# Warp Drive: Fact or Fiction?

Is the Warp Drive fact or fiction?

Can the Warp Drive be fact or fiction?

Warp Drives are Exotic solutions of the Einstein Field Equations of General Relativity that "allows" Faster Than Light Space Travel within the framework of General Relativity

Note that the word "allows" is between quotes.

The first of these Exotic solutions was discovered by the Mexican mathematician Miguel Alcubierre in 1994. The second was discovered by the Portuguese mathematican Jose Natario in 2001.

Alcubierre is PhD from University of Wales in Cardiff UK and Natario is PhD from University of Oxford UK.

Their works are here:

http://arxiv.org/abs/gr-qc/0009013

http://arxiv.org/abs/gr-qc/0110086

The Warp Drive is an entire family of solutions of the Einstein Field Equations of General Relativity like the Schwarzschild or the Reissner-Nordtstrom solutions are for Black Holes but Warp Drives, although mathematical elegant solutions faces some serious problems

an excellent description about the problems Warp Drive faces can be given by

http://arxiv.org/abs/gr-qc/0406083

http://arxiv.org/abs/0710.4474

I would like to discuss in ResearchGate the Warp Drive. Using the scientific works of arXiv or HAL to start to show how this theme can be interesting for people in General Relativity

abstract of arXiv:0710.4474

The General Theory of Relativity has been an extremely successful theory, with a well established experimental footing, at least for weak gravitational fields. Its predictions range from the existence of black holes, gravitational radiation to the cosmological models, predicting a primordial beginning, namely the big-bang. All these solutions have been obtained by first considering a plausible distribution of matter, and through the Einstein field equation, the spacetime metric of the geometry is determined. However, one may solve the Einstein field equation in the reverse direction, namely, one first considers an interesting and exotic spacetime metric, then finds the matter source responsible for the respective geometry. In this manner, it was found that some of these solutions possess a peculiar property, namely 'exotic matter,' involving a stress-energy tensor that violates the null energy condition. These geometries also allow closed timelike curves, with the respective causality violations. These solutions are primarily useful as 'gedanken-experiments' and as a theoretician's probe of the foundations of general relativity, and include traversable wormholes and superluminal 'warp drive' spacetimes. Thus, one may be tempted to denote these geometries as 'exotic' solutions of the Einstein field equation, as they violate the energy conditions and generate closed timelike curves. In this article, in addition to extensively exploring interesting features, in particular, the physical properties and characteristics of these 'exotic spacetimes,' we also analyze other non-trivial general relativistic geometries which generate closed timelike curves.

Can the Warp Drive be fact or fiction?

Warp Drives are Exotic solutions of the Einstein Field Equations of General Relativity that "allows" Faster Than Light Space Travel within the framework of General Relativity

Note that the word "allows" is between quotes.

The first of these Exotic solutions was discovered by the Mexican mathematician Miguel Alcubierre in 1994. The second was discovered by the Portuguese mathematican Jose Natario in 2001.

Alcubierre is PhD from University of Wales in Cardiff UK and Natario is PhD from University of Oxford UK.

Their works are here:

http://arxiv.org/abs/gr-qc/0009013

http://arxiv.org/abs/gr-qc/0110086

The Warp Drive is an entire family of solutions of the Einstein Field Equations of General Relativity like the Schwarzschild or the Reissner-Nordtstrom solutions are for Black Holes but Warp Drives, although mathematical elegant solutions faces some serious problems

an excellent description about the problems Warp Drive faces can be given by

http://arxiv.org/abs/gr-qc/0406083

http://arxiv.org/abs/0710.4474

I would like to discuss in ResearchGate the Warp Drive. Using the scientific works of arXiv or HAL to start to show how this theme can be interesting for people in General Relativity

abstract of arXiv:0710.4474

The General Theory of Relativity has been an extremely successful theory, with a well established experimental footing, at least for weak gravitational fields. Its predictions range from the existence of black holes, gravitational radiation to the cosmological models, predicting a primordial beginning, namely the big-bang. All these solutions have been obtained by first considering a plausible distribution of matter, and through the Einstein field equation, the spacetime metric of the geometry is determined. However, one may solve the Einstein field equation in the reverse direction, namely, one first considers an interesting and exotic spacetime metric, then finds the matter source responsible for the respective geometry. In this manner, it was found that some of these solutions possess a peculiar property, namely 'exotic matter,' involving a stress-energy tensor that violates the null energy condition. These geometries also allow closed timelike curves, with the respective causality violations. These solutions are primarily useful as 'gedanken-experiments' and as a theoretician's probe of the foundations of general relativity, and include traversable wormholes and superluminal 'warp drive' spacetimes. Thus, one may be tempted to denote these geometries as 'exotic' solutions of the Einstein field equation, as they violate the energy conditions and generate closed timelike curves. In this article, in addition to extensively exploring interesting features, in particular, the physical properties and characteristics of these 'exotic spacetimes,' we also analyze other non-trivial general relativistic geometries which generate closed timelike curves.

