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| [[Image:Alcubierre.png|thumbnail|350px|Two-dimensional visualization of the Alcubierre drive, showing the opposing regions of expanding and contracting spacetime that displace the central region.]]
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| The '''Alcubierre drive''' or '''Alcubierre metric''' (referring to [[Metric tensor#Lorentzian metrics from relativity|metric tensor]]) is a speculative idea based on a solution of [[Einstein field equations|Einstein's field equations]] in [[general relativity]] as proposed by theoretical physicist [[Miguel Alcubierre]], by which a spacecraft could achieve [[faster-than-light]] travel if a configurable energy-density field lower than that of vacuum (i.e. [[negative mass]]) could be created. Rather than exceeding the speed of light within its local [[frame of reference]], a spacecraft would traverse distances by contracting space in front of it and expanding space behind it, resulting in effective faster-than-light travel.
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| Objects cannot accelerate to the speed of light within normal spacetime; instead, the Alcubierre drive shifts space around an object so that the object would arrive at its destination faster than light would in normal space.<ref name="Krasnikov2003">{{cite journal|first=S. |last=Krasnikov|title=The quantum inequalities do not forbid spacetime shortcuts|journal=[[Physical Review D]] |year=2003|volume=67|pages=104013|doi=10.1103/PhysRevD.67.104013|arxiv = gr-qc/0207057 |bibcode = 2003PhRvD..67j4013K|issue=10}}</ref> Although the metric proposed by Alcubierre is mathematically valid in that it is consistent with the Einstein field equations, it may not be physically meaningful or indicate that such a drive could be constructed. The proposed mechanism of the Alcubierre drive implies a negative [[energy density]] and therefore requires [[exotic matter]], so if exotic matter with the correct properties does not exist then it could not be constructed. However, at the close of his original paper<ref name="Alcubierre">{{cite journal|last=Alcubierre |first=Miguel|title=The warp drive: hyper-fast travel within general relativity|journal=[[Classical and Quantum Gravity]] |year=1994|volume=11|pages=L73–L77|doi=10.1088/0264-9381/11/5/001|arxiv = gr-qc/0009013 |bibcode = 1994CQGra..11L..73A|issue=5}}</ref> Alcubierre argued (following an argument developed by physicists analyzing traversable [[wormhole]]s<ref>{{cite journal | first=Kip | last=Thorne | coauthors = Michael Morris, Ulvi Yurtsever| journal=[[Physical Review Letters]] | volume = 61 | issue=13| page=1446 | doi= 10.1103/PhysRevLett.61.1446 | title= Wormholes, Time Machines, and the Weak Energy Condition | year=1988 | url=http://authors.library.caltech.edu/9262/1/MORprl88.pdf | bibcode=1988PhRvL..61.1446M | pmid=10038800}}</ref><ref>See [http://www.npl.washington.edu/av/altvw81.html The Alcubierre Warp Drive] by John G. Cramer, where Cramer notes that "Alcubierre, following the lead of wormhole theorists, argues that quantum field theory permits the existence of regions of negative energy density under special circumstances, and cites the Casimir effect as an example."</ref>) that the [[Casimir effect|Casimir vacuum]] between parallel plates could fulfill the negative-energy requirement for the Alcubierre drive. Another possible issue is that although the Alcubierre metric is consistent with general relativity, general relativity does not incorporate quantum mechanics, and some physicists have presented arguments to suggest that a theory of [[quantum gravity]] which merged the two theories would eliminate those solutions in general relativity which allow for backwards time travel (''see'' the [[chronology protection conjecture]]), of which the Alcubierre drive is one.
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| ==History==
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| In 1994, Alcubierre proposed a method for changing the geometry of space by creating a wave that would cause the fabric of space ahead of a spacecraft to contract and the space behind it to expand.<ref name="Alcubierre" /> The ship would then ride this wave inside a region of flat space, known as a ''warp bubble'', and would not move within this bubble but instead be carried along as the region itself moves due to the actions of the drive.
