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Warp drive (Star Trek)

 

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Warp drive (Star Trek)


 
 

Warp in Star Trek

The Next Generation era

Plots involving the Enterprise going far too fast were a frequent feature in the original series (such as warp 14.1 in That Which Survives), and for The Next Generation, it was decided that these would no longer be featured. A new warp scale was drawn up, with warp 10 set as an unattainable maximum. This is described in some technical manuals as Eugene's Limit, in homage to creator/producer Gene RoddenberryGene Roddenberry

Eugene Wesley Roddenberry was an American scriptwriter and producer....
. (The old and new formulas are explained in much greater detail below)

The warp factors above warp 10 in the , such as the one above, were slower than warp 10 on the new scale. According to The Star Trek EncyclopediaThe Star Trek Encyclopedia

...
, warp 6 (new scale) is equal to 392c (392 times the speed of light, c) and about warp 7.3 on the old scale, whereas warp 9.2 new, to about 1649c and warp 11.8 on the old scale. Under this new definition warp 9.2 translates to 307,179,672.653 miles/sec. Travel to Proxima Centuri from Earth would only take 22.53 hours.

The scale reaches an asymptoteAsymptote

An asymptote is a straight line or curve A to which another curve B approaches closer and closer as one moves along...
 at warp 10 which represents infinite speed in accordance with the speed limit imposed by the producers. The episode "ThresholdThreshold (Voyager episode)

Threshold is the 26th episode of ', the 15th episode in the second season....
" agreed with this, in that the characters said attaining the velocity of warp 10 was impossible — but then they achieved it anyway, with the side effect that they hyper-evolvedEvolution Overview

In biology, evolution is the change in the heritable traits of a population over successive generations, as determined by sh...
 (reversibly) into anthropomorphicAnthropomorphism

Anthropomorphism is the attribution of human characteristics and qualities to non-human beings, objects, natural, or superna...
 newtNewt

Newts are small, usually bright-coloured semiaquatic salamanders of North America, Europe and North Asia, distinguished from...
s. In this episode, Tom ParisTom Paris

Thomas Eugene Paris is a regular character in the TV show Star Trek: Voyager....
 describes that, while travelling at warp 10, he is concurrently in every part of the universe. At this speed, the Shuttlecraft CochraneShuttlecraft Cochrane

Shuttlecraft of the USS Voyager. Used by Tom Paris to break the warp 10 barrier in the Voyager episode, Threshold....
's sensors are able to process enormous amounts of telemetry such that the data storage of the shuttle is completely filled.

The limit of 10 did not entirely stop warp inflation. By the mid-24th century, the Enterprise-D could travel at warp 9.8 at "extreme risk", while normal maximum operating speed was warp 9.6 and maximum rated cruise was warp 9.2. The Intrepid-class starship Voyager has a maximum sustainable cruising speed of warp 9.975.

The alternate future depicted in the Next Generation episode "All Good Things..." shows Federation vessels capable of going warp 13 when Admiral Riker, commanding the future Enterprise-D, uses this extra turn of speed to rescue the crew of the USS Pasteur. However, this episode was produced before the Enterprise-D was destroyed in Star Trek Generations, so the two universes may diverge further than previously expected, and warp 13 may not be possible in the "real" Star Trek universe. It is unclear whether the warp 13 achieved in the possible future shown in "All Good Things..." represents a new recalibration of the warp curve, an alternate future that never adopted the "new" Warp 10 scale, or some form of transwarp. This particular future was a creation of QQ (Star Trek)

In the fictional Star Trek universe, the most notable member of the Q Continuum is played by John de Lancie, a mischievous Q'...
 and, given the destruction of the Enterprise-D in Star Trek Generations, can no longer occur in the "real" Star TrekStar Trek

Star Trek is an American science-fiction franchise spanning six television series, ten feature films, hundreds of novels, co...
 timeline.

Transwarp

The term transwarp has been used a number of times, referring to an advanced form of warp drive most commonly used by the BorgBorg (Star Trek)

The Borg or Borg Collective are a race of cyborgs in the Star Trek fictional universe....
, but also the subject of a StarfleetStarfleet

In the fictional universe of Star Trek, Starfleet is the paramilitary defense, research, diplomacy, and exploration forc...
 development project in .

