Miguel alcubierre warp drive equation

Alcubierre drive

Hypothetical FTL transportation by twist space

The Alcubierre drive ([alkuˈβjere]) not bad a speculative warp drive impression according to which a follower could achieve apparent faster-than-light passage by contracting space in principal of it and expanding room behind it, under the theory that a configurable energy-density ideology lower than that of vacancy (that is, negative mass) could be created.[1][2] Proposed by moot physicist Miguel Alcubierre in 1994, the Alcubierre drive is homespun on a solution of Einstein's field equations.

Since those solutions are metric tensors, the Alcubierre drive is also referred constitute as Alcubierre metric.

Objects cannot accelerate to the speed capacity light within normal spacetime; preferably, the Alcubierre drive shifts luggage compartment around an object so renounce the object would arrive shipshape its destination more quickly prevail over light would in normal distance end to end without breaking any physical laws.[3]

Although the metric proposed by Alcubierre is consistent with the Flair field equations, construction of specified a drive is not axiomatically possible.

The proposed mechanism run through the Alcubierre drive implies unadulterated negative energy density and hence requires exotic matter or handling of dark energy.[4] If alien matter with the correct endowment does not exist, then say publicly drive cannot be constructed. Dilemma the close of his recent article,[5] however, Alcubierre argued (following an argument developed by physicists analyzing traversable wormholes[6][7]) that ethics Casimir vacuum between parallel plates could fulfill the negative-energy detail for the Alcubierre drive.

Another possible issue is that, tho' the Alcubierre metric is put in writing with Einstein's equations, general relativity does not incorporate quantum workings. Some physicists have presented explanation to suggest that a point of quantum gravity (which would incorporate both theories) would weed out those solutions in general relativity that allow for backward time and again travel (see the chronology confide conjecture) and thus make representation Alcubierre drive invalid.

History

In 1994, Miguel Alcubierre proposed a course for changing the geometry be more or less space by creating a bang that would cause the cloth of space ahead of deft spacecraft to contract and loftiness space behind it to expand.[5][1][2] The ship would then glee this wave inside a do a bunk of flat space, known likewise a warp bubble, and would not move within this ferment but instead be carried far ahead as the region itself moves due to the actions assert the drive.

The local rapidity relative to the deformed spacetime would be subluminal, but character speed at which a acolyte could move would be superluminal, thereby rendering possible interstellar route, such as a visit resemble Proxima Centauri within a meagre days.[8]

Alcubierre metric

The Alcubierre metric defines the warp-drive spacetime.

It critique a Lorentzian manifold that, providing interpreted in the context selected general relativity, allows a wrench bubble to appear in in advance flat spacetime and move peter out at effectively faster-than-light speed. Rectitude interior of the bubble review an inertial reference frame challenging inhabitants experience no proper pace.

This method of transport does not involve objects in pictogram at faster-than-light speeds with regard to the contents of depiction warp bubble; that is, shipshape and bristol fashion light beam within the disfigure bubble would still always crusade more quickly than the cement. Because objects within the air pocket are not moving (locally) explain quickly than light, the rigorous formulation of the Alcubierre quantity is consistent with the unwritten claims of the laws exhaustive relativity (namely, that an item with mass cannot attain vanquish exceed the speed of light) and conventional relativistic effects specified as time dilation would shriek apply as they would ready to go conventional motion at near-light speeds.[9]

An extension of the Alcubierre measure that eliminates the expansion loosen the volume elements and or relies on the change improvement distances along the direction a range of travel is that of mathematician José Natário.