## All Answers (38)

Deletedin a Warp Drive Spacetime you do not moves at all..itis the Spacetime that is moving

here is he abstract of the Alcubierre work

http://arxiv.org/abs/gr-qc/0009013

it is shown how, within the framework of general relativity and without the introduction of wormholes, it is possible to modify a spacetime in a way that allows a spaceship to travel with an arbitrarily large speed. By a purely local expansion of spacetime behind the spaceship and an opposite contraction in front of it, motion faster than the speed of light as seen by observers outside the disturbed region is possible. The resulting distortion is reminiscent of the ``warp drive'' of science fiction. However, just as it happens with wormholes, exotic matter will be needed in order to generate a distortion of spacetime like the one discussed here.

however Natario proposes a different approach

http://arxiv.org/abs/gr-qc/0110086

It is commonly believed that Alcubierre's warp drive works by contracting space in front of the warp bubble and expanding space behind it. We show that this expansion/contraction is but a marginal consequence of the choice made by Alcubierre, and explicitly construct a similar spacetime where no contraction/expansion occurs. Global and optical properties of warp drive spacetimes are also discussed.

Warp Drives are dynamical Spacetimes in motion..or by expansion/contraction of Spacetime(Alcubiere)or by the motion of one Spacetime region with respect to another at the rest(rate of strain stress tensor in fluid mechanics)(Natario)

however Warp Drives requires negative energy exotic matter to be generated and requires lots of it..at least ten times the mass of the visible Universe according to the work of Pfenning

http://arxiv.org/abs/gr-qc/9702026

We will apply the quantum inequality type restrictions to Alcubierre's warp drive metric on a scale in which a local region of spacetime can be considered ``flat''. These are inequalities that restrict the magnitude and extent of the negative energy which is needed to form the warp drive metric. From this we are able to place limits on the parameters of the ``Warp Bubble''. It will be shown that the bubble wall thickness is on the order of only a few hundred Planck lengths. Then we will show that the total integrated energy density needed to maintain the warp metric with such thin walls is physically unattainable.

of course there are solutions to overcome this(and other probllems that will be presented in this topic)

from ten times the mass of the Universe in exotic matter to sone tons a solution can be found here

http://hal.archives-ouvertes.fr/INSMI/hal-00599640/fr/

here is the abstract

Warp Drives are solutions of the Einstein Field Equations that allows Superluminal Travel within the framework of General Relativity. There are at the present moment two known solutions: The Alcubierre Warp Drive discovered in 1994 and the Natario Warp Drive discovered in 2001. However as stated by both Alcubierre and Natario themselves the Warp Drive violates all the known energy conditions because the stress energy momentum tensor(the right side of the Einstein Field Equations) for the Einstein tensor G00 is negative implying in a negative energy density. While from a classical point of view the negative energy is forbidden the quantum theory allows the existence of very small amounts of it being the Casimir effect a good example as stated by Alcubierre himself. But the stress energy momentum tensor of both Alcubierre and Natario Warp Drives have the speed of the ship raised to the square inside its mathematical structure which means to say that as fast the ship goes by then more and more amounts of negative energy are needed in order to maintain the Warp Drive. Since the total energy requirements to maintain the Warp Drive are enormous and since quantum theory only allows small amounts of it,many authors regarded the Warp Drive as unphysical and impossible to be achieved. We compute the negative energy density requirements for a Warp Bubble with a radius of 100 meters(large enough to contain a ship) moving with a speed of 200 times light speed(fast enough to reach stars at 20 light-years away in months not in years)and we verify that the negative energy density requirements are of about 1028 times the positive energy density of Earth!!!(We multiply the mass of Earth by c2 and divide by Earth volume for a radius of 6300km). However both Alcubierre and Natario Warp Drives as members of the same family of the Einstein Field Equations requires the so-called Shape Functions in order to be mathematically defined. We present in this work two new Shape Functions one for the Alcubierre and another for the NatarioWarp Drive Spacetimes that allows arbitrary Superluminal speeds while keeping the negative energy density at "low" and "affordable" levels.We do not violate any known law of quantum physics and we maintain the original geometries of both Alcubierre and Natario Warp Drive Spacetimes.

Deletedhey pal you do not understand the science behind Warp Dvive

unless you have works on arXiv or HAL your opininos are irrerelevant

Deleteddo you have ones ????

