Curvature (Displacement)

The displacement by curvature, warp drive, thrust by curvature, or simply curvature (from English warp), also called warp drive or warp drive is a currently fictional form of superluminal propulsion born in the universe created by the fiction of Star Trek. This thrust would allow a spacecraft to be propelled at a speed equivalent to several multiples of the speed of light, while avoiding the problems associated with relativistic time dilation. This type of propulsion is based on curving or distorting space-time, in such a way that it allows the ship to approach the destination point.

Thrust by curvature does not allow, nor is it capable of generating, instantaneous travel between two points at infinite speed, as has been suggested in some works of science fiction, in which imaginary technologies such as hyperdrive are used or the jump engine, but it is capable of making a big difference between relativistic conventional speeds.

One difference between warp drive and using hyperspace is that in warp drive, the ship does not enter a different universe (or dimension): a small bubble (curvature bubble) in space-time, and space-time distortions are generated so that the bubble moves away from the point of origin and approaches to your destiny. The distortions generated would be expansion behind the bubble (moving it away from the origin) and contraction in front of the bubble (moving it closer to the destination). The curvature bubble would be located in one of the space-time distortions, on which it would ride in a similar way to how surfers do on an ocean wave.

The warp drive (warp drive) is famous for being the method of propulsion used in the fictional universe of Star Trek.

Feasibility of warp drive

Among the different theoretical physicists who have analyzed this propulsion, progress was made with the first theoretical design of the WARP system. The best known of these designs is the Alcubierre motor (The warp drive: hyper-fast travel within general relativity, about the Alcubierre warp drive, published in 1994) and which assumes one of the terms used in the jargon of Star Trek: the curvature factor as a measure of the curvature (deformation) of space-time and that, although it allows traveling at great speed, it does not allow traveling faster than light (according to relativistic rules it is impossible to). If space-time is curved properly, strictly speaking, the object or ship is not moving at light speeds, it is in fact stationary in the space inside the bubble of curvature. This stationary situation of the ship, inside the bubble, would mean that the crew would not be affected by large accelerations/decelerations nor would there be a different passage of time, that is, they would not suffer the effect of time dilation, as in the case of traveling at speeds close to the speed of light in space-time, it is as if you were in a completely different universe, so traveling like this would give interesting results. The ship, when its warp drive is activated, would appear to an outside observer to be moving faster than light and would disappear from their field of vision in a short time as the ship's space-time expanded relative to that observer.

Miguel Alcubierre refers to the need for foreign matter (also called exotic matter) for the speed of curvature. The existence of exotic matter is not theoretical and the Casimir effect leads to the assumption of the existence of such matter. However, the generation of exotic matter, and its support, for the development of a warp thrust (or to keep the throat of a wormhole open) is impractical. Some methods or theories associated with the creation/sustainment of exotic matter point to the fact that exotic matter should be moving, locally, at a speed greater than that of light (and to the existence of so-called tachyons). Other theories suggest that this movement can be avoided at a speed greater than that of light, but it would imply the generation of a naked singularity in front of the curvature bubble. Whether by one method or another, the creation/sustainment of exotic matter, in particular, and the use of curvature thrusts violate, a priori, different energy conditions in the field of quantum field theory. Alcubierre concluded that the generation of a bubble of curvature was unfeasible since, according to his initial calculations, it would need more energy for its creation (and the distortions of space-time) than that existing in the universe.

A subsequent analysis by Dr. Van Den Broeck (On the (im)possibility of warp bubles, published in 1999), from the Catholic University of Leuven (Belgium) resulted in an energy lower than that initially calculated by Alcubierre (reduced by a factor of 10 raised to 61). However, this does not indicate that the proposal is realistic, as indicated by Van Den Broeck, since he calculated the energy required to transport several atoms at just under the equivalent of three solar masses.

However, a 2008 study by Richard K. Obousy and Gerald Cleaver of Baylor University (Texas) studying the effects of multidimensional space-time (as predicted by theory of strings), reduces the energy required to move a 1000 m³ ship at superluminal speeds to only 10⁴⁵ J (the equivalent of the energy contained in the mass of Jupiter).

In this same study, a theoretical maximum speed for a curvature motor of 10³² c is estimated, although it would be a useless limit from a practical point of view, since to reach that arbitrarily high speed would require more energy than is available in the universe.

At the beginning of the 21st century, building a warp drive is far from a reality, due to so much to the existing technology as well as to the high energy necessary for its development. There also seem to be other theoretical impediments to superluminal travel with this technology, such as the quantum instability of the bubble or Hawking radiation. However, there are no theoretical arguments against sublight warp travel. In 2012 NASA scientists announced that they were working on the feasibility of warp travel, but on a small scale and in laboratories.

New studies reveal a possibility closer to reality

Studies carried out between 2019 and 2021 demonstrated the possibility of superluminal travel, without the need for "Exotic Matter"

Dr. Harold G "Sonny" White warp drive pioneer and former NASA warp drive specialist has reported the discovery of a "warp bubble" real in the real world.

And, according to White, this first-of-its-kind breakthrough by his team at the Limitless Space Institute (LSI), which sets a new starting point for those trying to make a full-size, warp-capable spacecraft.

In an interview, White added that “our detailed numerical analysis of our custom Casimir cavities helped us identify a real, fabricable nano/microstructure, which is predicted to generate a negative vacuum energy density such that it would manifest a warp bubble.” at the real nanoscale, not an analogue, but something real.”

In other words, a warp bubble structure will manifest under these specific conditions. White cautioned that this does not mean we are close to building a fully functioning warp drive, as much more science needs to be done (updated 08/12/21).

"To be clear, our find is not a warp bubble analogue, it is an actual warp bubble, albeit humble and small," White told The Debrief &#34 hence the importance

Peer review and confirmation of the warp bubble

"While conducting analysis related to a DARPA-funded project to assess the possible structure of the energy density present in a Casimir cavity, as predicted by the dynamic vacuum model" Read in actual findings published in the peer-reviewed European Physical Journal, a nanoscale structure has been discovered that predicts a negative energy density distribution that closely matches the requirements of the Alcubierre metric.”.

Or put more simply, as White did in a recent email to The Debrief:

“To my knowledge, this is the first paper in the peer-reviewed literature to propose a workable nanostructure, which is predicted to manifest a true, albeit humble, strain bubble.

This serendipitous find, says White, not only confirms the "toroidal" predicted and negative energy aspects of a warp bubble, but also resulted in potential pathways that he and other researchers may follow when attempting to design, and someday build, a true-world warp-capable spacecraft.

In an email interview with The Debrief blog, Dr. White said that what they have identified is not an analogue of the warp bubble, but “a 'warp bubble' ' real though modest and tiny”.

The scientist —who led the NASA Eagleworks research group for years— affirmed that the significance of this discovery is very important and opens up the possibility of future practical applications unimaginable until now.

Explanatory video of Dr. Harold G "Sonny" White

Next: a nanoscopic ship

Eagleworks was NASA's advanced propulsion research group where White conducted research to solve the gigantic energy consumption problems opened up by the Alcubierre equations.

His work managed to cut those energy needs, proposing for the first time a possible solution so that humanity could travel to other star systems, as can now only be seen in science fiction series such as 'Star Trek&' #39;.

If we are ever able to develop theory and technology to the point where energy needs are manageable and materials strong enough.

That, for now, is something that is still centuries away.

The warp drive in Star Trek

Evolution of warp engines

In the Star Trek science fiction stories, the warp drive is supposed to have been invented, on Earth, by a fictional scientist named Zefram Cochrane. The movie Star Trek: First Contact shows how, in the year 2063, Cochrane makes the first warp trip of the human species, using an old intercontinental nuclear missile, modified to travel in space and, once there, generate a bubble of curvature. To create the bubble of curvature around the ship (and distort space-time for its displacement) Cochrane required an immense amount of energy (which he obtained thanks to the matter-antimatter reaction). This first voyage was a milestone, reaching a curvature factor of 1.0 and leading directly to the first contact with an extraterrestrial race: the Vulcans.

The proto-sequel Star Trek: Enterprise establishes that other civilizations had the warp drive before humans, such as the Vulcans, who had the most advanced warp drive technology of the 21st century. This series shows the trips of the first terrestrial ship capable of obtaining a curvature factor of 5.1 which, applying the curvature formula, is equivalent to about 39,767,468.5 km/s (kilometres per second)., reaching the closest star to Earth (Proxima Centauri, 4.25 light years away) in approximately 11.69 days. In the classical series (half of the 23rd century) the ships are capable of obtaining a curvature factor of 8 (distance from Earth to Proxima Centauri in 3.09 days).

It should be noted that the equivalent velocities of the warp factors have not been given in any Star Trek episode or movie. The values indicated in this article have been found (or extrapolated) in technical manuals or other electronic media owned by the Star Trek rights holders.