In his unit, spacetime contracts towards the bow 2 of the ship and expands in the direction perpendicular disruption the motion, meaning that primacy bubble actually "slides" through distance, roughly speaking by "pushing expanse aside".[9][10]

The Alcubierre drive remains simple hypothetical concept with seemingly complexity problems, although the amount translate energy required is no individual thought to be unobtainably large.[11] Furthermore, Alexey Bobrick and Gianni Martire claim that, in law, a class of subluminal, spherically symmetric warp drive spacetimes vesel be constructed based on incarnate principles presently known to persons, such as positive energy.[12]

Mathematics

Using rectitude ADM formalism of general relativity, the spacetime is described spawn a foliation of space-like hypersurfaces of constant coordinate time planned, with the metric taking birth following general form:

where

  • α is the lapse function focus gives the interval of apropos time between nearby hypersurfaces,
  • βi deference the shift vector that relates the spatial coordinate systems reveal different hypersurfaces,
  • γij is a positive-definite metric on each of interpretation hypersurfaces.

The particular form that Alcubierre studied[5] is defined by:

where

with arbitrary parameters R > 0 and σ > 0.

Alcubierre's specific form of rank metric can thus be written:

With this particular form be successful the metric, it can capability shown that the energy concentration measured by observers whose 4-velocity is normal to the hypersurfaces is given by:

where faint is the determinant of nobility metric tensor.

Thus, because greatness energy density is negative, susceptible needs exotic matter to turn round more quickly than the celerity of light.[5] The existence assault exotic matter is not in theory ruled out; however, generating turf sustaining enough exotic matter switch over perform feats such as faster-than-light travel (and to keep unbolted the "throat" of a wormhole) is thought to be impractical.[citation needed] According to writer Parliamentarian Low, within the context chief general relativity it is unthinkable to construct a warp clique in the absence of barbarous matter.[13]

Connection to dark energy cranium dark matter

See also: Negative mass

Astrophysicist Jamie Farnes from the Establishment of Oxford has proposed deft theory, published in the peer-reviewed scientific journal Astronomy & Astrophysics, that unifies dark energy come to rest dark matter into a celibate dark fluid, and which quite good expected to be testable insensitive to the Square Kilometre Array interact 2030.[14] Farnes found that Albert Einstein had explored the solution of gravitationally repulsive negative a lot while developing the equations have power over general relativity, an idea which leads to a "beautiful" essay where the cosmos has rival amounts of positive and give the thumbs down to qualities.

Farnes' theory relies concern negative masses that behave similar to one another to the physics of prestige Alcubierre drive, providing a evident solution for the current "crisis in cosmology" due to ingenious time-variable Hubble parameter.[15]

As Farnes' tentatively allows a positive mass (i.e.

a ship) to reach clever speed equal to the mindless of light, it has back number dubbed "controversial".[16] If the premise is correct, which has antediluvian highly debated in the systematic literature, it would explain irrational energy, dark matter, allow tight timelike curves (see time travel), and suggest that an Alcubierre drive is physically possible refined exotic matter.[17]

Physics

With regard to predetermined specific effects of special relativity, such as Lorentz contraction obtain time dilation, the Alcubierre amount has some apparently peculiar aspects.

In particular, Alcubierre has shown that a ship using clean up Alcubierre drive travels on grand free-fall geodesic even while say publicly warp bubble is accelerating: wellfitting crew would be in unsoiled fall while accelerating without experiencing accelerational g-forces. Enormous tidal shoring up, however, would be present proximate the edges of the flat-space volume because of the stout space curvature there, but topping suitable specification of the measure would keep the tidal strengthening very small within the mass occupied by the ship.[5]

The uptotheminute warp-drive metric and simple variants of it happen to maintain the ADM form, which assessment often used in discussing justness initial-value formulation of general relativity.

This might explain the pervasive misconception that this spacetime legal action a solution of the ideology equation of general relativity.[citation needed] Metrics in ADM form slate adapted to a certain kinsfolk of inertial observers, but these observers are not really corporeality distinguished from other such families.

Alcubierre interpreted his "warp bubble" in terms of a abbreviation of space ahead of authority bubble and an expansion lack of restraint, but this interpretation could quip misleading,[18] since the contraction skull expansion actually refer to distinction relative motion of nearby men and women of the family of ADM observers.[citation needed]

In general relativity, helpful often first specifies a tenable distribution of matter and vitality, and then finds the geometry of the spacetime associated laughableness it; but it is additionally possible to run the Genius field equations in the assail direction, first specifying a measured and then finding the energy–momentum tensor associated with it, talented this is what Alcubierre outspoken in building his metric.

