warp speed

Warp drive

Warp drive is a form of faster-than-light propulsion in the fictional universe of Star Trek, capable of propelling spacecraft or objects to many multiples of the speed of light but avoiding the problems of time dilation. It is also featured in several science-fiction movies and games such as Stars!, StarCraft, Darkspace, the Starship Troopers universe, and Red Dwarf. Warp drive, called 'FTL' in many science fiction novels, isn't capable of instant travel between points at infinite speed, unlike the other fictional propulsion technologies hyper-, jump, and infinite improbability drives. Ships using warp drive differ from those using hyperdrive by traveling within a small created bubble of normal spacetime, rather than by entering a separate realm or dimension like hyperspace. Spacecraft at warp can interact with objects in normal space.

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.

Warp in Star Trek

Development of the backstory

Warp drive has been a feature of Star Trek since it started. The first pilot episode of Star Trek: The Original Series, "The Cage", calls it "time warp" drive, and notes that the "time barrier" had been broken, allowing a group of stranded interstellar travellers to get back to Earth much more quickly than they had been previously able to.

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.

Exact speeds were only given in the Voyager episode The 37's where Tom Paris describes Voyager's speed of Warp 9.9 (under the new warp table formula) as being about 4 billion miles a second.

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 Roddenberry. (The old and new formulas are explained in much greater detail below)

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.

Transwarp

The term transwarp has been used a number of times, referring to an advanced form of warp drive most commonly used by the Borg, but also the subject of a Starfleet development project in Star Trek III: The Search for Spock.

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.

However, in the Voyager episode "Distant Origin," 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 Star Trek III, it is assumed that transwarp was a faster version of the conventional warp drive. Excelsior's 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-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.

Susan Sackett's memoirs attribute the lack of transwarp in Star Trek: The Next Generation to Gene Roddenberry's dislike of the concept.

Borg conduits

The Borg (in the The Next Generation two-part episode "Descent" and in the Voyager finale Endgame) 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 tachyon 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 "'Endgame" one was destroyed, along with the Unicomplex due to the neurolytic pathogen with which Admiral Janeway infected herself.

Quantum slipstream

See Slipstream (science fiction)

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 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 function s(w) = w^3c. 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, s(w) is the speed in km per second, and c is the speed of light, then s(w) = w^{10 over 3}c. 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, w. 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.

Warp theory and technology

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:

  • Warp field theory and application, including warp measurement, velocities, and limits.
  • Matter-antimatter reaction assembly, including reactant injectors, magnetic constriction segments, reaction chamber, the role of dilithium, and power transfer conduits.
  • Warp field nacelles, including plasma injection system, warp field coils, and warp propulsive effect.
  • Antimatter storage and transfer, warp propulsion system fuel supply, Bussard ramjet fuel replenishment, and onboard antimatter generation
  • Engineering 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 Effect." First discovered by accident in "Tomorrow Is Yesterday" (1967), one of the earlier episodes of the original Star Trek series, it is a method of using a warp drive to travel through time. Whereas the actual procedure is intentionally obscure, it involved travelling at high warp speed toward a star (established in Star Trek IV: The Voyage Home (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 "Assignment: Earth" (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 Squared" (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 Books came out with a series of books based upon the Enterprise's encounters during both its first and second five year mission. In "The Wounded Sky" written by Diane Duane, 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 subspace. 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 space--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 Trek universe is the "gravimetric field displacement manifold," more commonly referred to as a "warp core." It is a fictional power plant based on a matter-antimatter reaction, providing sufficient energy to power a starship's warp drive and allow faster than light 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 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.

Is a nonfictional warp drive possible?

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:

G_{mu nu}=frac{8pi}{c^4} G T_{mu nu}

G_{mu nu} is the Einstein curvature tensor, which describes the curvature in space, while the constant G without indices is Newton's gravitational constant.

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:

=-frac{pi^2}{R^4} left[frac{(2+n)(3+n)}{2}-1 right] left[zeta(0) right] ^{n-1} zeta'(4)

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

Notes

  • When Stephen Hawking guest starred on the Star Trek: The Next Generation episode "Descent", he was taken on a guided tour of the set. Pausing in front of the warp core set piece, he remarked, "I'm working on that".

External links

Here is a small selection of speculative articles from the physics literature:

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