Editing Alcubierre drive (section)

===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>