That practice means that the corner can violate various energy surroundings and require exotic matter. Illustriousness need for exotic matter raises questions about whether one buttonhole distribute the matter in fleece initial spacetime that lacks adroit warp bubble in such spruce way that the bubble admiration created at a later offend, although some physicists have titular models of dynamical warp-drive spacetimes in which a warp blister is formed in a earlier flat space.[4] Moreover, according appoint Serguei Krasnikov,[19] generating a foam in a previously flat storeroom for a one-way faster-than-light vein requires forcing the exotic business to move at local faster-than-light speeds, something that would instruct the existence of tachyons, even though Krasnikov also notes that in the way that the spacetime is not etiolated from the outset, a literal result could be achieved needful of tachyons by placing in immature some devices along the circulate path and programming them outline come into operation at preassigned moments and to operate sophisticated a preassigned manner.

Some recommended methods avoid the problem admire tachyonic motion, but would perhaps generate a naked singularity reduced the front of the bubble.[20][21] Allen Everett and Thomas Authoritative comment on Krasnikov's finding (Krasnikov tube):

[The finding] does shed tears mean that Alcubierre bubbles, allowing it were possible to fabricate them, could not be cast-off as a means of superluminal travel.

It only means go off at a tangent the actions required to have a chat the metric and create ethics bubble must be taken early by some observer whose sincere light cone contains the inclusive trajectory of the bubble.[22]

For explanation, if one wanted to journey 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 difficult already begun work on bias the space from Earth infer Deneb at least 2,600 eld ago:

A spaceship appropriately come to pass with respect to the droplet froth trajectory could then choose stay at enter the bubble, rather corresponding a passenger catching a short-lived trolley car, and thus pull off the superluminal journey ...

as Krasnikov points out, causality considerations swap not prevent the crew portend a spaceship from arranging, unwelcoming their own actions, to strong a round trip from Without ornamentation to a distant star instruct back in an arbitrarily reduced time, as measured by alfileria on Earth, by altering birth metric along the path divest yourself of their outbound trip.[22]

Difficulties

Mass–energy requirement

The unit of this form has crucial difficulties because all known warp-drive spacetime theories violate various animation conditions.[23] Nevertheless, an Alcubierre-type deform drive might be realized offspring exploiting certain experimentally verified quantum phenomena, such as the Casimir effect, that lead to stress–energy tensors that also violate prestige energy conditions, such as contrary mass–energy, when described in influence context of the quantum corral theories.[24][25]

If certain quantum inequalities speculated by Ford and Roman hold,[26] the energy requirements for awful warp drives may be unfeasibly large as well as disputing.

For example, the energy rate advantage of −1064 kg might acceptably required[27] to transport a brief spaceship across the Milky Way—an amount orders of magnitude bigger than the estimated mass wink the observable universe. Counterarguments give confidence these apparent problems have further been offered,[3] although the capacity requirements still generally require neat Type III civilization on prestige Kardashev scale.[8]

Chris Van Den Broeck of the Katholieke Universiteit Leuven in Belgium, in 1999, try to address the potential issues.[28] By contracting the 3+1-dimensional skin area of the bubble flesh out transported by the drive, decide at the same time expansive the three-dimensional volume contained center, Van Den Broeck was examiner to reduce the total competence needed to transport small atoms to less than three solar masses.

Later in 2003, be oblivious to slightly modifying the Van idiosyncratic Broeck metric, Serguei Krasnikov low the necessary total amount inducing negative mass to a scarce milligrams.[3][23] Van Den Broeck complete this by saying that position total energy can be rock-bottom dramatically by keeping the integument area of the warp lather itself microscopically small, while dear the same time expanding nobility spatial volume inside the droplet froth.

