View source for Alcubierre drive

{{Short description|Hypothetical FTL transportation by warping space}}
{{Use dmy dates|date=October 2020}}
[[Image:Alcubierre.png|thumbnail|upright=1.2|Two-dimensional visualization of an Alcubierre drive, showing the opposing regions of expanding and contracting spacetime that displace the central region]]

The '''Alcubierre drive''' ({{IPA|es|alkuˈβjere|}}) is a speculative [[warp drive]] idea according to which a spacecraft could achieve apparent [[faster-than-light]] travel by contracting space in front of it and expanding space behind it, under the assumption that a configurable [[energy density|energy-density]] field lower than that of [[vacuum]] (that is, [[negative mass]]) could be created.<ref name="AIAA-20190816" /><ref name="SA-20200301" /> Proposed by theoretical physicist [[Miguel Alcubierre]] in 1994, the Alcubierre drive is based on a solution of [[Einstein field equations|Einstein's field equations]]. Since those [[Solutions of the Einstein field equations|solutions]] are [[Metric tensor (general relativity)|metric tensors]], the Alcubierre drive is also referred to as '''Alcubierre metric'''.

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 more quickly than light would in normal space without breaking any [[physical laws]].<ref name="Krasnikov2003">{{Cite journal |last=Krasnikov |first=S. |date=2003 |title=The quantum inequalities do not forbid spacetime shortcuts |journal=[[Physical Review D]] |volume=67 |issue=10 |pages=104013 |arxiv=gr-qc/0207057 |bibcode=2003PhRvD..67j4013K |doi=10.1103/PhysRevD.67.104013 |s2cid=17498199}}</ref>

Although the metric proposed by Alcubierre is consistent with the Einstein field equations, construction of such a drive is not necessarily possible. The proposed mechanism of the Alcubierre drive implies a negative [[energy density]] and therefore requires [[exotic matter]] or manipulation of [[dark energy]].<ref name=Finazzi/> If exotic matter with the correct properties does not exist, then the drive cannot be constructed. At the close of his original article,<ref name="Alcubierre">{{Cite journal |last=Alcubierre |first=Miguel |date=1994 |title=The warp drive: hyper-fast travel within general relativity |journal=[[Classical and Quantum Gravity]] |volume=11 |issue=5 |pages=L73–L77 |arxiv=gr-qc/0009013 |bibcode=1994CQGra..11L..73A |doi=10.1088/0264-9381/11/5/001 |s2cid=4797900}}</ref> however, Alcubierre argued (following an argument developed by physicists analyzing traversable [[wormhole]]s<ref>{{Cite journal |last1=Thorne |first1=Kip |last2=Michael Morris |last3=Ulvi Yurtsever |date=1988 |title=Wormholes, Time Machines, and the Weak Energy Condition |url=http://authors.library.caltech.edu/9262/1/MORprl88.pdf |url-status=live |journal=[[Physical Review Letters]] |volume=61 |issue=13 |pages=1446–1449 |bibcode=1988PhRvL..61.1446M |doi=10.1103/PhysRevLett.61.1446 |pmid=10038800 |archive-url=http://archive.wikiwix.com/cache/20110223165343/http://authors.library.caltech.edu/9262/1/MORprl88.pdf |archive-date=23 February 2011}}</ref><ref>{{Cite web |last=Cramer |first=John G. |date=15 April 1996 |title=The Alcubierre Warp Drive |url=http://www.npl.washington.edu/av/altvw81.html |url-status=live |archive-url=https://web.archive.org/web/20120921185215/http://www.npl.washington.edu/av/altvw81.html |archive-date=21 September 2012 |quote=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 Einstein's equations, general relativity does not incorporate [[quantum mechanics]]. Some physicists have presented arguments to suggest that a theory of [[quantum gravity]] (which would incorporate both theories) would eliminate those solutions in general relativity that allow for backward time travel (see the [[chronology protection conjecture]]) and thus make the Alcubierre drive invalid.