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| ==Alcubierre metric==
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| The Alcubierre metric defines the warp-drive spacetime. It is a [[Lorentzian manifold]], which, if interpreted in the context of [[general relativity]], allows a warp bubble to appear in previously-flat spacetime and move away at effectively-[[superluminal]] speed. Inhabitants of the bubble feel no [[inertia]]l effects. This method of transport does not involve objects in motion at speeds faster than light with respect to the contents of the warp bubble; that is, a light beam within the warp bubble would still always move faster than the ship. As objects within the bubble are not moving (locally) faster than light, the mathematical formulation of the Alcubierre metric is consistent with the conventional claims of the laws of relativity (namely, that an object with mass cannot attain or exceed the speed of light) and conventional [[special relativity|relativistic]] effects such as [[time dilation]] would not apply as they would with conventional motion at near-light speeds. | |
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| The Alcubierre drive, however, remains a hypothetical concept with seemingly difficult problems, though the amount of energy required is no longer thought to be unobtainably large.<ref name="WDmorefeasible">{{cite web|url=http://www.space.com/17628-warp-drive-possible-interstellar-spaceflight.html|title=Warp Drive May Be More Feasible Than Thought, Scientists Say |first=Clara |last=Moskowitz |date=September 17, 2012 |publisher=[[Space.com]] |accessdate=01/10/2013}}</ref>
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| ==Mathematics of the Alcubierre drive==
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| Using the [[ADM formalism]] of [[general relativity]], the [[spacetime]] is described by a [[foliation]] of space-like [[hypersurface]]s of constant coordinate time ''t'', with the metric taking the following general form:
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| :<math>ds^2 = -\left(\alpha^2- \beta_i \beta^i\right)\,dt^2+2 \beta_i \,dx^i\, dt+ \gamma_{ij}\,dx^i\,dx^j</math>
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| where
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| :<math>\alpha</math> is the lapse function that gives the interval of proper time between nearby hypersurfaces,
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| :<math>\beta^i</math> is the shift vector that relates the spatial coordinate systems on different hypersurfaces, and
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| :<math>\gamma_{ij}</math> is a positive definite metric on each of the hypersurfaces.
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| The particular form that Alcubierre studied<ref name="Alcubierre" /> is defined by:
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| :<math>\alpha=1\,</math>
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| :<math>\beta^x=-v_s(t)f\left(r_s(t)\right)</math>
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| :<math>\beta^y = \beta^z =0 \,\!</math>
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| :<math>\gamma_{ij}=\delta_{ij} \,\!</math>
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| where
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| :<math>v_s(t)=\frac{dx_s(t)}{dt},</math>
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| :<math>r_s(t)=\sqrt{(x-x_s(t))^2+y^2+z^2},</math>
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| and
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| :<math>f(r_s)=\frac{\tanh(\sigma (r_s + R))-\tanh(\sigma (r_s - R))}{2 \tanh(\sigma R)},</math>
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| with arbitrary parameters <math>R > 0</math> and <math>\sigma > 0</math>. Alcubierre's specific form of the metric can thus be written
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| :<math>ds^2 = \left(v_s(t)^2 f(r_s(t))^2 -1\right)\,dt^2 - 2v_s(t)f(r_s(t))\,dx\,dt +dx^2 + dy^2 + dz^2.</math>
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| With this particular form of the metric, it can be shown that the energy density measured by observers whose 4-velocity is normal to the hypersurfaces is given by
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| :<math>-\frac{c^4}{8 \pi G} \frac{v_s^2 (y^2+z^2)}{4 g^2 r_s ^2} \left(\frac{df}{dr_s}\right)^2,</math>
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| where <math> g\! </math> is the determinant of the metric [[tensor]].
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| Thus, as the energy density is negative, one needs [[exotic matter]] to travel faster than the speed of light.<ref name="Alcubierre" /> The existence of exotic matter is not theoretically ruled out; however, generating and sustaining enough exotic matter to perform feats such as faster-than-light travel (and also to keep open the 'throat' of a [[wormhole]]) is thought to be impractical.{{Citation needed|date=October 2012}} Low has argued that within the context of general relativity, it is impossible to construct a warp drive in the absence of exotic matter.<ref>{{cite journal|last=Low |first=Robert J.|title=Speed Limits in General Relativity|journal=[[Classical and Quantum Gravity]]|year=1999|volume=16|pages=543–549|doi=10.1088/0264-9381/16/2/016|arxiv = gr-qc/9812067 |bibcode = 1999CQGra..16..543L|issue=2}}</ref>
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| ==Physics==
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| For those familiar with the effects of special relativity, such as [[Lorentz-Fitzgerald contraction hypothesis|Lorentz contraction]] and [[time dilation]], the Alcubierre metric has some apparently peculiar aspects. In particular, Alcubierre has shown that a ship using an Alcubierre drive travels on a free-fall geodesic even while the warp bubble is accelerating: its crew would be in free fall while accelerating without experiencing accelerational [[g-force]]s. Enormous [[tidal force]]s, however, would be present near the edges of the flat-space volume because of the large space curvature there, but suitable specification of the metric would keep them very small within the volume occupied by the ship.<ref name="Alcubierre" />
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| The original warp-drive metric and simple variants of it happen to have the [[ADM formalism|ADM form]], which is often used in discussing the initial-value formulation of general relativity. This may explain the widespread misconception that this spacetime is a ''solution'' of the field equation of general relativity.{{Citation needed|reason=that Natario paper does not seem to say it's a "misconception" that the Alcubierre drive is a solution, it just talks about the misconception that it requires space in front of the bubble to contract and space behind it to expand|date=August 2013}} Metrics in ADM form are ''adapted'' to a certain family of inertial observers, but these observers are not really physically distinguished from other such families. Alcubierre interpreted his "warp bubble" in terms of a contraction of space ahead of the bubble and an expansion behind, but this interpretation may be misleading<ref>{{cite journal|last=Natario|first=Jose|title=Warp drive with zero expansion|journal=[[Classical and Quantum Gravity]]|year=2002|volume=19|pages=1157–1166|doi=10.1088/0264-9381/19/6/308|arxiv = gr-qc/0110086 |bibcode = 2002CQGra..19.1157N|issue=6 }}</ref> because the contraction and expansion actually refers to the relative motion of nearby members of the family of ADM observers.
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| In general relativity, one often first specifies a plausible distribution of matter and energy, and then finds the geometry of the spacetime associated with it; but it is also possible to run the [[Einstein field equations]] in the other direction, first specifying a metric and then finding the [[stress–energy tensor|energy–momentum tensor]] associated with it, and this is what Alcubierre did in building his metric. This practice means that the solution can violate various [[energy conditions]] and require [[exotic matter]]. The need for exotic matter raises questions about whether one can distribute the matter in an initial spacetime that lacks a warp bubble in such a way that the bubble is created at a later time, although some physicists have proposed models of dynamical warp-drive spacetimes in which a warp bubble is formed in a previously flat space.<ref name=Finazzi>{{cite journal|author1=Finazzi, Stefano|author2=Liberati, Stefano|author3=Barceló, Carlos |title=Semiclassical instability of dynamical warp drives|journal=[[Physical Review D]]|year=2009|volume=79|pages=124017|doi=10.1103/PhysRevD.79.124017|bibcode = 2009PhRvD..79l4017F|issue=12 |arxiv = 0904.0141 }}</ref> Moreover, according to [[Serguei Krasnikov]],<ref name="Krasnikov1998">{{cite journal|first=S.|last=Krasnikov|title=Hyper-fast travel in general relativity|journal=[[Physical Review D]]|year=1998|volume=57|pages=4760|doi=10.1103/PhysRevD.57.4760|arxiv = gr-qc/9511068 |bibcode = 1998PhRvD..57.4760K|issue=8}}</ref> generating a bubble in a previously flat space for a ''one-way'' FTL trip requires forcing the exotic matter to move at local faster-than-light speeds, something that would require the existence of [[tachyons]], although Krasnikov also notes that when the spacetime is not flat from the outset, a similar result could be achieved without tachyons by placing in advance some devices along the travel path and programming them to come into operation at preassigned moments and to operate in a preassigned manner. Some suggested methods avoid the problem of tachyonic motion, but would probably generate a [[naked singularity]] at the front of the bubble.<ref>{{cite arXiv|eprint=gr-qc/9906050|first=Chris |last=Van den Broeck|title=On the (im)possibility of warp bubbles|class=gr-qc|year=1999}}</ref><ref name="Coule">{{cite journal |journal=[[Classical and Quantum Gravity]] |volume=15 |year=1998 |pages=2523–2537 |url=http://omnis.if.ufrj.br/~mbr/warp/etc/cqg15_2523.pdf |doi=10.1088/0264-9381/15/8/026 |title=No warp drive |last1=Coule |first1=D. H. |issue=8|bibcode = 1998CQGra..15.2523C }}</ref> Allen Everett and Thomas Roman comment<ref name="Everett1997">{{cite journal|first=Allen|last=Everett| coauthors= Thomas Roman| title=A Superluminal Subway: The Krasnikov Tube|journal=[[Physical Review D]]|year=1997|volume=56|pages=2100–2108|doi=10.1103/PhysRevD.56.2100|arxiv = gr-qc/9702049 |issue=4|bibcode = 1997PhRvD..56.2100E }}</ref> that Krasnikov's finding "does not mean that Alcubierre bubbles, if it were possible to create them, could not be used as a means of superluminal travel. It only means that the actions required to change the metric and create the bubble must be taken beforehand by some observer whose forward [[light cone]] contains the entire trajectory of the bubble." For example, if one wanted to travel to [[Deneb]] 2,600 light years away and arrive less than 2,600 years in the future according to external clocks, it would be required that someone had already begun work on warping the space from Earth to Deneb at least 2,600 years ago, in which case "A spaceship appropriately located with respect to the bubble trajectory could then choose to enter the bubble, rather like a passenger catching a passing trolley car, and thus make the superluminal journey." Everett and Roman also write that "as Krasnikov points out, causality considerations do not prevent the crew of a spaceship from arranging, by their own actions, to complete a ''round trip'' from the Earth to a distant star and back in an arbitrarily short time, as measured by clocks on the Earth, by altering the metric along the path of their outbound trip."