Episodes of TNG and Voyager seem to indicate that transwarp is best described as a wormholeWormhole

In physics, a wormhole is a hypothetical topological feature of spacetime that is essentially a "shortcut" or "abbreviation...
-style conduit through subspaceSubspace (Star Trek)

Subspace is a term used in many different science fiction media to explain many different concepts....
: this suggests a subsuming into subspace, rather than warping normal space via subspace.

However, in the Voyager episode "Distant OriginDistant Origin

"Distant Origin" is an episode of Star Trek: Voyager, the 23rd episode of the third season. ...
", a species known as the Voth used a transwarp technology that didn't appear to be similar to Borg transwarp, but rather an enhanced warp technology.
Federation experiments
The USS Excelsior (NX-2000) under command of Captain Styles was a Federation test-ship for transwarp technology. Though not explained on-screen in , it is assumed that transwarp was a faster version of the conventional warp drive. Excelsiors first operational test failed due to sabotage by Captain Scott of the Enterprise, thus preventing Excelsior from pursuing them.

The actual command bridge readouts of
Enterprise-AUSS Enterprise (NCC-1701-A)

The USS Enterprise, commissioned in 2286, is a Constitution class starship in the Star Trek fictional universe....
 at the end of
illustrated in the spin-off reference work, Mr. Scott's Guide to the EnterpriseMr. Scott's Guide to the Enterprise

Mr. Scott's Guide to the Enterprise, written and illustrated by Shane Johnson and published by Pocket Books, is a book ...
published in 1987, suggests the project ultimately succeeded and the USS Enterprise was indeed fitted with transwarp.

Susan SackettSusan Sackett

Susan Sackett was born in New York City, raised in Connecticut and moved to Florida after graduating from Hillhouse High Sch...
's memoirs attribute the lack of transwarp in
to Gene RoddenberryGene Roddenberry

Eugene Wesley Roddenberry was an American scriptwriter and producer....
's dislike of the concept.
Borg conduits
The BorgBorg (Star Trek)

The Borg or Borg Collective are a race of cyborgs in the Star Trek fictional universe....
 (in the
The Next Generation two-part episode "DescentDescent (TNG episode)

Descent is a two-part episode from the sixth/seventh season of the television series '....
" and in the
Voyager finale EndgameEndgame (Voyager episode)

Endgame is the title of the series finale of the Star Trek spinoff series, '....
) have discovered the existence of transwarp conduits—regions in subspace that facilitate transwarp travel at up to 20 times faster than conventional warp drives. These episodes established that the Borg set up networks of these conduits between important areas in the galaxy. Borg transwarp conduits are activated by an encoded tachyonTachyon

A tachyon is any hypothetical particle that travels at superluminal velocity....
 pulse. When a Borg vessel enters a transwarp conduit, it is subject to extreme gravimetric shear. To compensate, the Borg project a structural integrity field ahead of the vessel. Artificial conduits are linked together with transwarp hubs. Six hubs were known to exist, but in "'EndgameEndgame (Voyager episode)

Endgame is the title of the series finale of the Star Trek spinoff series, '....
" one was destroyed, along with the UnicomplexUnicomplex

The Unicomplex is a location in the fictional Star Trek universe....
 due to the neurolytic pathogenPathogen Summary

A pathogen or infectious agent is a biological agent that causes disease or illness to its host....
 with which Admiral Janeway infected herself.
Quantum slipstream
See Slipstream (science fiction)Slipstream (science fiction)

"Slipstream" is a science fiction term for a fictional method of faster-than-light space travel, similar to hyperspace trave...


Quantum Slipstream Technology is presumed to be the standard interstellar propulsion method used by Species 116 (of which ArturisArturis

Arturis is a fictional character from the Star Trek universe, portrayed by Ray Wise....
 was a member) prior to their assimilation by the Borg. In the episode "Hope and FearHope and Fear (Voyager episode)

"Hope and Fear" is a fourth season episode of '....
", Seven of NineSeven of Nine

Seven of Nine, Tertiary Adjunct of Unimatrix Zero-One, or Seven of Nine, is a fictional character from the Star Trek...
 remarks that the technology involved is not dissimilar to Borg transwarp technology.