==History==
In 1994, [[Miguel Alcubierre]] proposed a method for changing the [[Shape of the universe|geometry of space]] by creating a wave that would cause the fabric of space ahead of a [[Starship|spacecraft]] to contract and the space behind it to expand.<ref name="Alcubierre" /><ref name="AIAA-20190816">{{Cite journal |last=Agnew |first=J. |date=16 August 2019 |title=An Examination of Warp Theory and Technology to Determine the State of the Art and Feasibility |journal=[[American Institute of Aeronautics and Astronautics#Conferences|AIAA Propulsion and Energy Forum and Exposition]] |doi=10.2514/6.2019-4288 |isbn=978-1-62410-590-6 |s2cid=202443606}}</ref><ref name="SA-20200301">{{Cite news |last=Williams |first=Matt |date=1 March 2020 |title=Scientists Are Starting to Take Warp Drives Seriously, Especially This One Concept |work=ScienceAlert.com |url=https://www.sciencealert.com/scientists-are-starting-to-take-warp-drives-seriously-especially-this-one-concept}}</ref> 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. The local velocity relative to the deformed spacetime would be subluminal, but the speed at which a spacecraft could move would be superluminal, thereby rendering possible interstellar flight, such as a visit to ''[[Proxima Centauri]]'' within a few days.<ref name=":1">{{Cite journal |last1=Fil'chenkov |first1=M. |last2=Laptev |first2=Yu. |date=2017-10-01 |title=Galaxy travel via Alcubierre's warp drive |url=https://www.sciencedirect.com/science/article/pii/S0094576517301637 |journal=Acta Astronautica |language=en |volume=139 |pages=254–257 |doi=10.1016/j.actaastro.2017.07.011 |bibcode=2017AcAau.139..254F |issn=0094-5765}}</ref>

==Alcubierre metric==
The Alcubierre [[metric tensor|metric]] defines the warp-drive [[spacetime]]. It is a [[Lorentzian manifold]] that, if interpreted in the context of [[general relativity]], allows a warp bubble to appear in previously flat spacetime and move away at effectively faster-than-light speed. The interior of the bubble is an [[inertial reference frame]] and inhabitants experience no proper acceleration. This method of transport does not involve objects in motion at faster-than-light speeds with respect to the contents of the warp bubble; that is, a light beam within the warp bubble would still always move more quickly than the ship. Because objects within the bubble are not moving (locally) more quickly 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.<ref name=":3">{{cite book |last1=Alcubierre |first1=Miguel |date=2017 |pages=257–279 |place=Cham |isbn=978-3-319-55181-4 |last2=Lobo |first2=Francisco S. N.|title=Wormholes, Warp Drives and Energy Conditions |chapter=Warp Drive Basics |series=Fundamental Theories of Physics |volume=189 |doi=10.1007/978-3-319-55182-1_11 |arxiv=2103.05610 |bibcode=2017FTP...189..257A }}</ref>

An extension of the Alcubierre metric that eliminates the expansion of the volume elements and instead relies on the change in distances along the direction of travel is that of mathematician José Natário. In his metric, spacetime contracts towards the prow of the ship and expands in the direction perpendicular to the motion, meaning that the bubble actually "slides" through space, roughly speaking by "pushing space aside".<ref name=":3" /><ref>{{Cite book |last1=Everett |first1=Allen |title=Time Travel and Warp Drives |last2=Roman |first2=Thomas |date=2011 |publisher=University of Chicago Press |doi=10.7208/chicago/9780226225005.001.0001 |isbn=978-0-226-04548-1}}</ref>

The Alcubierre drive remains a hypothetical concept with seemingly difficult problems, although the amount of energy required is no longer thought to be unobtainably large.<ref name="WDmorefeasible">{{Cite web |last=Moskowitz |first=Clara |date=17 September 2012 |title=Warp Drive May Be More Feasible Than Thought, Scientists Say |url=http://www.space.com/17628-warp-drive-possible-interstellar-spaceflight.html |url-status=live |archive-url=https://web.archive.org/web/20130113193555/http://www.space.com/17628-warp-drive-possible-interstellar-spaceflight.html |archive-date=13 January 2013 |publisher=[[Space.com]]}}</ref> However, Alexey Bobrick and Gianni Martire claim that, in principle, a class of subluminal, spherically symmetric warp drive spacetimes can be constructed based on physical principles presently known to humanity, such as positive energy.<ref>{{Cite journal |last1=Bobrick |first1=Alexey |last2=Martire |first2=Gianni |date=2021-04-20 |title=Introducing physical warp drives |url=https://iopscience.iop.org/article/10.1088/1361-6382/abdf6e |journal=Classical and Quantum Gravity |volume=38 |issue=10 |pages=105009 |arxiv=2102.06824 |bibcode=2021CQGra..38j5009B |doi=10.1088/1361-6382/abdf6e |issn=0264-9381 |s2cid=231924903}}</ref> Furthermore, a study by Remo Garattini and Kirill Zatrimaylov shows that the amount of negative energy density required to sustain a warp bubble can in principle be reduced if the bubble is moving in an external gravitational field, such as that of a black hole.<ref>{{Cite journal |last1=Garattini |first1=Remo |last2=Zatrimaylov |first2=Kirill |date=2024-07-29 |title=Black Holes, Warp Drives, and Energy Conditions |url=https://www.sciencedirect.com/science/article/pii/S0370269324004684 |journal=Physics Letters B |volume=856 |arxiv=2408.04495 |bibcode=2024PhLB..85638910G |doi=10.1016/j.physletb.2024.138910|issn=0370-2693|s2cid=271554785}}</ref><ref>{{Cite news|url=https://www.sciencealert.com/what-would-happen-if-a-warp-drive-spaceship-flew-into-a-black-hole|title=What Would Happen if a Warp Drive Spaceship Flew Into a Black Hole?|first=Carolyn|last=Collins Petersen|work=Universe Today|via=ScienceAlert|url-status=live}}</ref>