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| ==Difficulties==
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| The metric of this form has significant difficulties because all known warp-drive spacetime theories violate various [[energy conditions]].<ref name="Van den Broeck">{{cite journal |last=Van den Broeck |first=Christian | bibcode=2000AIPC..504.1105V |doi= 10.1063/1.1290913| title = Alcubierre's warp drive: Problems and prospects| year= 2000|journal= AIP Conference Proceedings |volume =504| pages=1105–1110 }}</ref> Nevertheless, Alcubierre type warp might be realized by exploiting certain experimentally verified quantum phenomena, such as the [[Casimir effect]], that lead to [[stress–energy tensor]]s that also violate the energy conditions, such as negative [[Mass–energy equivalence|mass–energy]], when described in the context of the quantum field theories.<ref>Krasnikov (2003), p.13, "Moreover, by analogy with the Casimir effect, it is reasonable to assume that ρ in such a wormhole will be large (∼''L''<sup>−4</sup>), which would relieve one of having to seek additional sources of exotic matter."</ref><ref>Ford and Roman (1995), p.5, "...the Casimir effect may be useful as an illustration. Here one has a constant negative energy density..."</ref>
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| ===Mass–energy requirement===
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| If certain [[quantum inequalities]] conjectured by Ford and Roman hold,<ref>{{cite journal|first1=L. H. |last1=Ford |first2=T. A. |last2=Roman|title=Quantum field theory constrains traversable wormhole geometries|journal=[[Physical Review D]]|year=1996|pages=5496|volume=53|doi=10.1103/PhysRevD.53.5496|arxiv = gr-qc/9510071 |bibcode = 1996PhRvD..53.5496F|issue=10}}</ref> then the energy requirements for some warp drives may be unfeasibly large as well as negative. For example, the energy equivalent of −10<sup>64</sup> kg might be required<ref>{{cite journal|author=Pfenning, Michael J.; Ford, L. H.|title=The unphysical nature of 'Warp Drive'|journal=[[Classical and Quantum Gravity]]|year=1997|volume=14|pages=1743–1751|doi=10.1088/0264-9381/14/7/011|arxiv = gr-qc/9702026 |bibcode = 1997CQGra..14.1743P|issue=7 }}</ref> to transport a small spaceship across the Milky Way galaxy—an amount orders of magnitude greater than the estimated [[mass of the observable universe]]. Counterarguments to these apparent problems have also been offered.<ref name="Krasnikov2003"/>
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| Chris Van den Broeck of the [[Katholieke Universiteit Leuven|Catholic University of Louvain]] in Belgium, in 1999, tried to address the potential issues.<ref>{{cite journal|last=Van den Broeck |first=Chris|title=A 'warp drive' with more reasonable total energy requirements|journal=[[Classical and Quantum Gravity]] |year=1999|volume=16|pages=3973–3979|doi=10.1088/0264-9381/16/12/314|arxiv = gr-qc/9905084 |bibcode = 1999CQGra..16.3973V|issue=12 }}</ref> By contracting the 3+1-dimensional surface area of the bubble being transported by the drive, while at the same time expanding the three-dimensional volume contained inside, Van den Broeck was able to reduce the total energy needed to transport small atoms to less than three [[solar mass]]es. Later, by slightly modifying the Van den Broeck metric, [[Serguei Krasnikov]] reduced the necessary total amount of [[negative mass]] to a few milligrams.<ref name="Krasnikov2003"/><ref name="Van den Broeck"/>
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| In 2012, physicist [[Harold Sonny White (NASA Scientist)|Harold White]] and collaborators announced that modifying the geometry of exotic matter could reduce the mass–energy requirements for a macroscopic space ship from the equivalent of the planet [[Jupiter]] to that of the [[Voyager 1]] spacecraft (~700 kg)<ref name=WDmorefeasible/> or less,<ref name="io9">{{cite web |work=[[io9]] |title=How NASA might build its very first warp drive|url=http://io9.com/5963263/how-nasa-will-build-its-very-first-warp-drive |first=George |last=Dvorsky |date=November 26, 2012 |accessdate=01/10/2013}}</ref> and stated their intent to perform small-scale experiments in constructing warp fields.<ref name=WDmorefeasible/> White proposed changing the shape of the warp bubble from a sphere to a [[torus|doughnut shape]].<ref>{{cite web|last=White|first=Harold|title=Nasa Physicist|url=http://www.wired.co.uk/news/archive/2012-09/20/warp-drives}}</ref><ref>Paul Hoiland, [http://vixra.org/pdf/1111.0044v1.pdf ''Towards a more realistic Gravitomagnetic Displacement Drive''], page 30, viXra.org, 11 November 2011.</ref> Furthermore, if the intensity of the space warp can be oscillated over time, the energy required is reduced even more.<ref name=WDmorefeasible/> According to White, a modified [[Michelson–Morley experiment|Michelson–Morley interferometer]] could test the idea: one of the legs of the interferometer would appear to be a slightly different length when the test devices were energised.<ref name=io9/>
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| ===Placement of matter===
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| Krasnikov proposed that if [[tachyon|tachyonic matter]] cannot be found or used, then a solution might be to arrange for masses along the path of the vessel to be set in motion in such a way that the required field was produced. But in this case, the Alcubierre drive vessel can only travel routes that, like a railroad, have first been equipped with the necessary infrastructure. The pilot inside the bubble is causally disconnected with its walls and cannot carry out any action outside the bubble: the bubble cannot be used for the first trip to a distant star because the pilot cannot place infrastructure ahead of the bubble while "in transit". For example, travelling to [[Vega]] (which is 25 light-years from the Earth) requires arranging everything so that the bubble moving toward Vega with a superluminal velocity would appear; such arrangements will always take more than 25 years.<ref name="Krasnikov1998"/>
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| Coule has argued that schemes, such as the one proposed by Alcubierre, are infeasible because matter placed ''en route'' of the intended path of a craft must be placed at superluminal speed—that constructing an Alcubierre drive requires an Alcubierre drive even if the metric that allows it is physically meaningful. Coule further argues that an analogous objection will apply to ''any'' proposed method of constructing an Alcubierre drive.<ref name="Coule"/>
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| ===Survivability inside the bubble===
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| A paper by José Natário published in 2002 argues that crew members could not control, steer or stop the ship because the ship could not send signals to the front of the bubble.<ref>{{cite journal|arxiv=gr-qc/0110086 |bibcode=2002CQGra..19.1157N |doi=10.1088/0264-9381/19/6/308 |journal=[[Classical and Quantum Gravity]]|title=Warp drive with zero expansion|year=2002|last1=Natário|first1=José|volume=19|issue=6|pages=1157–1165}}</ref>
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| A more recent paper by Carlos Barceló, Stefano Finazzi, and Stefano Liberati uses quantum theory to argue that the Alcubierre drive at faster-than-light velocities is impossible mostly because extremely high temperatures caused by [[Hawking radiation]] would destroy anything inside the bubble at superluminal velocities and destabilize the bubble itself; the paper also argues that these problems are absent if the bubble velocity is subluminal, although the drive still requires exotic matter.<ref name=Finazzi />
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| ===Damaging effect on destination===
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| Brendan McMonigal, [[Geraint F. Lewis]], and Philip O'Byrne have argued that when an Alcubierre-driven ship decelerates from superluminal speed, the particles that its bubble has gathered would be released in energetic outbursts; in the case of forward-facing particles, energetic enough to destroy anyone at the destination directly in front of the ship.<ref>{{Cite web |first=Jason |last=Major |date=February 29, 2012 |url=http://www.universetoday.com/93882/warp-drives-may-come-with-a-killer-downside/#ixzz2FaZsXDuM |title=Warp Drives May Come With a Killer Downside |work=[[Universe Today]]}}</ref><ref>Brendan McMonigal, Geraint F. Lewis, and Philip O'Byrne [http://ut-images.s3.amazonaws.com/wp-content/uploads/2012/02/MatterOfMatter-revised-final.pdf The Alcubierre Warp Drive: On the Matter of Matter] – see conclusion: "These results suggest that any ship using an Alcubierre warp drive carrying people would need shielding to protect them from potential dangerously blueshifted particles during the journey, and any people at the destination would be gamma ray and high energy particle blasted into oblivion due to the extreme blueshifts for P+ region particles."</ref>
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| ===Wall thickness===
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| The amount of negative energy required for such a propulsion is not yet known. Pfenning and Allen Everett of [[Tufts University|Tufts]] hold that a warp bubble traveling at 10 times light-speed must have a wall thickness of no more than 10<sup>−32</sup> meters—close to the limiting [[Planck length]], <span class=nowrap>1.6 × 10<sup>−35</sup></span> meters. A bubble macroscopically large enough to enclose a ship of 200 meters would require a total amount of exotic matter equal to 10 billion times the mass of the observable universe, and straining the exotic matter to an extremely thin band of 10<sup>−32</sup> meters is considered impractical. Similar constraints apply to [[Krasnikov tube|Krasnikov's superluminal subway]]. Chris Van den Broeck recently constructed a modification of Alcubierre’s model which requires much less exotic matter but places the ship in a curved space-time “bottle” whose neck is about 10<sup>−32</sup> meters. So-called cosmic strings, hypothesized in some cosmological theories, involve very large energy densities in long, narrow lines, but{{Clarify|date=May 2011}} all known physically reasonable cosmic-string models have positive (positive space-time warping effects) energy densities. These results seem to make it rather unlikely that one could construct Alcubierre warp drives using exotic matter generated by quantum effects. | |
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| ===Causality violation and semiclassical instability===
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| Calculations by physicist Allen Everett show that warp bubbles could be used to create [[closed timelike curve]]s in general relativity, meaning that the theory predicts that they could be used for backwards [[time travel]].<ref>{{cite journal | last = Everett | first = Allen E. | title = Warp drive and causality | journal = Physical Review D | volume = 53 | issue = 12 | pages = 7365–7368 | date = 15 June 1996 | url = http://exvacuo.free.fr/div/Sciences/Dossiers/Time/A%20E%20Everett%20-%20Warp%20drive%20and%20causality%20-%20prd950914.pdf | doi = 10.1103/PhysRevD.53.7365 | accessdate = 24 July 2013|bibcode = 1996PhRvD..53.7365E }}</ref> While it is possible the fundamental laws of physics might allow closed timelike curves, the [[chronology protection conjecture]] hypothesizes that in all cases where the classical theory of general relativity allows them, quantum effects would intervene to eliminate the possibility, making these spacetimes impossible to realize (a possible type of effect that would accomplish this, discussed in more detail in the chronology protection conjecture article, is a buildup of vacuum fluctuations on the border of the region of spacetime where time travel would first become possible, causing the energy density to become high enough to destroy the system that would otherwise become a time machine). Some results in [[semiclassical gravity]] appear to support the conjecture, including a calculation dealing specifically with quantum effects in warp drive spacetimes which suggested that warp bubbles would be semiclassically unstable,<ref name=Finazzi /><ref name=Barcelo>{{cite arXiv |author1=Barceló, Carlos|author2=Finazzi, Stefano|author3=Liberati, Stefano |eprint = 1001.4960| title=On the impossibility of superluminal travel: the warp drive lesson|class=gr-qc |year=2010 |accessdate= 6 August 2013}}</ref> but ultimately the conjecture can only be decided by a full theory of [[quantum gravity]].<ref>{{cite journal | last = Visser | first = Matt | title = The reliability horizon for semi-classical quantum gravity: Metric fluctuations are often more important than back-reaction | journal = Physical Letters B | volume = 415 | issue = 1 | pages = 8–14 | date = December 1997 | url = http://arxiv.org/abs/gr-qc/9702041 | doi = 10.1016/S0370-2693(97)01226-4 | accessdate = 24 July 2013|arxiv = gr-qc/9702041 |bibcode = 1997PhLB..415....8V }}</ref>
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| Miguel Alcubierre briefly discusses some of these issues in a series of lecture slides posted online,<ref>http://ccrg.rit.edu/files/FasterThanLight.pdf</ref> where he writes "beware: in relativity, any method to travel faster than light can in principle be used to travel back in time (a time machine)." In the next slide he brings up the chronology protection conjecture, and writes "The conjecture has not been proven (it wouldn’t be a conjecture it it had), but there are good arguments in its favor based on quantum field theory. Notice that the conjecture does not prohibit faster than light travel. It just states that if a method to travel faster than light exists, and one tries to use it to build a time machine, something will go wrong: the energy accumulated will explode, or it will create a black hole."