Deletedhttp://io9.com/5889628/warp-drives-may-come-with-a-killer-downside

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Warp Drives May Come With A Killer Downside

Planning a little space travel to see some friends on Kepler 22b?

Thinking of trying out your newly-installed FTL3000 Alcubierre Warp Drive to get you there in no time? Better not make it a surprise visit - your arrival may end up disintegrating anyone there when you show up.

"Warp" technology and faster-than-light (FTL) space travel has been a staple of science fiction for decades. The distances in space are just so vast and planetary systems - even within a single galaxy - are spaced so far apart, such a concept is needed to make casual human exploration feasible (and fit within the comforts of people's imagination as well… nobody wants to think about Kirk and Spock bravely going to some alien planet while everyone they've ever known dies of old age!)

While many factors involving FTL travel are purely theoretical - and may remain in the realm of imagination for a very long time, if not ever - there are some concepts that play well with currently-accepted physics.

The Alcubierre warp drive is one of those concepts.

Proposed by Mexican theoretical physicist Miguel Alcubierre in 1994, the drive would propel a ship at superluminal speeds by creating a bubble of negative energy around it, expanding space (and time) behind the ship while compressing space in front of it. In much the same way that a surfer rides a wave, the bubble of space containing the ship and its passengers would be pushed at velocities not limited to the speed of light toward a destination.

Of course, when the ship reaches its destination it has to stop. And that's when all hell breaks loose.

Researchers from the University of Sydney have done some advanced crunching of numbers regarding the effects of FTL space travel via Alcubierre drive, taking into consideration the many types of cosmic particles that would be encountered along the way. Space is not just an empty void between point A and point B… rather, it's full of particles that have mass (as well as some that do not.) What the research team - led by Brendan McMonigal, Geraint Lewis, and Philip O'Byrne - has found is that these particles can get "swept up" into the warp bubble and focused into regions before and behind the ship, as well as within the warp bubble itself.

When the Alcubierre-driven ship decelerates from superluminal speed, the particles its bubble has gathered are released in energetic outbursts. In the case of forward-facing particles the outburst can be very energetic - enough to destroy anyone at the destination directly in front of the ship.

"Any people at the destination," the team's paper concludes, "would be gamma ray and high energy particle blasted into oblivion due to the extreme blueshifts for [forward] region particles."

In other words, don't expect much of a welcome party.

Another thing the team found is that the amount of energy released is dependent on the length of the superluminal journey, but there is potentially no limit on its intensity.

"Interestingly, the energy burst released upon arriving at the destination does not have an upper limit," McMonigal told Universe Today in an email. "You can just keep on traveling for longer and longer distances to increase the energy that will be released as much as you like, one of the odd effects of General Relativity. Unfortunately, even for very short journeys the energy released is so large that you would completely obliterate anything in front of you."

So how to avoid disintegrating your port of call? It may be as simple as just aiming your vessel a bit off to the side… or, it may not. The research only focused on the planar space in front of and behind the warp bubble; deadly postwarp particle beams could end up blown in all directions!

Luckily for Vulcans, Tatooinians and any acquaintances on Kepler 22b, the Alcubierre warp drive is still very much theoretical. While the mechanics work with Einstein's General Theory of Relativity, the creation of negative energy densities is an as-of-yet unknown technology - and may be impossible.

Which could be a very good thing for us, should someone out there be planning a surprise visit our way!

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from arXiv

http://arxiv.org/abs/1202.5708

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The Alcubierre warp drive allows a spaceship to travel at an arbitrarily large global velocity by deforming the spacetime in a bubble around the spaceship. Little is known about the interactions between massive particles and the Alcubierre warp drive, or the effects of an accelerating or decelerating warp bubble. We examine geodesics representative of the paths of null and massive particles with a range of initial velocities from -c to c interacting with an Alcubierre warp bubble travelling at a range of globally subluminal and superluminal velocities on both constant and variable velocity paths. The key results for null particles match what would be expected of massive test particles as they approach +/- c. The increase in energy for massive and null particles is calculated in terms of v_s, the global ship velocity, and v_p, the initial velocity of the particle with respect to the rest frame of the origin/destination of the ship. Particles with positive v_p obtain extremely high energy and velocity and become "time locked" for the duration of their time in the bubble, experiencing very little proper time between entering and eventually leaving the bubble. When interacting with an accelerating bubble, any particles within the bubble at the time receive a velocity boost that increases or decreases the magnitude of their velocity if the particle is moving towards the front or rear of the bubble respectively. If the bubble is decelerating, the opposite effect is observed. Thus Eulerian matter is unaffected by bubble accelerations/decelerations. The magnitude of the velocity boosts scales with the magnitude of the bubble acceleration/deceleration.