==Mathematics==
Using the [[ADM formalism]] of [[general relativity]], the [[spacetime]] is described by a [[foliation]] of space-like [[hypersurface]]s of constant coordinate time {{mvar|t}}, with the metric taking the following general form:

:<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>

where
* {{mvar|α}} is the lapse function that gives the interval of proper time between nearby hypersurfaces,
* {{mvar|β<sup>i</sup>}} is the shift vector that relates the spatial coordinate systems on different hypersurfaces,
* {{mvar|γ<sub>ij</sub>}} is a positive-definite metric on each of the hypersurfaces.

The particular form that Alcubierre studied<ref name="Alcubierre" /> is defined by:

:<math>\begin{align}
 \alpha &= 1,\\
 \beta^x &= -v_s(t)f\big(r_s(t)\big),\\
 \beta^y &= \beta^z = 0,\\
 \gamma_{ij} &= \delta_{ij},
\end{align}</math>

where

:<math>\begin{align}
 v_s(t) &= \frac{dx_s(t)}{dt},\\
 r_s(t) &= \sqrt{\big(x - x_s(t)\big)^2 + y^2 + z^2},\\
 f(r_s) &= \frac{\tanh\big(\sigma (r_s + R)\big) - \tanh\big(\sigma (r_s - R)\big)}{2 \tanh(\sigma R)},
\end{align}</math>

with arbitrary parameters {{math|''R'' > 0}} and {{math|''σ'' > 0}}. Alcubierre's specific form of the metric can thus be written:

:<math>ds^2 = \left(v_s(t)^2 f\big(r_s(t)\big)^2 - 1\right)\,dt^2 - 2v_s(t)f\big(r_s(t)\big)\,dx\,dt + dx^2 + dy^2 + dz^2.</math>

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:

:<math>-\frac{c^4}{8 \pi G} \frac{v_s^2 \left(y^2 + z^2\right)}{4 g^2 r_s ^2} \left(\frac{df}{dr_s}\right)^2,</math>

where {{mvar|g}} is the determinant of the metric [[tensor]].

Thus, because the energy density is negative, one needs [[exotic matter]] to travel more quickly 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 to keep open the "throat" of a [[wormhole]]) is thought to be impractical.{{Citation needed|date=October 2012}} According to writer Robert Low, 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. |date=1999 |title=Speed Limits in General Relativity |journal=[[Classical and Quantum Gravity]] |volume=16 |issue=2 |pages=543–549 |arxiv=gr-qc/9812067 |bibcode=1999CQGra..16..543L |doi=10.1088/0264-9381/16/2/016 |s2cid=6540037}}</ref>

== Connection to dark energy and dark matter ==
{{see also|Negative mass|}}Astrophysicist [[Jamie Farnes]] from the [[University of Oxford]] has proposed a theory, published in the peer-reviewed scientific journal ''[[Astronomy & Astrophysics]]'', that unifies [[dark energy]] and [[dark matter]] into a single [[dark fluid]], and which is expected to be testable by the [[Square Kilometre Array]] around 2030.<ref name="EA-20181205">{{Cite web |date=5 December 2018 |title=Bringing balance to the universe: New theory could explain missing 95 percent of the cosmos |url=https://www.eurekalert.org/pub_releases/2018-12/uoo-bbt120318.php |website=[[EurekAlert!]]}}</ref> Farnes found that [[Albert Einstein]] had explored the idea of gravitationally repulsive negative masses while developing the equations of [[general relativity]], an idea which leads to a "beautiful" hypothesis where the [[cosmos]] has equal amounts of positive and negative qualities. Farnes' theory relies on [[negative mass]]es that behave identically to the physics of the Alcubierre drive, providing a natural solution for the current "crisis in cosmology" due to a time-variable [[Hubble parameter]].<ref name="ARX-2018">{{Cite journal |last=Farnes |first=J. S. |year=2018 |title=A Unifying Theory of Dark Energy and Dark Matter: Negative Masses and Matter Creation within a Modified ΛCDM Framework |journal=Astronomy & Astrophysics |volume=620 |page=A92 |arxiv=1712.07962 |bibcode=2018A&A...620A..92F |doi=10.1051/0004-6361/201832898 |s2cid=53600834}}</ref>

