Although the idea of warping space as a means of propulsion has enjoyed theoretical study by physicists such as Miguel Alcubierre, who has speculatively designed his own drive, no actual technological approach has been proposed. Currently there is no way known in which either naturally or artificially there could exist a finite and bounded space-time region within which, the local effect of the laws of physics would present the view of a “normal” space-time; yet, concurrently external to the bounded space-time region (in the immediate area of the boundary), there would exist a “warped” space-time; in which the relative velocities’ (of the bounded space-time and any material thing within the bounded space, relative to say, the distant stars not near the boundry), could (by a natural or artificial process) exceed the speed of light.
The difficulty is in the concept of the boundary and exactly what is boundable, and bounded. The underlying premise (experimentally shown to be true) of all of physics since Galileo, is that the true “laws of physics” are “laws” because they are expressly unbounded, save by themselves. That is, the first principle of both Special Relativity and General Relativity. The principle states that the laws of physics in describing all phenomena, must operate with transcendence in respect to the relative motions of the bodies (and whatever phenomena they are practicing) in question.
That is, the motions of the moon about the earth conform to Kepler, Newton, and Einstein’s laws of physics; as does the motion of the planets around the sun; as do the motions of whole galaxies around galaxy clusters. In the same way the General Theory says that matter should be diverted into a curved path near a massive body. Yet since the Special Theory of Relativity says matter is equal to energy; light which is mass less energy, is curved in its path just like normal matter when it passes near a massive body. The laws of physics don’t care; they operate without regard to any boundaries, save their own.
Whatever are the effects of near and at light-speed velocity by ponderable bodies of matter (matter such as material space ships and their crews), will occur upon those bodies because the laws of nature will respect no boundaries, save their own. And where the laws themselves do set of boundaries (such as the speed of light for ponderable bodies of real matter), the laws of physics will operate upon those bodies through any boundary either natural or man-made, so as to conform the motion of those bodies the laws themselves.
The episode "Metamorphosis," from the original series, establishes a backstory for the invention of warp drive, stating that it was invented by Zefram Cochrane of Alpha Centauri. Cochrane is repeatedly referred to afterwards, but the exact details of the first warp trials were not shown until the second Star Trek: The Next Generation movie, Star Trek: First Contact. The movie depicts Cochrane as inventing warp drive on Earth in 2063 (two years after the date speculated by the first edition of the Star Trek Chronology). He used a fission reactor to heat plasma to send through the warp coils to make a warp bubble, which he could use to move the ship into subspace to go faster than the speed of light. This directly led to the first contact with the Vulcans.
The later prequel series Star Trek: Enterprise firmly establishes that many other civilizations had warp drive before humans, notably the Vulcans, who had more advanced warp drive technology than humans even in the 22nd century. Enterprise, set in 2151 onwards, shows the voyages of the first Earth ship capable of traveling at warp factor 5.2 which under the old warp table formula, is about 140 times the speed of light. Using that formula, the velocity is the warp factor cubed times the speed of light or 5.23 × 186,282.397 miles/sec or 5.23 c, which is 26,192,795.27 miles per second. This velocity would allow a Federation Starship traveling from Earth at a constant warp 5.2 to reach Proxima Centauri, Earth's closest extrasolar stellar body, at 4.25 light years (ly) (4.25 × 6 trillion miles) distance (Alpha Centauri, of the same trinary star system, is 4.36 ly away) in approximately 11.09 days. By the time of Captain Kirk's era in mid 23rd century, Warp factor 8 was within the capabilities of Starships (which was not exceeded often due to the strain placed on the engines). Warp 8 was 83 c (512 c) or about 95,376,587.264 miles/sec. This would allow travel from Earth to Proxima Centauri in only 3.03 days, approximately the same amount of time it took Apollo 11 to travel from the Earth to the Moon in July, 1969. By the time of the original Star Trek's third season, the ship's maximum speed had been increased slightly to Warp 9, although invaders on the ship (Nomad, the Kelvans etc.) had managed to increase engine efficiency drastically.
The warp factors above warp 10 in the TOS, such as the one above, were slower than warp 10 on the new scale. According to The 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 Centauri from Earth would only take 22.53 hours.
The scale reaches an asymptote at warp 10 which represents infinite speed in accordance with the speed limit imposed by the producers. The Star Trek: Voyager episode "Threshold" 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-evolved (reversibly) into anthropomorphic newts. In this episode, Tom Paris describes that, while travelling at warp 10, he is concurrently in every part of the universe. At this speed, the Shuttlecraft Cochrane'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 Q and, given the destruction of the Enterprise-D in Star Trek Generations, can no longer occur in the "real" Star Trek timeline.
Episodes of TNG and Voyager seem to indicate that transwarp is best described as a wormhole-style conduit through subspace: This suggests a subsuming into subspace, rather than warping normal space via subspace.
The actual command bridge readouts of Enterprise-A at the end of Star Trek IV: The Voyage Home illustrated in the spin-off reference work, Mr. Scott's Guide to the Enterprise published in 1987, suggests the project ultimately succeeded and the USS Enterprise was indeed fitted with transwarp.
Quantum Slipstream Technology is presumed to be the standard interstellar propulsion method used by Species 116 (of which Arturis was a member) prior to their assimilation by the Borg. In the Voyager episode "Hope and Fear", Seven of Nine remarks that the technology involved is not dissimilar to Borg transwarp technology.
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 function . 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 Spock'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 Beauty" 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 Star Trek: The Next Generation and the subsequent series, Star Trek artist Michael Okuda 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 km per second, and c is the speed of light, 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 asymptotically. 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 derivative, 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 Star Trek: The Next Generation (such as "Descent" (1993)) contradicted these speeds and Star Trek: Deep Space Nine depicted Federation Starfleet strategic operations (fleet movements) which would have been impossible under the Okuda scale. Star Trek: Voyager, though its premise was generally based on the Okuda scale, had several notable instances, such as in the episode "Parallax" or "The '37s" (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 Star Trek: Enterprise 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 Klingon Homeworld of Qo'noS at warp 5 as a four-day journey, placing it just one light-year away from Earth — far closer than the nearest stellar system, Alpha Centauri.
A more in-depth discussion of warp propulsion systemsis explained in the book Star Trek: The Next Generation Technical Manual by Rick Sternbach and Michael Okuda. Chapter 5, "Warp Propulsion Systems", discusses the following topics:
However, the shows often contradicted both the TNG and DS9 technical manuals.
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 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 deuterium, an isotope of hydrogen, 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 relativity.
Many of the futuristic technologies featured in the series have actually been created (such as the hypospray) or are currently being researched (e.g., the VISOR). In 1996, NASA established the Breakthrough Propulsion Physics Program, which sponsored some speculative work on warp drives. This program was discontinued in 2002.
While thought experiments 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 relativity to construct spacetime 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 drive, 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. In his book The Physics of Star Trek, Lauren Krauss states that while it is possible to permit superluminal travel via a warp drive, huge amounts of negative energy are required to make it work.
The following formula (Einstein Field Equation), based on general relativity, theoretically permits the travel of an object faster than light provided that spacetime is curved:
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.
Here is a small selection of speculative articles from the physics literature: