Warp drive

In the fictional universe of Star Trek, the warp drive is a form of faster-than-light propulsion. It is however a very serious research topic in factual science.

Contents

1 Fictional history 2 Warp velocities 3 Warp theory and technology 4 Warp and the environment 5 Could there be an actual warp drive? 6 See also 7 External links 7.1 Websites 7.2 Documents

Fictional history

On Earth it was invented by Zefram Cochrane, in 2063, as depicted in Star Trek: First Contact (though information from The Original Series indicates warp drive was first used in 2018). According to the latest Star Trek series, Enterprise, 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.

In the Star Trek pilot episode "The Cage", warp was mentioned with the term "time warp". The episode revealed that the "time barrier" had recently been broken, but since this was given as news to a group of shipwrecked interstellar travelers, it could not refer to the breaking of the light barrier, as has been suggested. (It is worth noting that the pilot episode featured a number of things inconsistent with the rest of the series.)

The step to featuring actual time travel happened later in the show. The rapid advancement of the show caused the step not to be left too high - only a jump right to the fourth movie, The Voyage Home, is needed. Later, in the movie First Contact, the Enterprise does the time warp again, in pursuit of the Borg.

The speed of warp travel is usually given only in warp factors. It is generally assumed that warp 1 is the speed of light, and that at higher factors speed increases exponentially. Several episodes of the original series placed the Enterprise in peril by having it go at absurdly high warp factors, once as high as warp 14.6 ("That Which Survives").

Realising that this was a problem and wanting to remove this plot element, the creators of Star Trek: The Next Generation decided that warp 10 should be the maximum. Backstage treknobabble suggests that the warp scale was recalibrated, with the new warp 5 being the old warp 6, and warp 10 being infinite speed and unattainable. The producers indicated that vessels could only reach warp 9.x with an infinite number of 9s. This was done to give entities such as Q and The Traveler a loophole to travel at very fast speeds. For example, it had been estimated that the Traveler had been propelling the Enterprise at warp 9.999996. The Voyager episode "Threshold" agreed with this, in that the characters said it was impossible—but then they achieved it anyway, with the side effect that they hyper-evolved (reversibly) into anthropomorphic newts (although many fans, production staff, and even the writer and producer of the episode Brannon Braga generally ignore the events of that episode).

The term "transwarp" has been used a number of times, referring an advanced form of warp drive most commonly used by the Borg, but also the subject of an unsuccessful Starfleet development project in Star Trek III: The Search for Spock. Just as the generation of a warp field around a starship is required to enter warp speed without using infinite amounts of energy, thereby breaking the light barrier (a theoretically impossible event in our universe), so a transwarp field is required to reach very high FTL speeds (making a ship capable of crossing galactic distances in a very short time). At least the Borg (in the Star Trek: The Next Generation two-part episode "Descent" and in the Star Trek: Voyager final episode "Endgame") have discovered anomalies called "transwarp conduits"—regions in subspace that facilitate transwarp travel. Artificial conduits are linked together with transwarp hubs. Six hubs were known to exist, but one was destroyed in the Voyager episode "Endgame".

Warp velocities

In the Original Series, according to Gene Roddenberry and his Trek episode writer's guide, warp factors were supposedly converted to multiples of light speed with the cubic function <math>s(w) = w^3c<math>. With that being said, that means the table for the Original Series warp speed is as follows:

Warp Factor	c	Velocity (all figures approximate)
Warp 1	1c	3.0x105 km/s
Warp 1.5	3.375c	1.0x106 km/s
Warp 2	8c	2.4x106 km/s
Warp 3	27c	8.0x106 km/s
Warp 4	64c	1.9x107 km/s
Warp 5	125c	3.7x107 km/s
Warp 6	216c	6.5x107 km/s
Warp 7	343c	1.0x108 km/s
Warp 8	512c	1.5x108 km/s
Warp 9	729c	2.2x108 km/s
Warp 9.25	~791c	2.4x108 km/s
Warp 9.5	~857c	2.6x108 km/s
Warp 9.75	~926c	2.8x108 km/s
Warp 10	1,000c	3.0x108 km/s
Warp 11	1,331c	4.0x108 km/s
Warp 14.6	~3,112c	9.3x108 km/s
Warp 15	3,375c	1.0x109 km/s

However, this cannot possibly be the whole story, as it would make the Enterprise far too slow for the voyages depicted in the television series. These speeds do not even correlate with solid facts and figures in some of the episodes, for example in That Which Survives the Enterprise travels at Warp 8.4 for 11.33 hours and traverses 990.7 light years (as indicated in Spock's dialogue), which makes the speed more than 600,000 times the speed of light, which is an order of magnitude larger than even Warp 15. There is also the fact that the Enterprise could quite easily travel to and from the edge of the galaxy at will (Is There in Truth No Beauty and By Any Other Name), a journey which should take years at the typical Warp 8, if Warp 8 is merely a cube of the warp factor.