As Farnes' theory allows a positive mass (i.e. a ship) to reach a speed equal to the speed of light, it has been dubbed "controversial".<ref name="BT-2019">{{Cite web |date=29 October 2019 |title=Astrophysicist claims "dark fluid" fills the missing 95% of the Universe |url=https://bigthink.com/surprising-science/astrophysicist-dark-fluid-missing-95-percent-universe |website=[[Big Think]]}}</ref> If the theory is correct, which has been highly debated in the scientific literature, it would explain dark energy, dark matter, allow [[closed timelike curve]]s (see [[time travel]]), and suggest that an Alcubierre drive is physically possible with [[exotic matter]].<ref name=":0">{{Cite journal |last=Socas-Navarro |first=H. |date=2019-05-30 |title=Can a negative-mass cosmology explain dark matter and dark energy? |journal=Astronomy & Astrophysics |volume=626 |pages=A5 |arxiv=1902.08287 |bibcode=2019A&A...626A...5S |doi=10.1051/0004-6361/201935317 |issn=0004-6361 |doi-access=free}}</ref>

==Physics==
With regard to certain specific 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 a suitable specification of the metric would keep the tidal forces very small within the volume occupied by the ship.<ref name="Alcubierre" />

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 might 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 could be misleading,<ref name=":2">{{Cite journal |last=Natario |first=Jose |date=2002 |title=Warp drive with zero expansion |journal=[[Classical and Quantum Gravity]] |volume=19 |issue=6 |pages=1157–1166 |arxiv=gr-qc/0110086 |bibcode=2002CQGra..19.1157N |doi=10.1088/0264-9381/19/6/308 |s2cid=15859984}}</ref> since the contraction and expansion actually refer to the relative motion of nearby members of the family of ADM observers.{{citation needed|date=June 2018}}

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 |last1=Finazzi |first1=Stefano |last2=Liberati, Stefano |last3=Barceló, Carlos |date=2009 |title=Semiclassical instability of dynamical warp drives |journal=[[Physical Review D]] |volume=79 |issue=12 |pages=124017 |arxiv=0904.0141 |bibcode=2009PhRvD..79l4017F |doi=10.1103/PhysRevD.79.124017 |s2cid=59575856}}</ref> Moreover, according to [[Serguei Krasnikov]],<ref name="Krasnikov1998">{{Cite journal |last=Krasnikov |first=S. |date=1998 |title=Hyper-fast travel in general relativity |journal=[[Physical Review D]] |volume=57 |issue=8 |pages=4760–4766 |arxiv=gr-qc/9511068 |bibcode=1998PhRvD..57.4760K |doi=10.1103/PhysRevD.57.4760 |s2cid=55825213}}</ref> generating a bubble in a previously flat space for a ''one-way'' faster-than-light 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 name="Broeck">{{Cite arXiv |eprint=gr-qc/9906050 |first=Chris |last=Van den Broeck |title=On the (im)possibility of warp bubbles |date=1999}}</ref><ref name="Coule">{{Cite journal |last=Coule |first=D. H. |date=1998 |title=No warp drive |url=http://omnis.if.ufrj.br/~mbr/warp/etc/cqg15_2523.pdf |journal=[[Classical and Quantum Gravity]] |volume=15 |issue=8 |pages=2523–2537 |bibcode=1998CQGra..15.2523C |doi=10.1088/0264-9381/15/8/026 |s2cid=250843331 |archive-url=https://web.archive.org/web/20070627000243/http://omnis.if.ufrj.br/~mbr/warp/etc/cqg15_2523.pdf |archive-date=27 June 2007}}</ref> Allen Everett and Thomas Roman comment on Krasnikov's finding ([[Krasnikov tube]]):

<blockquote>[The 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.<ref name="Everett1997">{{Cite journal |last1=Everett |first1=Allen |last2=Roman, Thomas |date=1997 |title=A Superluminal Subway: The Krasnikov Tube |journal=[[Physical Review D]] |volume=56 |issue=4 |pages=2100–2108 |arxiv=gr-qc/9702049 |bibcode=1997PhRvD..56.2100E |doi=10.1103/PhysRevD.56.2100 |s2cid=19017879}}</ref></blockquote>