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| ==Experiments==
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| {{main|Warp-field experiments}}
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| In 2012, a [[NASA]] laboratory announced that they have constructed an [[interferometer]] that they claim will detect the spatial distortions produced by the expanding and contracting spacetime of the Alcubierre metric. The work has been described in ''Warp Field Mechanics 101'', a NASA paper by [[Harold Sonny White (NASA Scientist)|Harold Sonny White]].<ref name="Roundup">{{cite web|title=Roundup|url=http://www.jsc.nasa.gov/roundup/online/2012/0712.pdf|publisher=Lyndon B. Johnson Space Center|date=July 2012|accessdate=2013-10-01}}</ref><ref>{{cite web|last=Dr. Harold “Sonny” White|title=Warp Field Mechanics 101|url=http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20110015936_2011016932.pdf|publisher=NASA Johnson Space Center|date=2011-09-30|accessdate=2013-01-28}}</ref> Alcubierre has expressed skepticism about the experiment, saying "from my understanding there is no way it can be done, probably not for centuries if at all".<ref>[https://twitter.com/malcubierre/status/362011821277839360 Miguel Alcubierre's twitter feed, 29 July 2013]</ref> Results have been reported as "inconclusive".<ref name="2013SSC">{{cite web|last=Dr. Harold “Sonny” White|title=2013 Starship Congress: Warp Field Physics, an Update|url=http://www.youtube.com/watch?v=ucyBMB_PWr8|publisher=Icarus Interstellar|date=2013-08-17|accessdate=2013-08-17}}</ref>
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| ==In science fiction==
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| [[Faster-than-light]] travel often appears in [[science fiction]], where a wide variety of imaginary propulsion methods are postulated; not all of these are based on the Alcubierre drive or any other physical theory.
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| The ''[[Star Trek]]'' television series used the term "[[warp drive]]" to describe their method of faster than light travel. The Alcubierre theory, or anything similar, did not exist when the series was conceived, but Alcubierre stated in an email to [[William Shatner]] that his theory was directly inspired by the term used in the show,<ref>{{cite web|last=Shapiro|first=Alan|title=The Physics of Warp Drive|url=http://www.alan-shapiro.com/the-physics-of-warp-drive/|accessdate=2 June 2013|archiveurl=http://archive.is/4OcgV|archivedate=2013-01-16}}</ref> and references it in his 1994 paper.<ref>{{Cite journal
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| | last1 = Alcubierre | first1 = Miguel
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| | title = The warp drive: Hyper-fast travel within general relativity
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| | doi = 10.1088/0264-9381/11/5/001
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| | journal = Classical and Quantum Gravity
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| | volume = 11
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| | issue = 5
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| | pages = L73
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| | year = 1994
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| |arxiv = gr-qc/0009013 |bibcode = 1994CQGra..11L..73A }} {{open access}}</ref>
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| ==See also==
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| *[[Exact solutions in general relativity]] (for more on the sense in which the Alcubierre spacetime is a solution)
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| *[[Spacecraft propulsion]]
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| *[[Faster-than-light]]
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| *[[Krasnikov tube]]
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| *[[Warp-field experiments]]
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| **[[White–Juday warp-field interferometer]]
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| ==Notes==
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| {{Reflist|2}}
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| <div class="references-small">
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| ==References==
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| *{{cite journal|author=Lobo, Francisco S. N.; & Visser, Matt|title=Fundamental limitations on 'warp drive' spacetimes|journal=[[Classical and Quantum Gravity]]|year=2004|volume=21|pages=5871–5892|doi=10.1088/0264-9381/21/24/011|arxiv = gr-qc/0406083 |bibcode = 2004CQGra..21.5871L|issue=24 }}
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| *{{cite journal|author=Hiscock, William A.|title=Quantum effects in the Alcubierre warp drive spacetime|journal=[[Classical and Quantum Gravity]]|year=1997|volume=14|pages=L183–L188|doi=10.1088/0264-9381/14/11/002|arxiv = gr-qc/9707024 |bibcode = 1997CQGra..14L.183H|issue=11 }}
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| *{{cite book|author=Berry, Adrian|title=The Giant Leap: Mankind Heads for the Stars|publisher=Headline|year=1999|isbn=0-7472-7565-3}} Apparently a popular book by a science writer, on space travel in general.