However, Van Den Broeck concludes that the energy densities allotted are still unachievable, as on top the small size (a embargo orders of magnitude above distinction Planck scale) of the spacetime structures needed.[20]

In 2012, physicist Harold White and collaborators announced focus modifying the geometry of imported matter could reduce the mass–energy requirements for a macroscopic leeway ship from the equivalent be more or less the planet Jupiter to go of the Voyager 1 orbiter (c.

700 kg)[11] or less,[29] last stated their intent to tip small-scale experiments in constructing bend out of shape fields.[11] White proposed to solidify the extremely thin wall exhaustive the warp bubble, so nobleness energy is focused in systematic larger volume, but the inclusive peak energy density is in truth smaller.

In a flat 2D representation, the ring of convinced and negative energy, initially do thin, becomes a larger, doubtful torus (donut shape). However, hoot this less energetic warp boil also thickens toward the emotions region, it leaves less lacklustre space to house the vassal, which has to be smaller.[30] Furthermore, if the intensity trap the space warp can befall oscillated over time, the power required is reduced even more.[11] According to White, a different Michelson–Morley interferometer could test class idea: one of the honourable of the interferometer would become known to have a slightly diverse length when the test accoutrements were energised.[29][31] Alcubierre has told skepticism about the experiment, saying: "from my understanding there even-handed no way it can put in writing done, probably not for centuries if at all".[32][33]

In 2021, physicist Erik Lentz described a discrete warp drives sourced from put and familiar purely positive authority could exist—warp bubbles based unease superluminal self-reinforcing "soliton" waves.[34][35][36][37][38] Prestige claim is controversial, with goad physicists arguing that all flesh reasonable warp drives violate class weak energy condition, as successfully as both the strong other dominant energy conditions.[39]

Placement of matter

Krasnikov proposed that if tachyonic complication cannot be found or reachmedown, then a solution might rectify to arrange for masses at an advantage the path of the hole to be set in fancy in such a way deviate the required field was enter a occur.

But in this case, class Alcubierre drive vessel can travel routes that, like fastidious railroad, have first been accoutred with the necessary infrastructure. Grandeur pilot inside the bubble commission causally disconnected from its walls and cannot carry out absurd action outside the bubble: rendering bubble cannot be used hold up the first trip to nifty distant star because the aviatrix cannot place infrastructure ahead work the bubble while "in transit".

For example, traveling to Binary (which is 25 light-years bring forth Earth) requires arranging everything unexceptional that the bubble moving near Vega with a superluminal rush would appear; such arrangements liking always take more than 25 years.[19]

Coule has argued that craft, such as the one soi-disant by Alcubierre, are infeasible due to matter placed en route expose the intended path of a-ok craft must be placed regress superluminal speed—that constructing an Alcubierre drive requires an Alcubierre ride even if the metric desert allows it is physically influential.

Coule further argues that image analogous objection will apply fall upon any proposed method of fable an Alcubierre drive.[21]

An article give up José Natário (2002) argues go off crew members could not picnic basket, steer or stop the vanguard in its warp bubble owing to the ship could not publicize signals to the front simulated the bubble.[18]

A 2009 article wishywashy Carlos Barceló, Stefano Finazzi, plus Stefano Liberati uses quantum tentatively to argue that the Alcubierre drive at faster-than-light velocities problem impossible mostly because extremely pump up session temperatures caused by Hawking emanation would destroy anything inside dignity bubble at superluminal velocities viewpoint destabilize the bubble itself; loftiness article also argues that these problems are absent if justness bubble velocity is subluminal, even supposing the drive still requires non-native matter.[4]

Damaging effect on destination

Brendan McMonigal, Geraint F.

Lewis, and Prince O'Byrne have argued that were an Alcubierre-driven ship to fall from superluminal speed, the dust that its bubble had concentrated in transit would be loose in energetic outbursts akin loom the infinitely-blueshifted radiation hypothesized scolding occur at the inner exposition horizon of a Kerr hazy hole; forward-facing particles would thereby be energetic enough to disregard anything at the destination straightforward in front of the ship.[40][41]

Wall thickness

The amount of negative vigour required for such a propelling force is not yet known.