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:

<blockquote>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&nbsp;... 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 Earth to a distant star and back in an arbitrarily short time, as measured by clocks on Earth, by altering the metric along the path of their outbound trip.<ref name="Everett1997" /></blockquote>

==Difficulties==
===Mass–energy requirement===
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 |date=2000 |title=Alcubierre's warp drive: Problems and prospects |journal=AIP Conference Proceedings |volume=504 |pages=1105–1110 |bibcode=2000AIPC..504.1105V |doi=10.1063/1.1290913}}</ref> Nevertheless, an Alcubierre-type warp drive 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>

If certain [[quantum inequalities]] conjectured by Ford and Roman hold,<ref>{{Cite journal |last1=Ford |first1=L. H. |last2=Roman |first2=T. A. |date=1996 |title=Quantum field theory constrains traversable wormhole geometries |journal=[[Physical Review D]] |volume=53 |issue=10 |pages=5496–5507 |arxiv=gr-qc/9510071 |bibcode=1996PhRvD..53.5496F |doi=10.1103/PhysRevD.53.5496 |pmid=10019835 |s2cid=18106362}}</ref> 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 |last1=Pfenning |first1=Michael J. |last2=Ford, L. H. |date=1997 |title=The unphysical nature of 'Warp Drive' |journal=[[Classical and Quantum Gravity]] |volume=14 |issue=7 |pages=1743–1751 |arxiv=gr-qc/9702026 |bibcode=1997CQGra..14.1743P |doi=10.1088/0264-9381/14/7/011 |s2cid=15279207}}</ref> to transport a small spaceship across the Milky Way—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" /> although the energy requirements still generally require a Type III civilization on the [[Kardashev scale]].<ref name=":1" />

Chris Van Den Broeck of the [[Katholieke Universiteit Leuven]] in Belgium, in 1999, tried to address the potential issues.<ref>{{Cite journal |last=Van Den Broeck |first=Chris |date=1999 |title=A 'warp drive' with more reasonable total energy requirements |journal=[[Classical and Quantum Gravity]] |volume=16 |issue=12 |pages=3973–3979 |arxiv=gr-qc/9905084 |bibcode=1999CQGra..16.3973V |doi=10.1088/0264-9381/16/12/314 |s2cid=15466313}}</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 in 2003, 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" /> Van Den Broeck detailed this by saying that the total energy can be reduced dramatically by keeping the surface area of the warp bubble itself microscopically small, while at the same time expanding the spatial volume inside the bubble. However, Van Den Broeck concludes that the energy densities required are still unachievable, as are the small size (a few orders of magnitude above the [[Planck scale]]) of the spacetime structures needed.<ref name=Broeck/>

In 2012, physicist [[Harold G. White|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 (c. 700&nbsp;kg)<ref name=WDmorefeasible/> or less,<ref name="io9">{{Cite web |last=Dvorsky |first=George |date=26 November 2012 |title=How NASA might build its very first warp drive |url=http://io9.com/5963263/how-nasa-will-build-its-very-first-warp-drive |url-status=live |archive-url=https://web.archive.org/web/20130110031042/http://io9.com/5963263/how-nasa-will-build-its-very-first-warp-drive |archive-date=10 January 2013 |website=[[io9]]}}</ref> and stated their intent to perform small-scale experiments in constructing warp fields.<ref name=WDmorefeasible/> White proposed to thicken the extremely thin wall of the warp bubble, so the energy is focused in a larger volume, but the overall peak energy density is actually smaller. In a flat 2D representation, the ring of positive and negative energy, initially very thin, becomes a larger, fuzzy [[torus]] (donut shape). However, as this less energetic warp bubble also thickens toward the interior region, it leaves less flat space to house the spacecraft, which has to be smaller.<ref>{{Cite magazine |last=Steadman |first=Ian |title=Nasa physicist says warp drive is more feasible than thought |magazine=Wired UK |url=https://www.wired.co.uk/news/archive/2012-09/20/warp-drives |url-status=live |archive-url=https://web.archive.org/web/20160408225609/http://www.wired.co.uk/news/archive/2012-09/20/warp-drives |archive-date=8 April 2016}}</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 have a slightly different length when the test devices were energised.<ref name=io9/><ref name="Harold Sonny White">{{Cite journal |last=White |first=Harold |date=2013 |title=Warp Field Mechanics 101 |url=https://ntrs.nasa.gov/api/citations/20110015936/downloads/20110015936.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://ntrs.nasa.gov/api/citations/20110015936/downloads/20110015936.pdf |archive-date=2022-10-09 |url-status=live |journal=Journal of the British Interplanetary Society |volume=66 |pages=242–247 |bibcode=2013JBIS...66..242W}}</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] {{webarchive|url=https://web.archive.org/web/20140109183703/https://twitter.com/malcubierre/status/362011821277839360 |date=9 January 2014 }}.</ref><ref name="2013SSC">{{Cite web |last=White |first=Harold |date=17 August 2013 |title=2013 Starship Congress: Warp Field Physics, an Update |url=https://www.youtube.com/watch?v=ucyBMB_PWr8 |url-status=live |archive-url=https://web.archive.org/web/20131120181345/http://www.youtube.com/watch?v=ucyBMB_PWr8 |archive-date=20 November 2013 |publisher=Icarus Interstellar}}</ref>