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| *{{Cite conference
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| | last1 = Taylor | first1 = T. S.
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| | last2 = Powell | first2 = T. C.
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| | doi = 10.2514/6.2003-4991
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| | chapter = Current Status of Metric Engineering with Implications for the Warp Drive
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| | title = 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit
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| | date = 20–23 July 2003
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| | isbn = 978-1-62410-098-7
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| | location = Huntsville, Alabama
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| | id = AIAA-2003-4991
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| }} {{closed access}}
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| *{{Cite journal
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| | last1 = Puthoff | first1 = H. E.
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| | doi = 10.4006/1.3029218
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| | title = SETI, the Velocity‐of‐Light Limitation, and the Alcubierre Warp Drive: An Integrating Overview
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| | journal = Physics Essays
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| | volume = 9
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| | issue = 1
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| | pages = 156–158
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| |date=March 1996
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| | bibcode = 1996PhyEs...9..156P
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| | url = http://www.earthtech.org/publications/seti.pdf <!-- alternate: http://www.intalek.com/Index/Projects/Research/seti.pdf -->
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| }}
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| *Amoroso, Richard L. (2011) Orbiting the Moons of Pluto: Complex Solutions to the Einstein, Maxwell, Schrodinger & Dirac Equations, New Jersey: World Scientific Publishers; ISBN 978-981-4324-24-3, see Chap. 15, pp. 349–391, Holographic wormhole drive: Philosophical breakthrough in faster than light "Warp Drive" technology. (Amoroso claims to have solved problems of the Alcubierre metric such as need for large negative mass energy.)
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| </div>
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| ==External links==
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| *[http://members.shaw.ca/mike.anderton/WarpDrive.pdf The warp drive: hyper-fast travel within general relativity] – Alcubierre's original paper ''(PDF File)''
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| *[http://doc.cern.ch//archive/electronic/other/ext/ext-2004-110.pdf Problems with Warp Drive Examined] – ''(PDF File)''
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| *[http://omnis.if.ufrj.br/~mbr/warp/ Marcelo B. Ribeiro's Page on Warp Drive Theory]
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| *[http://w210.ub.uni-tuebingen.de/dbt/volltexte/2001/240/pdf/09warp.html A short video clip of the hypothetical effects of the warp drive.]
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| *[http://arxiv.org/pdf/gr-qc/9906050 The (Im) Possibility of Warp Drive (Van den Broeck)]
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| *[http://arxiv.org/pdf/gr-qc/0107097 Reduced Energy Requirements for Warp Drive (Loup, Waite)]
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| *[http://link.aps.org/doi/10.1103/PhysRevD.62.044005 Warp Drive Space-Time (González-Díaz)]
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| *[http://www.universetoday.com/wp-content/uploads/2012/02/MatterOfMatter-revised-final.pdf The Alcubierre Warp Drive: On the Matter of Matter (McMonigal, Lewis, O'Byrne)] – ''(PDF File)''
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| *{{cite web |title=Ideas Based On What We’d Like To Achieve |publisher=NASA |url=http://www.nasa.gov/centers/glenn/technology/warp/ideachev_prt.htm}} It describes the concept in laymans terms
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| *[http://www.youtube.com/watch?v=ynxD-BaDxRk Society for Scientific Exploration (SSE) Keynote address]- Faster-than-light Space Travel?
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| {{Time travel}}
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| {{DEFAULTSORT:Alcubierre Drive}}
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| [[Category:Interstellar travel]]
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| [[Category:Warp drive theory]]
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| [[Category:Lorentzian manifolds]]
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| [[Category:Science fiction themes]]
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| [[Category:Hypothetical technology]]
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| [[Category:1994 introductions]]
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