but you have to very quickly and aggressively suppress their observables. Let's turn this on its head: we can in principle construct a spacelike values-surface at time today and let it evolve. A problem we have with this is that the presence of either or both of not-yet-formed or formed-but-eventually-evaporating black holes makes a complete calculation of some far future values-surface impossible in principle, as far as we know, which means in the absence some new fundamental theory of quantum gravity that has yet to be discovered. Putting an Alcubierre drive onto the same today values-surface likewise blocks the complete calculation of the future values-surface, in principle. Dusting the cosmos with lots of Alcubierre drives makes things much worse. But maybe that's OK, because the cosmos appears to be dusted with lots of black holes and configurations of matter (like our own Virgo cluster) that will inevitably mostly settle into giant black holes that may one day evaporate. This means we can't really make a concrete prediction about the far future of our cosmos, in principle. I wouldn't sweat it, because we can't set down much more than the barest approximation of the real values-surface in practice anyway. So since we already have problems with causality thanks to gravitational singularities (or if you prefer, apparent trapping surfaces), and we have excellent evidence of them existing in our universe, an argument that "X poses problems for causality and therefore must be unphysical" is not especially compelling. Instead, the problem grinds down into [a] laying out an initial values surface gets harder, especially if we can't rely on a programme of pushing it further and further back in time so that unusual configurations of matter (black holes, Alcubierre bubbles) have the ability to develop through dynamical laws (which is what we do with physical cosmology, for instance); and [b] writing down the dynamical laws that relate neighbouring values-surfaces (which gets harder because we need more than the Lorentz symmetry group and GL(4). It might be fun to try to make [a] and [b] work in the presence of various FTL mechanisms, and indeed to some extent we do this in very specific settings (cosmic inflation, for instance). However, from the time of the CMB to now there is nothing to suggest a need to account for FTL material (or normal material embedded in a dynamical spacetime that moves it around FTL-style) at any scale, from the cosmological to the laboratory. The theory would undoubtedly be much more complicated than what we already have (which has already evolved and become more complicated as more evidence has become available), so there would not be much point to it. Finally, two extracts from the Geroch paper: "[I]n a similar vein, there exist solutions of Einstein’s equation in general relativity that manifest closed causal curves. But we do not ... allow observers to build time-machines at their pleasure. Instead, we permit observers to construct initial conditions — and then we require that they live with the consequences of those conditions." which is exactly the opposite of Alcubierre's approach in https://arxiv.org/abs/gr-qc/0009013v1 where he starts with a time machine first, and never describes the initial conditions before it exists. One would usually expect that for any artifact such as a spacecraft, there is a time before which it is fully built and switched on. One might compare that with an eternal Schwarzschild black hole and a black hole that forms via gravitational collapse of a massive star (or direct collapse of matter in the early universe). And, "from the present viewpoint the problems associated with superluminal signals do not seem nearly as severe as they did at first glance", a statement that is likely safe should such signals ever be proven.

timetravel. The idea is, that you travel always forward in time and you reach the same space time point at which you started. Much in the same way that you can travel always forward on a tire (torus) and still reach your starting point. Something like this may or may not happen on a metric which permits FTL, for example the Alcubierre metric does not permit travel on such curves. [1] But it would actually be easy to perform the same analysis on a Godel solution [2], which would permit closed timelike curves. Edith: Added the comment about the Godel solution. [1] Alcubierre, 2000 http://arxiv.org/pdf/gr-qc/0009013v1.pdf [2] https://en.wikipedia.org/wiki/G%C3%B6del_metric

movement between the two endpoints. Even when factoring outside observers... > The violation occurs relative to reference frames outside of the warp bubble where special relativity fully applies. ...how would this apply if the information in question is constrained to that warp bubble between its transmission and receipt? What would there be to observe? If we're talking about side effects of that communication (say, our Alcubierre messenger pigeon drops a feather back into "normal" space somehow), would the propagation of those side effects not just revert back to being subluminal? That is: from every local perspective, the pigeon is traveling subluminally, so this should still apply in the event the pigeon or any signal from it escapes its bubble and reenters "normal" spacetime, no? > Here, explicitly looks like a worked out example: http://exvacuo.free.fr/div/Sciences/Dossiers/Time/A%20E%20Ev... Thanks, this is useful. ...unfortunately, I don't know if it's really agreeing with you. Or me, for that matter. Namely, it seems to admit that the metric as Alcubierre describes[1] would not produce a closed timelike curve; the paper instead describes ways to produce custom metrics separate from Alcubierre's which introduce the possibility of CTCs, in which case it seems like the answer would simply be to... just not do that, right? Indeed, the paper speculates that there might be other mechanisms that would prevent such a metric from being constructed (specifically naming Hawking's chronology protection conjecture). That is: > But the ability to perform such FTL tricks implies the possibility of constructing a closed timelike curve so long as you're talking about a localized phenomenon like a warp drive or tachyon where special relativity holds outside of a negligible area. Only, from what I can gather, if these equations are indeed the only ones at play, which even that paper admits might not be the case. ---- [1]: https://arxiv.org/pdf/gr-qc/0009013v1.pdf