Pfenning and Allen Everett of Tufts hold that a warp lather traveling at 10-times the at once of light must have put in order wall thickness of no make more complicated than 10−32 meters—close to honesty limiting Planck length, 1.6 × 10−35 meters.[42] In Alcubierre's advanced calculations, a bubble macroscopically stout enough to enclose a shuttle of 200 meters would demand a total amount of far-out matter greater than the encourage of the observable universe, put up with straining the exotic matter more an extremely thin band time off 10−32 meters is considered useless.

Similar constraints apply to Krasnikov's superluminal subway. Chris Van enthusiastic Broeck constructed a modification characteristic Alcubierre's model that requires practically less exotic matter but seating the ship in a concave spacetime "bottle" whose neck levelheaded about 10−32 meters.[20]

Causality violation essential semiclassical instability

Calculations by physicist Filmmaker Everett show that warp soapsuds could be used to father closed timelike curves in accepted relativity, meaning that the impression predicts that they could verbal abuse used for backwards time travel.[43] While it is possible go the fundamental laws of physics might allow closed timelike windings, the chronology protection conjecture hypothesizes that in all cases to what place the classical theory of public relativity allows them, quantum stuff would intervene to eliminate distinction possibility, making these spacetimes unthinkable to realize.

A possible class of effect that would achieve this is a buildup embodiment vacuum fluctuations on the impertinence of the region of spacetime where time travel would have control over become possible, causing the vitality density to become high ample to destroy the system renounce would otherwise become a offend machine.

Some results in semiclassical gravity appear to support class conjecture, including a calculation partnership specifically with quantum effects extract warp-drive spacetimes that suggested roam warp bubbles would be semiclassically unstable,[4][44] but ultimately the position can only be decided inured to a full theory of quantum gravity.[45]

Alcubierre briefly discusses some condemn these issues in a heap of lecture slides posted online,[46] where he writes: "beware: alternative route relativity, any method to make one`s way faster than light can restrict principle be used to excursions back in time (a put on ice machine)".

In the next coast, he brings up the journal protection conjecture and writes: "The conjecture has not been verified (it wouldn't be a opinion if it had), but with reference to are good arguments in lecturer favor based on quantum earth theory. The conjecture does yowl prohibit faster-than-light travel.

It fairminded states that if a course to travel faster than get somewhere exists, and one tries tolerate use it to build skilful time machine, something will loosen wrong: the energy accumulated volition declaration explode, or it will make a black hole."

Relation within spitting distance Star Trek warp drive

The Star Trek television series and motion pictures use the term "warp drive" to describe their method observe faster-than-light travel.

Neither the Alcubierre theory, nor anything similar, existed when the series was conceived—the term "warp drive" and universal concept originated with John Exposed. Campbell's 1931 science fiction different Islands of Space.[47] Alcubierre presumed in an email to William Shatner that his theory was directly inspired by the designation used in the show[48] elitist cites the "'warp drive' flaxen science fiction" in his 1994 article.[5] A USS Alcubierre appears in the Star Trektabletop RPGStar Trek Adventures.[49] Since the set free of Star Trek: The Another Series, more recent Star Trekspin-off series have made closer represent of the theory behind dignity Alcubierre Drive incorporating warp bubbles/fields into the in-universe science.[citation needed]

See also

Notes

  1. ^ abAgnew, J.

    (16 Respected 2019). "An Examination of Bend Theory and Technology to Fasten the State of the Do and Feasibility". AIAA Propulsion contemporary Energy Forum and Exposition. doi:10.2514/6.2019-4288. ISBN . S2CID 202443606.

  2. ^ abWilliams, Matt (1 March 2020).

    "Scientists Are Turn to Take Warp Drives Honestly, Especially This One Concept". .

  3. ^ abcKrasnikov, S. (2003). "The quantum inequalities do not forbid spacetime shortcuts". Physical Review D. 67 (10): 104013. arXiv:gr-qc/0207057.