This discrepancy between the behavior of warp speeds in the show and the simple formula of the warp factor cubed was picked up by fans in the 1970's and 80's who published books like Star Trek Maps (all published material is considered non-canon, even if it is by Paramount-approved Pocket Books) where the idea of an additional factor, referred to as the Chi factor or the Cochrane factor, was used in the warp calculations. The idea was that since warp drive pulls in space, you get higher speeds in areas where there is high density of mass, and lower speeds in areas of low density. If we take a warp factor and cube it, we take that product and multiply it by the number 1292.7238 (the Chi or Cochrane factor), to get the actual speed that the ship travels at (this is the number that was factored out of the factoids from That Which Survives). The Cochrane factor represents an "average" density of space in the UFP. Other areas of space will have different values for it. This is one way to explain the relationship bewteen stated warp factors and actual calculable speeds as given in the dialogue in the episodes. Although it is not actually canon, it at least explains how the ships behaved as they did, without having to find higher exponents to factor the warp base numbers by, as Star Trek artist Michael Okuda did later for TNG (which nobody on the show ended up paying attention to anyways).

For the later series, Okuda devised a formula based on the older one but with important differences. For warp 1–9, if w is the warp factor, s is the speed in km per second, and c is the speed of light, then <math>s(w) = w^{10 \over 3}c<math>. 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.

Here is a table with new-style warp factors and their approximate values in kilometers per second and multiples of c:

Warp Factor	c	Velocity
Warp 1	1c	3.0x105 km/s
Warp 2	10.079c	3.0x106 km/s
Warp 3	38.941c	1.2x107 km/s
Warp 4	101.59c	3.0x107 km/s
Warp 5	213.75c	6.4x107 km/s
Warp 6	392.50c	1.2x108 km/s
Warp 7	656.13c	2.0x108 km/s
Warp 8	1,024c	3.1x108 km/s
Warp 9	1,516.4c	4.5x108 km/s
Warp 9.2	1,649c	4.9x108 km/s
Warp 9.6	1,909c	5.7x108 km/s
Warp 9.9	3,053c	9.2x108 km/s
Warp 9.9753	6,000c	1.8x109 km/s
Warp 9.99	7,912c	2.3x109 km/s
Warp 9.9999	199,516c	6.0x1010 km/s

Here is a table of the times it would take to cover a number of distances. Since Warp 1 is c, the distances for warp 1 (in years) is the light year distance. Earth's solar system is approximately 1.2x10¹⁰ km wide.

Warp	Across Sol System	To Alpha Centauri	Across Sector	Across Federation	Across Galaxy	To Andromeda Galaxy
Warp 1	11 hours	4.36 years	20 years	1,000 years	100,000 years	2,000,000 years
Warp 2	1 hour	6 months	1 year	100 years	10,000 years	200,000 years
Warp 3	17 minutes	6 weeks	6 months	25 years	2,564 years	51,000 years
Warp 4	6.5 minutes	18 days	2 months	10 years	990 years	19,800 years
Warp 5	3 minutes	8.4 days	34 days	4.6 years	467 years	9,345 years
Warp 6	1.7 minutes	4.6 days	18.6 days	2.5 years	255 years	5,102 years
Warp 7	1 minute	2.8 days	11.3 days	1.52 years	152 years	3,048 years
Warp 8	38 seconds	1.7 days	7.1 days	1 year	100 years	1,953 years
Warp 9	26 seconds	1.2 days	4.8 days	8 months	66 years	1,319 years
Warp 9.2	24 seconds	1.1 days	4.4 days	7 months	61 years	1,217 years
Warp 9.6	20.7 seconds	23 hours	3.8 days	6 months	53 years	1,051 years
Warp 9.9	13 seconds	14 hours	2.4 days	3.8 months	33.3 years	660 years
Warp 9.9752	6.6 seconds	7.1 hours	1.2 days	1.9 months	16.9 years	335 years
Warp 9.99	5 seconds	5.4 hours	22 hours	1.4 months	12.8 years	254 years
Warp 9.9999	.2 seconds	12.8 minutes	52 minutes	1.6 days	6 months	10 years

The later series were better at keeping to these speeds than the original, however they were still far from perfect. Later episodes of Star Trek: The Next Generation contradicted these speeds (such as "Descent") 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 37's," 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 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. This plot hole has later been wrapped up by various sources that suggest that there is a spatial rift that allowed the Enterprise to arrive at the Klingon homeworld in such a short length of time, and that it was the Vulcans who provided Enterprise with the whereabouts of this shortcut. It should be noted, however that such a high speed for Warp Five is consistent with the extremely high speed given for Warp 8.4 in That Which Survives, which has the speed at over 600,000 times lightspeed (therefore Warp 5 would be 161,500 times lightspeed). In those terms, four days travel at Warp Five places the Klingon homeworld at 1,772 light years (or 536 parsecs) away from Earth.

Warp theory and technology

For a more in-depth discussion of warp propulsion systems, refer to the 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 tech manuals.