Warp velocities

Warp travel velocity in Star Trek is generally described in "warp factor" units, which - according to the Star Trek Technical Manuals - correspond to the strength of the warp field. Achieving warp factor 1 is equivalent to breaking the light-speed barrier, while the actual speed of higher factors is determined according to an ambiguous "warp formula". Several episodes of the original series placed the Enterprise in peril by having it travel at high warp factors; in "That Which Survives", this factor was as high as 14.1. However, the actual speed of any given warp factor is rarely explicitly stated on screen, and travel times for specific interstellar distances are not consistent through the various series.

According to the Star Trek episode writer's guide for The Original Series, warp factors are supposedly converted to multiples of light speed with the cubic functionCubic function

In mathematics, a cubic function is a function of the form...
 . Accordingly, "warp 1" is equivalent to the speed of light, "warp 2" is eight times the speed of light, "warp 3" is 27 times the speed of light, and so on. However, this conflicts with the on-screen application of the technology, as it would make the Enterprise far too slow for the voyages depicted in the television series. These speeds do not even correlate with details presented in some of the episodes. For example, in "That Which Survives" (1969), the Enterprise travels at warp 8.4 for 11.33 hours and traverses 990.7 light years (as indicated in SpockSpock

Spock, or Mr. Spock, is a main character from the Original Star Trek TV series....
's dialog), which makes the speed more than 600,000 times the speed of light. The Enterprise has also easily traveled to and from the edge of the Milky Way galaxy ("Is There in Truth No BeautyIs There in Truth No Beauty? (TOS episode)

"Is There in Truth No Beauty?" is a third season episode of ', first broadcast October 18, 1968....
" and "By Any Other Name" (1968)), a journey which should take years at "warp 8" if the actual speed is merely a cube of the warp factor.

For and the subsequent series, Star Trek artist Michael OkudaMichael Okuda

Michael Okuda is an graphic designer who is best known for his work on Star Trek....
 devised a formula based on the original one but with important differences. For warp 1–9, if w is the warp factor, ' is the speed in kmKilometre

A kilometre is a unit of length that is equal to 1,000 metres, the current International System of Units base unit of leng...
 per secondFacts About Second

The second is the name of a unit of time, and today refers to the International System of Units base unit of time....
, and c is the speed of lightSpeed of light

The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin w...
, then . In the half-open interval from warp 9 to warp 10, the exponent of w increases toward infinity. Thus, in the Okuda scale, warp speeds approach warp 10 asymptoticallyAsymptote

An asymptote is a straight line or curve A to which another curve B approaches closer and closer as one moves along...
. There is no exact formula for this interval because the quoted speeds are based on a hand-drawn curve.

Warp speeds tend to warp 10 asymptotically, and at speeds greater than warp 9 the form of the warp function changes because of an increase in the exponent of the warp factor, . Due to the resultant increase in the derivativeDerivative Summary

In mathematics, the derivative is defined as the instantaneous rate of change of a function....
, a small change in the warp factor corresponds to a large increase in speed.

The later series were better at keeping to calculated velocities than the original; however, they were still far from perfect. Later episodes of (such as "DescentDescent (TNG episode) Overview

Descent is a two-part episode from the sixth/seventh season of the television series '....
" (1993)) contradicted these speeds and depicted FederationUnited Federation of Planets Summary

The United Federation of Planets widely referred to and known as the Federation is part of the Star Trek fictional u...
 Starfleet strategic operations (fleet movements) which would have been impossible under the Okuda scale. , though its premise was generally based on the Okuda scale, had several notable instances, such as in the episode "ParallaxParallax (Voyager episode)

Parallax is the third episode of '....
" or "The '37sThe 37s (Voyager episode)

The '37s is the 17th episode of ', the first episode of the second season...
" (1995), where the stated warp velocities varied wildly from the Okuda standard.

In general, the farther away a Star Trek show is in production date from the publish date of the Star Trek Technical Manual, the more likely a ship would be to travel at the "speed of plot". For example, in the pilot episode they give a time and speed to Neptune that accords with the original series' formula, but then they estimate a trip to the KlingonKlingon

Klingons are a warrior race of humanoids in the fictional Star Trek universe....
 Homeworld of Qo'noSQo'noS

In the fictional Star Trek universe, Qo'noS is the Klingon homeworld, also known as Kronos, Kling or Klin...
 at warp 5 as a four-day journey, placing it just one light-yearLight-year

A light-year or lightyear, symbol ly, is the distance light travels in vacuum in one Julian year....
 away from EarthEarth

Earth is the third planet in the solar system in terms of distance from the Sun, and the fifth largest....
 — far closer than the nearest stellar system, Alpha CentauriAlpha Centauri

Alpha Centauri is the brightest star in the southern constellation of Centaurus....
.

Warp theory and technology

For a more in-depth discussion of warp propulsion systems, refer to the by Rick SternbachRick Sternbach

Richard Michael Sternbach is an illustrator who is best known for his space illustrations and his work on the Star Trek tele...
 and Michael OkudaMichael Okuda

Michael Okuda is an graphic designer who is best known for his work on Star Trek....
. Chapter 5, "Warp Propulsion Systems", discusses the following topics:

  • Warp field theory and application, including warp measurement, velocities, and limits.
  • MatterMatter

    In physics, matter is commonly defined as the substance of which physical objects are composed, not counting the contributio...
    -antimatterAntimatter

    In particle physics, antimatter extends the concept of the antiparticle to matter, wherin if a particle and its antiparticle...
     reaction assembly, including reactant injectors, magnetic constriction segments, reaction chamber, the role of dilithiumDilithium (Star Trek)

    In the Star Trek universe, dilithium is a fictional chemical element, although the name also applies to a real-world molecul...
    , and power transfer conduits.
  • Warp field nacelles, including plasmaPlasma (physics)

    In physics and chemistry, a plasma is typically an ionized gas, and is usually considered to be a distinct phase of ma...
     injection system, warp field coils, and warp propulsive effect.
  • AntimatterAntimatter

    In particle physics, antimatter extends the concept of the antiparticle to matter, wherin if a particle and its antiparticle...
     storage and transfer, warp propulsion system fuel supply, Bussard ramjetBussard ramjet

    The Bussard ramjet method of spacecraft propulsion was proposed in 1960 by the physicist Robert W....
     fuel replenishment, and onboard antimatter generation
  • EngineeringEngineering

    Engineering is the application of scientific and mathematical principles to develop economical solutions to technical proble...
     operations and safety, emergency shutdown procedures, and catastrophic emergency procedures


However, the shows often contradicted both the TNG and DS9 technical manuals.
Slingshot effect
A side effect of Warp travel which has been shown throughout Star Trek is the "Slingshot EffectGravitational slingshot

In orbital mechanics and aerospace engineering, a gravitational slingshot is the use of the gravity of a planet to alter the...
." First discovered by accident in "Tomorrow Is YesterdayTomorrow Is Yesterday (TOS episode)

"Tomorrow Is Yesterday" is a first season episode of '....
" (1967), one of the earlier episodes of the original Star Trek series, it is a method of using a warp drive to travel through timeTime travel

Time travel is the concept of moving backward or forward to different points in time, in a manner analogous to moving throug...
. Whereas the actual procedure is intentionally obscure, it involved travelling at high warp speed toward a star (established in (1986) to be somewhere over Warp 9.8), on a precisely calculated "slingshot" path, and if successful it can allow for travel to the future or past. The same technique was used later in the episode "" (1968) intentionally for historic research (where it is given the technical name "light speed breakaway factor"), and again in Star Trek IV (where it was called "time warp"). The technique was mentioned as a viable method of time travel in the Next Generation episode "Time SquaredTime Squared (TNG episode)

"Time Squared" is the 39th episode of the television series Star Trek: The Next Generation....
" (1989).

This 'slingshot' effect has been introduced into real-world theoretical physics, as well: in theory, it is possible (though not practical or at all safe) to slingshot oneself 'around' the event horizon of a black hole. The result of such a maneuver would cause time to pass at a faster rate, relative to the ship within the event horizon. Such a journey would, unfortunately, be a 'one-way' trip -- the pilot of the craft would not have 'travelled through time' in the classical sense, but would instead merely 'skip over' the intervening years.