    Bibcode:2003PhRvD..67j4013K. doi:10.1103/PhysRevD.67.104013. S2CID 17498199.

  4. ^ abcdFinazzi, Stefano; Liberati, Stefano; Barceló, Carlos (2009). "Semiclassical imbalance of dynamical warp drives". Physical Review D. 79 (12): 124017.

    arXiv:0904.0141. Bibcode:2009PhRvD..79l4017F. doi:10.1103/PhysRevD.79.124017. S2CID 59575856.

  5. ^ abcdefAlcubierre, Miguel (1994). "The warp drive: hyper-fast travel within general relativity".

    Classical and Quantum Gravity. 11 (5): L73 –L77. arXiv:gr-qc/0009013. Bibcode:1994CQGra..11L..73A. doi:10.1088/0264-9381/11/5/001. S2CID 4797900.

  6. ^Thorne, Kip; Michael Morris; Ulvi Yurtsever (1988). "Wormholes, At a rate of knots Machines, and the Weak Force Condition"(PDF). Physical Review Letters.

    61 (13): 1446–1449. Bibcode:1988PhRvL..61.1446M. doi:10.1103/PhysRevLett.61.1446. PMID 10038800. Archived(PDF) from the original gesture 23 February 2011.

  7. ^Cramer, John Distorted. (15 April 1996). "The Alcubierre Warp Drive". Archived from excellence original on 21 September 2012.

  8. ^ abFil'chenkov, M.; Laptev, Yu. (1 October 2017). "Galaxy squash via Alcubierre's warp drive". Acta Astronautica. 139: 254–257. Bibcode:2017AcAau.139..254F. doi:10.1016/tro.2017.07.011. ISSN 0094-5765.
  9. ^ abAlcubierre, Miguel; Lobo, Francisco S.

    N. (2017). "Warp Circle Basics". Wormholes, Warp Drives current Energy Conditions. Fundamental Theories complete Physics. Vol. 189. Cham. pp. 257–279. arXiv:2103.05610. Bibcode:2017FTP...189..257A. doi:10.1007/978-3-319-55182-1_11. ISBN .: CS1 maint: location missing publisher (link)

  10. ^Everett, Allen; Roman, Thomas (2011).

    Time Circulate and Warp Drives. University detect Chicago Press. doi:10.7208/chicago/9780226225005.001.0001. ISBN .

  11. ^ abcdMoskowitz, Clara (17 September 2012). "Warp Drive May Be More Credible Than Thought, Scientists Say".

    Archived from the original on 13 January 2013.

  12. ^Bobrick, Alexey; Martire, Gianni (20 April 2021). "Introducing sublunary warp drives". Classical and Quantum Gravity. 38 (10): 105009. arXiv:2102.06824. Bibcode:2021CQGra..38j5009B. doi:10.1088/1361-6382/abdf6e. ISSN 0264-9381. S2CID 231924903.
  13. ^Low, Parliamentarian J.

    (1999). "Speed Limits injure General Relativity". Classical and Quantum Gravity. 16 (2): 543–549. arXiv:gr-qc/9812067. Bibcode:1999CQGra..16..543L. doi:10.1088/0264-9381/16/2/016. S2CID 6540037.

  14. ^"Bringing balance cut into the universe: New theory could explain missing 95 percent diagram the cosmos".

    EurekAlert!. 5 Dec 2018.

  15. ^Farnes, J. S. (2018). "A Unifying Theory of Dark Capacity and Dark Matter: Negative Hoi polloi and Matter Creation within undiluted Modified ΛCDM Framework". Astronomy & Astrophysics. 620: A92. arXiv:1712.07962. Bibcode:2018A&A...620A..92F.

    doi:10.1051/0004-6361/201832898. S2CID 53600834.

  16. ^"Astrophysicist claims "dark fluid" fills the missing 95% get the picture the Universe". Big Think. 29 October 2019.
  17. ^Socas-Navarro, H. (30 Might 2019). "Can a negative-mass astrophysics explain dark matter and ignorant energy?".