Warp and the environment

In the Season 7 Next Generation episode "Force of Nature", it was revealed that warp drive is bad for the environment, and in some areas it could lead to the fissuring of space. Travel faster than warp 5 is banned, but there is argument among fans as to whether the ban exists only in the affected areas of space, or in all areas. If it is a universal limit, it is widely ignored and not even mentioned in later episodes and series. Some fans have speculated that a technological solution was found, possibly involving the moving warp engines on the USS Voyager. However, if it is not universal, and only applies to affected regions of space, then Captains Picard and Janeway are not in violation of code (and the definition of the ban as a "plot tool" could be redefined). Additionally, the ban on travel in excess of warp 5 has a stipulation that such travel is in fact allowed in cases of emergency. One could easily argue that, after the ban, all the cases in which Picard traveled in excess of warp 5 would be due to an emergency. There is even a case, in a later episode, of Picard ordering faster than warp 5 travel and someone reminding him of the ban. And it could certainly be considered that the Voyager's stranded status in the Delta Quadrant qualifies as a form of emergency, since being that far from the relative security of the Federation is a survival risk.

Addendum: Voyager was designed (according to the startrek.com library) to go faster than warp 5 without causing damage such as fissuring of space.

Could there be an actual warp drive?

As many Star Trek fans know, many of the futuristic technologies featured on Star Trek have actually been created (such as the hypospray) or are currently being researched (e.g., the VISOR). The warp drive is no exception. NASA is researching interstellar travel and has a website called Space Transportation and the section "Advanced Space Transportation Program" [1] (http://www.highway2space.com/ast/astp.html) states "The ASTP is also conducting fundamental research on the cutting edge of modern science and engineering, including fission, fusion and antimatter propulsion, and breakthrough physics theories that might enable thrusting against space-time itself and faster-than-light travel."

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 method for FTL travel, based on Einstein's theory of general relativity. They recognize that it is impossible to go faster than the speed of light. However, given enough energy it is possible to change the shape of space, i.e., to warp it. In which case, a starship using this system would need only travel a few kilometers per hour. This theory, known as the Alcubierre drive, has the convenient feature that its terminology is in accord with Trek jargon: "warp factors" measure the warping of space, not actual speed.

See also

• Alcubierre drive
• Faster-than-light
• Timeline of black hole physics
• Timeline of gravitational physics and relativity

External links

Websites

• NASA's Marshall Space Flight Center's Space Transportation website (http://www.highway2space.com)
• Template:Memoryalpha
• Warp Drive Without Exotic Energy (http://arxiv.org/html/gr-qc/9903068)

Documents

The following documents require the free Adobe Acrobat Reader. Download here (http://www.adobe.com/products/acrobat/readstep2.html).

• Article in rebuttal of Natario article (http://65.108.189.168/Docs/WAS%20DR%20NATARIO%20RIGHT.pdf)
• Shield Article (http://arxiv.org/PS_cache/gr-qc/pdf/0207/0207109.pdf)
• A Causally Connected Superluminal Warp Drive Spacetime (http://arxiv.org/PS_cache/gr-qc/pdf/0202/0202021.pdf)
• Reduced Energy Warp Drive (http://arxiv.org/PS_cache/gr-qc/pdf/0107/0107097.pdf)
• EMG Warp Drive article (http://65.108.189.168/Docs/EGMwarpdrive.pdf)
• Exotic Energy & Propulsion within Maxwell Equations (http://65.108.189.168/Docs/Exotic_Mater_and_Propulsion.pdf)
• The Gravity Drive Experiment (http://65.108.189.168/Docs/The%20Gravity%20Drive%20Experiment.pdf)
• A Review of the Unitel Project (http://65.108.189.168/Docs/A_Physical_Review_of_The_Unitel_Project.pdf)
• On Randall-Sundrum Brane Detuning and Hyperspace Drives (http://www.mathpreprints.com/math/Preprint/paultrr/20031222/1/On_RS_Model_detuning_of_brane_tension.pdf)
• A Warp Drive with a more reasonable total energy requirement (http://omnis.if.ufrj.br/~mbr/warp/etc/cqg16_3973.pdf)
• A Superluminal Subway: The Krasnikov Tube (http://omnis.if.ufrj.br/~mbr/warp/etc/PRD56_2100.pdf)
• Quantum Inequality Restrictions on Negative Energy Densities in Curved Spacetimes (http://arxiv.org/PS_cache/gr-qc/pdf/9805/9805037.pdf)
• The unphysical nature of "Warp Drive" (http://arxiv.org/PS_cache/gr-qc/pdf/9702/9702026.pdf)
• Fundamental Limitations on warp drive spacetimes (http://www.arxiv.org/PS_cache/gr-qc/pdf/0406/0406083.pdf)
• PROBLEMS WITH WARP DRIVE EXAMINED: Accepted for Publication in the Euro-Asian Journal of Applied Science (http://doc.cern.ch//archive/electronic/other/ext/ext-2004-110.pdf)de:Warpantrieb

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