Editing Alcubierre drive (section)

==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>