and charges (which we conventionally get to by considering the spin statistics of gravitational waves in General Relativity), all the Standard Model particles have the same gravitational charge. That includes everything involved in a Casimir experiment, including "vacuum energy" if any. However, so far most of the thought that has gone into "how do we scatter matter around flat spacetime to induce an Alcubierre metric on it" requires stuff with the opposite gravitational charge. Back to the language of metric theories of gravitation: if there is only one gravitational charge that everything possesses, then everything couples to a single metric tensor. If we allow for a gravitational charge that has both positive and negative signs, so far as we know (from among other things analysis under the PPNF[1]) we are forced (by the Universality of Free Fall) into having matter couple to a metric tensor according to the sign of its charge. This is what we would call a bimetric theory of gravity, and such theories have been studied for decades motivated by understanding the very early universe https://en.wikipedia.org/wiki/Bimetric_gravity Generically, one asks "where's all the stuff that falls differently?" and almost inevitably has to say "it fell out of our universe much earlier than the formation of the cosmic microwave background, or decayed into ordinary stuff, or dilute away much faster during the metric expansion than ordinary stuff and became undetectably sparse before the first stars shone", or in other words that either the second metric tensor has decayed to all zeroes everywhere in the observable universe, or that nothing is in the observable universe that couples to it. Otherwise there are lots and lots of bullets to bite about why we don't see any observables that would support the second metric. Alcubierre's "drive" paper (he has left a copy at https://arxiv.org/abs/gr-qc/0009013v1 ) uses one metric, not two. The warp bubble is also eternal. Importing a whole extra metric tensor into our fundamental theory of gravity is a really high price to pay for having a mechanism which can produce a non-eternal warp bubble (one that forms in the finite past and un-forms in the finite future). And then one has to really spread around a lot of matter that couples with (i.e., it sources as well as follows) the second metric if one hopes to steer the warp bubble. We probably end up in some ratholes of inventing entire chemistries and nuclear physics of "negatively gravitationally charged" matter, and then figure out how it interacts with normal matter when they're confined together in some system. So although a terse "well maybe it's hiding in the Casimir effect" massively underplays what is needed, or what the consequences would be of reproducible Cavendish (or other gravimeter) experiments on Casimir apparatuses that show that when the plates are being drawn together they are also lighter (in a weight-is-the-quantity-that-bathroom-scales-measure sense). Show it happens at all first, even if it's a very very weak effect, then take seriously thoughts about scaling it up. - -- [1] PPNF, or PPN formalism: https://en.wikipedia.org/wiki/Parameterized_post-Newtonian_f...

create stars, including relativistic stars (neutron stars are an example) and black holes by depositing practically an infinite variety of matter into a region of flat spacetime. (In fact, if we use a solar mass of hydrogen gas then Raychaudhuri's focusing theorem makes it hard to avoid it coming together as a star eventually, and then probably a white dwarf). Likewise, "large scale structure formation" is nearly inevitable with a handful of parameters which in the standard cosmology we capture and try to measure. There's lots of ways in an expanding universe to wind up with galaxies. We can even get silly and contrive extremely unlikely initial configurations of known matter and simulate what happens. We can even simplify known matter by removing physical features that complicate the picture. This can even be useful. Historically one started with perfectly spherical arrangements of gas that does not self-interact (doesn't clump together, doesn't repel, doesn't induce twisting or spiralling) to try to understand the formation of spheroidal objects like stars, planets, and black holes. Then as tools to simulate such collapses became better and faster, adding back in the stripped-out physical aspects of real interacting matter (which clumps into molecules, and those in turn break apart as they get hot, etc., and probably never found in perfect spheres rather than discoids or blobs) for a better approximation of such systems. No known matter has the properties necessary to create negative energy. If we start with an extremely simple form of a purely classical non-interacting negative-energy-density non-relativistic dust that we can drop into the stress-energy tensor of the Einstein Field Equations, we can do some simulations and see what happens. [3] But we are complicating something wholly fictional. Nothing known has the requisite property (negative energy), and so there is no path to adding more complex behaviours to such a basic test set up to try to approach a physically plausible system. Such an unknown substance is politely called "exotic matter" for the simple reason that it foreign to our solar system. "Unobtanium" is just as fair, if a little less polite. And that, for me, leads to it being an uninteresting family of solutions. In the very unlikely event we find some mechanism to generate any negative energy, then great, general interest will revive (and we'll start asking questions about what suppresses that negative energy such that it is undetected in our solar system and in various-sized systems (galaxy clusters, etc) we see in our sky). Until then, I will tend to see such solutions to the Einstein Field Equations as starting with highly contrived metrics ab initio. I don't object to anyone investigating such things on strictly that basis: Schwarzschild's solution was highly contrived too, and was a matter-free eternal setup. But there were already pretty spherical gravitating systems around to examine (Schwarzschild lived on one!) and Newtonian methods to study those were useful for validating the Schwarzschild solution for objects wholly outside their own Schwarschild radius. But we should also think about the work of Kerr on axisymmetric rotating systems : it too was a contrived vacuum solution, but almost nobody (and certainly not Kerr himself [1]) thinks that we should think of the inside-the-horizons region as physical (and probably most relativists don't, for various reasons). - -- [1] Alcubierre has left a copy at https://arxiv.org/abs/gr-qc/0009013v1 -- note the very first sentence of the abstract ("within the framework of relativity"). [2] "... negative mass instead of positive: that's NOTHING to do with physics." Around 28:05 at https://youtu.be/jji2pgfq7oE?t=1685 -- this lecture also shows that a very simple complication of an exact solution, just adding angular momentum to Schwarzschild -- is both very hard work and will often produce obvious garbage. Even Kerr's solution, as he himself says, is part garbage. Fortunately the garbage in Kerr's solution is hidden behind an event horizon, so we can decide not to care at all about that for systems that aren't dense enough to have event horizons, and can say that the inner parts of black holes are for all practical purposes purely a theoretical problem, since we know no way of investigating what goes on in there. Relatedly, Kerr at around that point in the video points out that we know how to arrange matter to form a rotating black hole with the features of the Kerr solution, and frankly, to me, since that is a true statement, that overrides any theoretical objections about the interior garbage. (We don't know how to arrange matter to form a warp bubble, and warp bubbles have nice quiet interiors and distant exteriors, but have tremendous garbage in the thin shell). [3] Results tend to follow a pattern that we can think about using the idea of a gravitational charge. Unlike the electromagnetic charge, where like charges to repel, the gravitational charge causes like charges to attract. All known matter -- including dark matter -- has the same gravitational charge. So protons, neutrinos, photons, whatever the hell dark matter is, and so on all tend to collapse into structures like galaxies. "Negative" stuff has the opposite gravitational charge. Things with the opposite elecromagnetic charge tend to attract one another, but things with the opposite gravitational charge tend to repel one another. So if we brought a small amount of "negative" matter, with its opposite gravitational charge, into our solar system, it would be thrown out by all the normally-charged stuff (the sun, the earth, etc). Things get really absurd when one couples equally-massed equally-but-oppositely-gravitationally-charged matter together: you can create infinite power in some other charge (like the electromagnetic one) for instance. Again, this oppositely-gravitationally-charged negative stuff is called exotic because if there wasn't much of it in the early universe, it's all been thrown out of it since, and if there was much of it in the early universe, where the hell are all the side-effects ? (if we're talking about a tiny percent of negative stuff, a fraction of baryonic matter, then wormholes and warp bubbles should fill our sky almost as much as stars do, making all sorts of weird observables from gravitational lensing far from galaxies to odd emissions and absorption lines on light from distant quasars).

vacuum spacetime, so there's no mass in the middle to keep the bubble local to it (or source it, or however you want to look at it). He says so at the end of his paper[1]. It's important to remember that there is no observational evidence supporting Alcubierre's metric; it concords with nothing. However, one can still attempt to answer the questions he himself raised, and Lobo & Visser do just that in their 2004 paper[2], where they note that the geometry of the Alcubierre metric requires an even-more-unusual-than-dark-energy stabilizing term even at arbitrarily low warp-bubble velocities. - -- [1] https://doi.org/10.1088/0264-9381/11/5/001 https://arxiv.org/abs/gr-qc/0009013 (short, not especially difficult, fewer than 20 equations, 4 refs) See the text bracketing eqns (18) & (19) [2] https://doi.org/10.1088/0264-9381/21/24/011 https://arxiv.org/abs/gr-qc/0406083 (twice as long, but mostly developed through more than 120 equations, 38 refs incl. [1])

sufficiently flat to use an Israel-Darmois[1] approach, or add matter. A: Adding matter is hard. Practically anything either breaks the metric or alternatively requires releases from well-tested constraints on the eigenvalues and eigenvectors of the stress-energy tensor. There is really no point in rehashing Lobo & Visser [2] here, although it would be a decent public service if a good science communicator explained its results. At least Alcubierre's original paper[3] is short and easily digestible. Everyone should read from the paragraph before eq. (18) to the paragraph following eq. (19). - -- Ultimately though "B"s are slogans, and matching them with pithier "A" slogans won't make "B"s go away (cf. young Earth creationists and anti-vaxxer). Perhaps it's more fruitful to make it easy for people caught in the middle to distinguish between a sloganeer with no idea of the content of the physical theories involved, and someone who at least knows the standard theory and how to use it before attempting to depart from it (thus excluding e.g. Sonny White). - -- [1] Misner, Thorne, & Wheeler, §21.13. [2] Lobo & Visser (!) https://doi.org/10.1088/0264-9381/21/24/011 https://arxiv.org/abs/gr-qc/0406083 [3] Alcubierre https://doi.org/10.1088/0264-9381/11/5/001 https://arxiv.org/abs/gr-qc/0009013