In 2021, physicist Erik Lentz described a way warp drives sourced from known and familiar purely positive energy could exist—warp bubbles based on superluminal self-reinforcing "soliton" waves.<ref name="physicsworld1">{{Cite news |date=19 March 2021 |title=Spacecraft in a 'warp bubble' could travel faster than light, claims physicist |work=Physics World |url=https://physicsworld.com/a/spacecraft-in-a-warp-bubble-could-travel-faster-than-light-claims-physicist/ |access-date=22 April 2021}}</ref><ref name="auto">{{Cite news |last=Dunham |first=Will |date=11 March 2021 |title=There's light-speed travel in 'Star Wars' and 'Star Trek.' Is it possible? |language=en |work=Reuters |url=https://www.reuters.com/article/us-space-exploration-lightspeed-idCAKBN2B32NA |access-date=22 April 2021}}</ref><ref name="auto1">{{Cite journal |last=Lentz |first=Erik W. |date=9 March 2021 |title=Breaking the warp barrier: hyper-fast solitons in Einstein–Maxwell-plasma theory |url=https://iopscience.iop.org/article/10.1088/1361-6382/abe692 |journal=Classical and Quantum Gravity |language=en |volume=38 |issue=7 |pages=075015 |arxiv=2006.07125 |bibcode=2021CQGra..38g5015L |doi=10.1088/1361-6382/abe692 |issn=0264-9381 |s2cid=219635854 |access-date=22 April 2021}}</ref><ref>{{Cite web |last=Gast |first=Robert |title=Star Trek's Warp Drive Leads to New Physics |url=https://www.scientificamerican.com/article/star-treks-warp-drive-leads-to-new-physics/ |access-date=2021-12-21 |website=[[Scientific American]] |date=October 2021 |language=en}}</ref><ref>{{Cite web |date=9 March 2021 |title=Breaking the warp barrier for faster-than-light travel |url=https://www.uni-goettingen.de/en/3240.html?id=6192 |access-date=2021-12-23 |website=Georg-August-Universität Göttingen |language=en}}</ref> The claim is controversial, with other physicists arguing that all physically reasonable warp drives violate the [[Energy condition#Weak energy condition|weak energy condition]], as well as both the [[Energy condition#Strong energy condition|strong]] and [[Energy condition#Dominant energy condition|dominant]] energy conditions.<ref>{{cite journal |url=https://journals.aps.org/prd/abstract/10.1103/PhysRevD.105.064038|title=Generic warp drives violate the null energy condition |author=Jessica Santiago |author2=Sebastian Schuster |author3=Mark Visser|journal=Physical Review D |volume=105 |issue=6 |article-number=064038 |date=15 March 2022 |page=064038 |doi=10.1103/PhysRevD.105.064038|arxiv=2105.03079 |bibcode=2022PhRvD.105f4038S |s2cid=234095711 }}</ref>

===Placement of matter===
Krasnikov proposed that if [[tachyon]]ic 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 from 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, traveling to [[Vega]] (which is 25 light-years from 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" />

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" />

===Survivability inside the bubble===
An article by José Natário (2002) argues that crew members could not control, steer or stop the ship in its warp bubble because the ship could not send signals to the front of the bubble.<ref name=":2" />

A 2009 article 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 article also argues that these problems are absent if the bubble velocity is subluminal, although the drive still requires exotic matter.<ref name=Finazzi />