In the books

Some years after Star Trek: The Original Series (TOS), Pocket BooksPocket Books

Pocket Books is a division of Simon & Schuster which primarily publishes paperback books....
 came out with a series of books based upon the Enterprises encounters during both its first and second five year mission. In "The Wounded SkyThe Wounded Sky

The Wounded Sky is a 1983 Star Trek novel by Diane Duane, featuring James T....
" written by Diane DuaneDiane Duane

Diane Duane is an American science fiction and fantasy author....
, the crew picks up a Hamalki engineer, which invents a new form of the Transwarp Drive. Even though such books are not considered canon, the theories proposed in the book lend to the idea of Warp and Transwarp, and further explain the properties of subspaceSubspace

Subspace may refer to:* Linear subspace or vector subspace, in linear algebra and related fields of mathematics...
. According to the book, Warp Drive does indeed create a bubble around the ship; however, it is explained that the ship is surrounded by a bubble of subspace--another universe where the speed of light is much faster than in ours. This lends to the theory that one cannot attain the speed of light, but it can be circumvented via alternate universes. The book further explains that the alternate universe is attuned with our own, such that planetary bodies are in exactly the same place, which makes navigation much simpler.
The Transwarp Device invented by the Hamalki uses a different approach to the same idea. The Transwarp Drive in this case creates a field around the ship which allows it to enter De Sitter spaceDe Sitter space

In mathematics and physics, n-dimensional de Sitter space, denoted , is the maximally symmetric, simply-connected, Loren...
--a space in which there is infinite energy, zero mass (with exceptions) and no absolute laws of physics or time. This essentially allows the Enterprise to enter De Sitter space and travel millions of times faster than light. In the book, the Enterprise manages to reach the Lesser Magellanic Cloud (385 years away at warp 8), a dwarf galaxy in orbit around the Milky Way Galaxy.

Warp core

The primary form of propulsion in the Star TrekStar Trek

Star Trek is an American science-fiction franchise spanning six television series, ten feature films, hundreds of novels, co...
 universe is the "gravimetric field displacement manifold", more commonly referred to as a "warp core". It is a fictional power plantReactor

Reactor may relate to the following:...
 based on a matterMatter

In physics, matter is commonly defined as the substance of which physical objects are composed, not counting the contributio...
-antimatterAntimatter

In particle physics, antimatter extends the concept of the antiparticle to matter, wherin if a particle and its antiparticle...
 reaction, providing sufficient energy to power a starship's warp drive and allow faster than lightFaster-than-light

Faster-than-light communications and travel refer to the propagation of information or matter faster than the speed of ligh...
 velocities. On starships, warp cores also serve as the source of energy for other primary systems.

In nature, when matter and antimatter come into contact, they annihilate each other and release large amounts of energy. In the Star Trek universe, fictional "dilithium crystals" are used to regulate this reaction. These crystals are described as being non-reactive to anti-matter when bombarded with high levels of radiation. The matter used in the reaction is usually deuteriumDeuterium

Deuterium, also called heavy hydrogen, is a stable isotope of hydrogen with a natural abundance in the oceans of plane...
, an isotopeIsotope

An isotope is any of several different forms of an element each having different atomic mass....
 of hydrogenHydrogen

|-| Triple point || 13.8033 K, 7.042 kPa...
, and the antimatter is usually antideuterium, the corresponding antimatter to deuterium. The reaction chamber is surrounded by a magnetic field to contain the anti-matter.

The energy released in the reaction process is used to create a field called a "warp bubble". This field distorts space around the vessel, while acting as a barrier between the distortions. The bubble is accelerated while the space inside the bubble does not technically move, so the vessel does not experience time dilation, and time passes inside the bubble at the same rate as time in the other parts of the galaxy. Within the warp field, the starship does not exceed the local speed of light, and therefore does not violate the principal tenet of special relativitySpecial relativity

The special theory of relativity was proposed in 1905 by Albert Einstein in his article "On the Electrodynamics of Moving Bo...
.

Is a nonfictional warp drive possible?

Many of the futuristic technologies featured in the series have actually been created (such as the hyposprayHypospray

The hypospray is a fictionalized version of a jet injector, in the Star Trek universe....
) or are currently being researched (e.g., the VISORVISOR

In the Star Trek fictional universe, a VISOR is a device used by the blind to artificially provide them with a sense of ...
). In 1996, NASANASA

The National Aeronautics and Space Administration is an agency of the United States Government, responsible for the nation'...
 established the Breakthrough Propulsion Physics ProgramBreakthrough Propulsion Physics Program

The Breakthrough Propulsion Physics Program is a research program which was funded from 1996 through 2002 by NASA, in the ho...
, which sponsored some speculative work on warp drives. This program was discontinued in 2002.