Transcurvature

This term has been used to refer to advanced forms of propulsion that exceed the limits of traditional warp drives. In general, this transcurvature system is commonly used by the Borg, although Starfleet also did some experiments along these lines, as seen in Star Trek III: The Search for Spock. Some episodes of Star Trek: Voyager and Star Trek: The Next Generation seem to indicate that the bending system employed by the Borg is best described as a conduit (of the wormhole type).) through subspace (it is a characteristic of space-time which facilitates superluminal transit, in the form of interstellar travel or information transmission), in which the ship is introduced, moving inside it to the destination point.

The Borg discovered the existence of the transwarp conduits and set up networks of conduits between major sectors of the galaxy in order to move rapidly through the galaxy. That can be seen in the episode of the Voyager series titled Endgame. These transcurvature conduits used by the Borg are activated by a pulse of tachyons (particles that move at superluminal speeds and allow travel, equivalent to twenty times the speed of traditional warp drives. In addition, the Borg use transcurvature coils to generate temporary transcurved canals.

Curvature speed. Curvature factor

The unit used with the speed of curvature is the factor of curvature. The equivalence between curvature factors obtained by warp reactors and velocities measured in multiples of the speed of light is somewhat ambiguous.

Curvature factors are obtained by applying the following cubic formula:

s(w)=w3c{displaystyle s(w)=w^{3}c}

where w is the curvature factor, s(w){displaystyle s(w)} is the measured speed in normal space and c It's the speed of light. According to this formula, curvature 1 is equivalent to the speed of light, curvature 2 equals eight times the speed of light, curvature 3 equals 27 times the speed of light, etc.

However, this scale conflicts with the usual use, since the speed reached would be insufficient to allow the trips that appear in television series. Some episodes of the original series placed the ship Enterprise in danger if it traveled at high curvature factors (in the episode That witch survives this factor was set at 14.1).

For Star Trek: The Next Generation and subsequent series, Star Trek writer Michael Okuda devised a new formula based on the original, but with one important difference.

For bend factors between 1 and 9, a slightly faster bend factor was applied than the original series, but the speed still varied by a fixed power of the factor:

s(w)=w103c{displaystyle s(w)=w^{10 over 3}c}

But in the half-open interval between warp 9 and warp 10, the exponent affecting w was made to increment uncontrollably. convergent and, as we approach curvature 10 asymptotically, the exponent becomes infinite. For this reason, according to the Okuda scale, the velocities obtained when approaching curvature 10 also tend to infinity.

Michael Okuda's new warp scale.

The new scale places the curvature factor of 10 as an unattainable maximum (identified as the Eugene Limit on series creator Gene Roddenberry's page). The curvature factor 10 is an asymptote that initially represents infinite velocity. In the Star Trek: Voyager episode titled Critical Moment (Threshold) one of the characters manages to reach curvature factor 10, but with the consequence of undergoing genetic hyperevolution.

In the different series, there is only one episode in which a specific equivalence is given. This is the 37th episode of the Voyager series where the navigator Tom Paris describes the speed of Voyager when reaching the factor 9.9 as 6.44×10¹² m/s, which It would be equivalent to more than 21,000 times the speed of light.

As a reference about sustained (cruising) curvature factors, it should be noted that, in the mid-24th century, the ship Enterprise-D travels at a curvature factor of 9.2 and the Intrepid Voyager class ship can sustain a factor of 9.975.

On the other hand, there is a slight inconsistency in the series of The New Generation. In the two-part episode All Good Things (season 7 episodes 25 and 26) Captain Picard is sent to the future by Q, where he meets a modified Enterprise D, captained by William Riker, capable of reaching warp speed 13. However, within the plot of the series this future never comes to exist, therefore many consider that the warp scale could have been readjusted in said future or simply that the barrier created by Michael Okuda had not been implemented at the time of writing those episodes.

Curvature Core

The primary form of propulsion in the Star Trek universe is gravimetric field displacement, more commonly defined as core warp. The warp core is a fictitious energy system based on the matter-antimatter reaction that provides enough energy to generate the distortion of Space-time. The matter-antimatter reaction is controlled by so-called dilithium crystals (crystals that supposedly do not show any reaction when bombarded with high levels of radiation). The reaction chamber is surrounded by a magnetic field that allows the antimatter to be contained and to avoid reactions with the matter of the ship.

The energy released during the reaction is used to create the curvature field called the curvature bubble. This field distorts the space around the ship and accelerates it while the space inside the bubble is technically not shifting, so the ship does not experience any time dilation. Time passes inside the bubble, at the same rate as at the point of origin or destination.

Visualization of a warp bubble.