===Damaging effect on destination===
Brendan McMonigal, [[Geraint F. Lewis]], and Philip O'Byrne have argued that were an Alcubierre-driven ship to decelerate from superluminal speed, the particles that its bubble had gathered in transit would be released in energetic outbursts akin to the infinitely-blueshifted radiation hypothesized to occur at the inner event horizon of a [[Kerr metric|Kerr black hole]]; forward-facing particles would thereby be energetic enough to destroy anything at the destination directly in front of the ship.<ref>{{Cite web |last=Major |first=Jason |date=29 February 2012 |title=Warp Drives May Come With a Killer Downside |url=http://www.universetoday.com/93882/warp-drives-may-come-with-a-killer-downside/#ixzz2FaZsXDuM |url-status=live |archive-url=https://web.archive.org/web/20121210175842/http://www.universetoday.com/93882/warp-drives-may-come-with-a-killer-downside/#ixzz2FaZsXDuM |archive-date=10 December 2012 |website=[[Universe Today]]}}</ref><ref>{{Cite journal |last1=McMonigal |first1=Brendan |last2=Lewis |first2=Geraint F. |last3=O'Byrne |first3=Philip |date=20 March 2012 |title=Alcubierre warp drive: On the matter of matter |journal=Physical Review D |volume=85 |issue=6 |page=064024 |arxiv=1202.5708 |bibcode=2012PhRvD..85f4024M |doi=10.1103/PhysRevD.85.064024 |quote=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. |s2cid=3993148}}</ref>

===Wall thickness===
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 the speed of light 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.<ref>{{Cite arXiv |arxiv=gr-qc/9805037 |first=Michael John |last=Pfenning |title=Quantum Inequality Restrictions on Negative Energy Densities in Curved Spacetimes. |pages=1692 |year=1998}}</ref> In Alcubierre's original calculations, a bubble macroscopically large enough to enclose a ship of 200 meters would require a total amount of exotic matter greater than 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 constructed a modification of Alcubierre's model that requires much less exotic matter but places the ship in a curved spacetime "bottle" whose neck is about 10<sup>−32</sup> meters.<ref name=Broeck/>

===Causality violation and semiclassical instability===
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. |date=15 June 1996 |title=Warp drive and causality |url=http://exvacuo.free.fr/div/Sciences/Dossiers/Time/A%20E%20Everett%20-%20Warp%20drive%20and%20causality%20-%20prd950914.pdf |url-status=live |journal=Physical Review D |volume=53 |issue=12 |pages=7365–7368 |bibcode=1996PhRvD..53.7365E |doi=10.1103/PhysRevD.53.7365 |pmid=10020029 |archive-url=https://web.archive.org/web/20131012115010/http://exvacuo.free.fr/div/Sciences/Dossiers/Time/A%20E%20Everett%20-%20Warp%20drive%20and%20causality%20-%20prd950914.pdf |archive-date=12 October 2013}}</ref> While it is possible that 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 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 that suggested that warp bubbles would be semiclassically unstable,<ref name=Finazzi /><ref name="Barcelo">{{Cite arXiv |eprint=1001.4960 |class=gr-qc |author=Barceló, Carlos |author2=Finazzi, Stefano |title=On the impossibility of superluminal travel: the warp drive lesson |date=2010 |author3=Liberati, Stefano}}</ref> but ultimately the conjecture can only be decided by a full theory of [[quantum gravity]].<ref>{{Cite journal |last=Visser |first=Matt |date=December 1997 |title=The reliability horizon for semi-classical quantum gravity: Metric fluctuations are often more important than back-reaction |journal=Physics Letters B |volume=415 |issue=1 |pages=8–14 |arxiv=gr-qc/9702041 |bibcode=1997PhLB..415....8V |doi=10.1016/S0370-2693(97)01226-4 |s2cid=118984236}}</ref>

Alcubierre briefly discusses some of these issues in a series of lecture slides posted online,<ref>{{Cite web |title=Faster than light |url=http://ccrg.rit.edu/files/FasterThanLight.pdf |archive-url=https://web.archive.org/web/20160318223348/http://ccrg.rit.edu/files/FasterThanLight.pdf |archive-date=18 March 2016 |access-date=2017-01-25}}</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 if it had), but there are good arguments in its favor based on quantum field theory. 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."