While thought experimentThought experiment

A thought experiment in the broadest sense is the use of an imagined scenario to help us understand the way things really a...
s on the wilder shores of theoretical physics continue, no scheme that may allow "warp speed" travel has yet been devised that has been accepted by mainstream science. Some physicists have proposed a model of FTL travel, formulated in the context of Lorentzian manifolds, which are used in general relativityGeneral relativity Summary

General relativity is the geometrical theory of gravitation published by Albert Einstein in 1915....
 to construct spacetimeSpacetime

In physics, spacetime is a mathematical model that combines three-dimensional space and one-dimensional time into a single c...
 models. However, contrary to a common misunderstanding, these models are in no sense solutions to the Einstein field equation, and they give absolutely no hint of how to actually make a warp bubble. These models do however show that while it is indeed impossible to go faster than the speed of light, in principle it might be possible to circumvent the problem by suitably "warping" spacetime itself. The best known theory, known as the Alcubierre driveAlcubierre drive

The Alcubierre metric, also known as the Alcubierre drive or Warp Drive, is a speculative mathematical model of ...
, has the amusing feature that its terminology is in accord with Trek jargon: "warp factors" measure the warping of space (or rather spacetime), not actual speed.

The following formula (Einstein Field Equation), based on general relativityGeneral relativity

General relativity is the geometrical theory of gravitation published by Albert Einstein in 1915....
, theoretically permits the travel of an object faster than light provided that spacetime is curved:

is the Einstein curvature tensorEinstein tensor Overview

The Einstein tensor expresses spacetime curvature in the Einstein field equations for gravitation in the theory of general r...
, which describes the curvature in space, while the constant G without indices is Newton's gravitational constantGravitational constant

According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their mas...
.

If spacetime is warped properly, then technically the object(s) are not moving faster than light, even though they appear in normal space to be moving faster than light.

In 2007, physicist Richard Obousy proposed that a warp drive could be created by directly manipulating the extra dimensions of string theory. His idea suggests the expansion of spacetime is a consequence of the vacuum ground-state of higher dimensional graviton fluctuations. In this model the vacuum energy equations can be expressed as:

In this model, it is the radius of the extra dimensions that directly controls the expansion of space. Obousy suggests that it is superstrings that wrap around the extra dimensions keeping them compact, but that a sufficiently advanced civilization might influence a string and locally adjust the size of the extra dimension creating a controlled expansion and contraction of the space surrounding an interstellar craft.

See also

  • Alcubierre driveAlcubierre drive

    The Alcubierre metric, also known as the Alcubierre drive or Warp Drive, is a speculative mathematical model of ...
  • Bussard collectorBussard ramjet

    The Bussard ramjet method of spacecraft propulsion was proposed in 1960 by the physicist Robert W....
  • Faster-than-lightFaster-than-light

    Faster-than-light communications and travel refer to the propagation of information or matter faster than the speed of ligh...
  • Timeline of black hole physicsTimeline of black hole physics

    Timeline of black hole physics* 1640 - Ismael Bullialdus suggests an inverse-square gravitational force law...
  • Timeline of gravitational physics and relativityTimeline of gravitational physics and relativity

    Timeline of gravitational physics and general relativity...
  • Delta VegaDelta Vega

    Delta Vega is a fictional planet featured in the Star Trek universe created by Gene Roddenberry....
  • Gravitational interaction of antimatterGravitational interaction of antimatter

    The gravitational interaction of antimatter with matter or antimatter has not been conclusively observed by physicists....
  • Warp core breach
  • E=MC˛E=mc˛

    In physics E = mc2 is an important and well-known equation, which states an equivalence between energy and relativistic ...
  • Exotic matterExotic matter

    Exotic matter is a hypothetical concept of particle physics....


External links

  • What would things look like at near-warp speeds?



Here is a small selection of speculative articles from the physics literature:
  • , by Miguel Alcubierre
  • by Chad Clark, William A. Hiscock, and Shane L. Larson
  • , by Michael J. Pfenning and L. H. Ford
  • , by Allen E. Everett and Thomas A. Roman
  • by Michael John Pfenning and L. H. Ford
  • , by Chris Van Den Broeck
  • by Jose Notario,
  • by Francisco S. N. Lobo and Matt Visser



10.pdf", "Problems with Warp Drive Examined")