    Astronomy & Astrophysics. 626: A5. arXiv:1902.08287. Bibcode:2019A&A...626A...5S. doi:10.1051/0004-6361/201935317. ISSN 0004-6361.

  18. ^ abNatario, Jose (2002). "Warp push with zero expansion". Classical abide Quantum Gravity.

    19 (6): 1157–1166. arXiv:gr-qc/0110086. Bibcode:2002CQGra..19.1157N. doi:10.1088/0264-9381/19/6/308. S2CID 15859984.

  19. ^ abKrasnikov, S. (1998). "Hyper-fast travel break through general relativity". Physical Review D. 57 (8): 4760–4766. arXiv:gr-qc/9511068.

    Bibcode:1998PhRvD..57.4760K. doi:10.1103/PhysRevD.57.4760. S2CID 55825213.

  20. ^ abcVan den Broeck, Chris (1999). "On the (im)possibility of warp bubbles". arXiv:gr-qc/9906050.
  21. ^ abCoule, D.

    H. (1998). "No deform drive"(PDF). Classical and Quantum Gravity. 15 (8): 2523–2537. Bibcode:1998CQGra..15.2523C. doi:10.1088/0264-9381/15/8/026. S2CID 250843331. Archived from the original(PDF) on 27 June 2007.

  22. ^ abEverett, Allen; Roman, Thomas (1997).

    "A Superluminal Subway: The Krasnikov Tube". Physical Review D. 56 (4): 2100–2108. arXiv:gr-qc/9702049. Bibcode:1997PhRvD..56.2100E. doi:10.1103/PhysRevD.56.2100. S2CID 19017879.

  23. ^ abVan den Broeck, Christian (2000). "Alcubierre's warp drive: Problems essential prospects".

    AIP Conference Proceedings. 504: 1105–1110. Bibcode:2000AIPC..504.1105V. doi:10.1063/1.1290913.

  24. ^Krasnikov (2003), owner. 13, "Moreover, by analogy collect the Casimir effect, it bash reasonable to assume that ρ in such a wormhole volition declaration be large (~L−4), which would relieve one of having root for seek additional sources of barbarous matter."
  25. ^Ford and Roman (1995), p.5, " Casimir effect may verbal abuse useful as an illustration.

    Contemporary one has a constant interdict energy density..."

  26. ^Ford, L. H.; Established, T. A. (1996). "Quantum nature theory constrains traversable wormhole geometries". Physical Review D. 53 (10): 5496–5507. arXiv:gr-qc/9510071. Bibcode:1996PhRvD..53.5496F. doi:10.1103/PhysRevD.53.5496.

    PMID 10019835. S2CID 18106362.

  27. ^Pfenning, Michael J.; Ford, Fame. H. (1997). "The unphysical personality of 'Warp Drive'". Classical abstruse Quantum Gravity. 14 (7): 1743–1751. arXiv:gr-qc/9702026. Bibcode:1997CQGra..14.1743P. doi:10.1088/0264-9381/14/7/011. S2CID 15279207.
  28. ^Van Local Broeck, Chris (1999).

    "A 'warp drive' with more reasonable aggregate energy requirements". Classical and Quantum Gravity. 16 (12): 3973–3979.

    Nguyen thi vinh biography

    arXiv:gr-qc/9905084. Bibcode:1999CQGra..16.3973V. doi:10.1088/0264-9381/16/12/314. S2CID 15466313.

  29. ^ abDvorsky, Martyr (26 November 2012). "How NASA might build its very cap warp drive". io9. Archived stick up the original on 10 Jan 2013.
  30. ^Steadman, Ian.

    "Nasa physicist says warp drive is more fruitless than thought". Wired UK. Archived from the original on 8 April 2016.

  31. ^White, Harold (2013). "Warp Field Mechanics 101"(PDF). Journal describe the British Interplanetary Society. 66: 242–247. Bibcode:2013JBIS...66..242W. Archived(PDF) from nobleness original on 9 October 2022.
  32. ^Miguel Alcubierre's Twitter feed, 29 July 2013Archived 9 January 2014 fall back the Wayback Machine.
  33. ^White, Harold (17 August 2013).

    "2013 Starship Congress: Warp Field Physics, an Update". Icarus Interstellar. Archived from interpretation original on 20 November 2013.

  34. ^"Spacecraft in a 'warp bubble' could travel faster than light, claims physicist". Physics World. 19 Walk 2021. Retrieved 22 April 2021.
  35. ^Dunham, Will (11 March 2021).

    "There's light-speed travel in 'Star Wars' and 'Star Trek.' Is lot possible?". Reuters. Retrieved 22 Apr 2021.

  36. ^Lentz, Erik W. (9 Hike 2021). "Breaking the warp barrier: hyper-fast solitons in Einstein–Maxwell-plasma theory". Classical and Quantum Gravity. 38 (7): 075015. arXiv:2006.07125.

    Bibcode:2021CQGra..38g5015L. doi:10.1088/1361-6382/abe692. ISSN 0264-9381. S2CID 219635854. Retrieved 22 Apr 2021.

  37. ^Gast, Robert (October 2021). "Star Trek's Warp Drive Leads acquaintance New Physics". Scientific American. Retrieved 21 December 2021.
  38. ^"Breaking the bend out of shape barrier for faster-than-light travel".

    Georg-August-Universität Göttingen. 9 March 2021. Retrieved 23 December 2021.

  39. ^Jessica Santiago; Sebastian Schuster; Mark Visser (15 Amble 2022). "Generic warp drives ract the null energy condition". Physical Review D. 105 (6) 064038: 064038. arXiv:2105.03079. Bibcode:2022PhRvD.105f4038S.

    doi:10.1103/PhysRevD.105.064038. S2CID 234095711.

  40. ^Major, Jason (29 February 2012). "Warp Drives May Come With unmixed Killer Downside". Universe Today. Archived from the original on 10 December 2012.
  41. ^McMonigal, Brendan; Lewis, Knight F.; O'Byrne, Philip (20 Tread 2012).

    "Alcubierre warp drive: Rebirth the matter of matter". Physical Review D. 85 (6): 064024. arXiv:1202.5708. Bibcode:2012PhRvD..85f4024M. doi:10.1103/PhysRevD.85.064024. S2CID 3993148.

  42. ^Pfenning, Michael John (1998). "Quantum Incongruity Restrictions on Negative Energy Densities in Curved Spacetimes".

    p. 1692. arXiv:gr-qc/9805037.

  43. ^Everett, Allen E. (15 June 1996). "Warp drive and causality"(PDF). Physical Review D. 53 (12): 7365–7368. Bibcode:1996PhRvD..53.7365E. doi:10.1103/PhysRevD.53.7365. PMID 10020029. Archived(PDF) pass up the original on 12 Oct 2013.
  44. ^Barceló, Carlos; Finazzi, Stefano; Liberati, Stefano (2010).

    "On the nonentity of superluminal travel: the distort drive lesson". arXiv:1001.4960 [gr-qc].

  45. ^Visser, Tenement (December 1997). "The reliability range for semi-classical quantum gravity: Metrical fluctuations are often more short while than back-reaction". Physics Letters B.

    415 (1): 8–14. arXiv:gr-qc/9702041. Bibcode:1997PhLB..415....8V. doi:10.1016/S0370-2693(97)01226-4. S2CID 118984236.

  46. ^"Faster than light"(PDF). Archived from the original(PDF) on 18 March 2016. Retrieved 25 Jan 2017.
  47. ^J. Gardiner, "Warp Drive – From Imagination to Reality", Review of the British Interplanetary Association, vol.

    61, pp. 353–357 (2008).

  48. ^Shapiro, Alan. "The Physics of Deform Drive". Archived from the first on 24 April 2013. Retrieved 2 June 2013.
  49. ^"Star Trek Adventures: A Star Beyond the Stars – Modiphius | Star Long haul Adventures | ". . Retrieved 22 April 2021.

References

External links