==Relation to ''Star Trek'' warp drive==
The ''[[Star Trek]]'' television series and films use the term "warp drive" to describe their method of faster-than-light travel. Neither the Alcubierre theory, nor anything similar, existed when the series was conceived—the term "warp drive" and general concept originated with [[John W. Campbell]]'s 1931 science fiction novel ''[[Islands of Space]]''.<ref>J. Gardiner, "Warp Drive – From Imagination to Reality", [[Journal of the British Interplanetary Society]], vol. 61, pp. 353–357 (2008).</ref> 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/ |archive-url=https://web.archive.org/web/20130424012220/http://www.alan-shapiro.com/the-physics-of-warp-drive/ |archive-date=24 April 2013 |access-date=2 June 2013}}</ref> and cites the "'warp drive' of science fiction" in his 1994 article.<ref name="Alcubierre" /> A USS ''Alcubierre'' appears in the ''Star Trek'' [[Tabletop role-playing game|tabletop RPG]] ''[[Star Trek Adventures]]''.<ref>{{Cite web |title=Star Trek Adventures: A Star Beyond the Stars – Modiphius {{!}} Star Trek Adventures {{!}} DriveThruRPG.com |url=https://www.drivethrurpg.com/product/242391/Star-Trek-Adventures-A-Star-Beyond-the-Stars |access-date=2021-04-22 |website=www.drivethrurpg.com |language=en}}</ref> Since the release of ''[[Star Trek: The Original Series]]'', more recent ''Star Trek'' [[Spin-off (media)|spin-off]] series have made closer use of the theory behind the Alcubierre Drive incorporating warp bubbles/fields into the in-universe science.{{Citation needed|reason=Which spin-off series? What episodes?|date=October 2024}}

==See also==
* [[EmDrive]]
* [[Exact solutions in general relativity]] (for more on the sense in which the Alcubierre spacetime is a solution)
* [[IXS Enterprise|IXS ''Enterprise'']]
* [[Quantum vacuum thruster]]
* [[Reactionless drive]]
* [[Spacecraft propulsion]]
* [[Unruh effect]]

==Notes==
{{reflist}}

==References==
* {{Cite journal |last=Hiscock |first=William A. |date=1997 |title=Quantum effects in the Alcubierre warp drive spacetime |journal=[[Classical and Quantum Gravity]] |volume=14 |issue=11 |pages=L183–L188 |arxiv=gr-qc/9707024 |bibcode=1997CQGra..14L.183H |doi=10.1088/0264-9381/14/11/002 |s2cid=1884428}}
* {{Cite journal |last1=Lobo |first1=Francisco S. N. |last2=Visser |first2=Matt |date=2004 |title=Fundamental limitations on 'warp drive' spacetimes |journal=[[Classical and Quantum Gravity]] |volume=21 |issue=24 |pages=5871–5892 |arxiv=gr-qc/0406083 |bibcode=2004CQGra..21.5871L |doi=10.1088/0264-9381/21/24/011 |s2cid=119010055}}

==External links==
* {{Cite web |title=Ideas Based on What We'd Like To Achieve |url=http://www.nasa.gov/centers/glenn/technology/warp/ideachev_prt.htm |archive-url=https://web.archive.org/web/20130409135139/http://www.nasa.gov/centers/glenn/technology/warp/ideachev_prt.htm |archive-date=9 April 2013 |access-date=2 July 2008 |publisher=NASA}} It describes the concept in laymans terms.
<!-- *[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.]
 07/24/2016 mwr0 deadlink - I think I found the proper replacement in the one below (indicates major website restructuring).
 -->
* {{Cite web |title=Can We Travel Faster Than Light? with Dr. Miguel Alcubierre|date=June 6, 2019|publisher=Event Horizon|website=YouTube|url=https://www.youtube.com/watch?v=JafY92PhgKU}} (hosted by [[John Michael Godier]]).
<!-- *{{Cite web |date=January 21, 2022 |title=Miguel Alcubierre: Faster than the Speed of Light |url=https://www.youtube.com/watch?v=_u36-iKApko |website=YouTube |publisher=Astrofisica UC}} This YouTube video has been taken private. -->
* [http://publikationen.uni-tuebingen.de/xmlui/bitstream/handle/10900/48159/pdf/09warp.html A short video clip of the hypothetical effects of the warp drive.]
* [https://web.archive.org/web/20061109042431/http://omnis.if.ufrj.br/~mbr/warp/ Marcelo B. Ribeiro's Page on Warp Drive Theory].
* {{Cite journal |last=González-Díaz |first=Pedro |date=14 July 2000 |title=Warp Drive Space-Time |journal=Physical Review D |publisher=[[American Physical Society]] |volume=62 |issue=4 |pages=044005 |arxiv=gr-qc/9907026 |bibcode=2000PhRvD..62d4005G |doi=10.1103/PhysRevD.62.044005 |s2cid=59940462}}
* {{Skeptoid|id=4922|number=922|title=Testing Alcubierre's Warp Drive.|date=February 6, 2024}}

{{Time travel}}
{{Relativity}}

{{DEFAULTSORT:Alcubierre Drive}}
[[Category:Interstellar travel]]
[[Category:Warp drive theory]]
[[Category:Lorentzian manifolds]]
[[Category:Science fiction themes]]
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[[Category:1994 introductions]]
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