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in Alcubierre Warp Drive the energy is located above and below the ship....in the front of the ship there exists empty space..or the region where spacetime contracts in the front.....a photon sent to the front of the ship will suffer from blueshifts there is nothing to prevent the photon to suffer a blueshift

but fortunately we have another Warp Drive geometryy..the Natario Warp Drive in this Warp Drive the energy surrounds all the ship the ship is in the center of a sphere of negative energy....a photon sent to the front will be deflected by this field of negative energy so the blueshift do not occurs

but the analysis the work arXiv:1202.5708 made for Alcubierre Warp Drive perhaps needs to be repeated..for the Natario Warp Drive

for details on Horizons or Doppler blushifts see this one

http://hal.archives-ouvertes.fr/INSMI/hal-00599657/fr/

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Although both Alcubierre and Natario Spacetimes belongs to the same family of Einstein Field Equations of General Relativity and both have many resemblances between each other ,the Energy Density distribution in the Alcubierre Warp Drive is different than the one found in the Natario Warp Drive.The Horizons will arise in both Spacetimes when approaching Superluminal(Warp) speeds however due to a different distribution of Energy Density the Natario Warp Drive behaves slightly different when compared to the Alcubierre one. The major differences between the Natario and Alcubierre Warp Drive Spacetimes occurs when we study the Infinite Doppler Blueshifts that affect the Alcubierre Spacetime but not affect the Natario one because while in Alcubierre Spacetime the Negative Energy is distributed in a toroidal region above and below the ship perpendicular to the direction of the motion while in front of the ship.the space is empty having nothing to prevent a photon to reach the Horizon because in this case the Horizon lies on empty space,in the Natario Spacetime the Energy Density is distributed in a spherical shell that covers the entire ship and a photon sent to the front will be deflected by this shell of Negative Energy before reaching the Horizon because the Horizon also lies inside this shell and not on "empty" space.This shell avoids the occurrence of Infinite Doppler Blueshifts in the Natario Warp Drive Spacetime.We examine in this work the major differences between both Natario and Alcubierre Spacetimes outlining the repulsive character of the Negative Energy Density.The creation of a Warp Bubble in Alcubierre or Natario Spacetimes is beyond the scope of Classical General Relativity and will have to wait until the arrival of a real Quantum Gravity theory that must encompass Superluminal Non-Local Quantum Entanglement Effects in order to deal with the Horizon problem added to the Geometrical features of Classical General Relativity plus it must also provide a way to generate large outputs of Negative Energy Densities.Since this theory is ahead of our scientific capabilities,we discuss in the end of this work an approach that could be performed by our science in a short period of term.to increase our knowledge about the Warp Drive as a Dynamical Spacetime.

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Tapio Ala-Nissila· Aalto UniversityDeletedit was considered in the paper arXiv gr-qc/0406083 for the Alcubierre Warp Drive....he used linearized gravity etc..

.i am trying to reproduce the same analysis for the Natario Warp Drive

however Warp Drive requires exotic matter with negative energy and except for the Casimir Effect no one knows how to generate the large amounts of it ....Quantum Physics allows nanograms of it and we need thousands of kilograms....we dont need 10 or 20 times the mass of the Universe in Exotic Matter to generate the Warp Drive effect but we need a surplus of Exotic Matter that is beyond the scope of Quantum Physics

plus if we have the Exotic Matter we would have the right side of the Einstein Field Equations of General Relativity

the Spacetime Distortion that allows the ship to go Faster Than Light belongs to the left side of the Einstein Field Equations and unfortunately no one knows how to make the "back-reaction" ...how to link both sides of the Einstein Field Equations.....

the stability of the Warp Drive depends on the mass of the ship....following the line of reason of arXiv gr-qc/0406083

imagine that i want to carry a ship with 20 metric tons (Space Shuttle) inside a Warp Bubble and at 200 times light speed....i will need a huge amount of negative energy...but the positive mass of the ship reacts with the negative mass of the Exotic Field ..this means to say that the positive mass of the ship also dictates the amount of negative energy needed to carry the ship at superluminal speeds

now for a shjp with 3.250.000 metric tons (Star Trek Enterprise) the amounts of negative energy would higher than the ones for a ship with only 20 metric tons

here is arXiv gr-qc/0406083

http://arxiv.org/abs/gr-qc/0406083

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"Warp drive" spacetimes are useful as "gedanken-experiments" that force us to confront the foundations of general relativity, and among other things, to precisely formulate the notion of "superluminal" communication. We verify the non-perturbative violation of the classical energy conditions of the Alcubierre and Natario warp drive spacetimes and apply linearized gravity to the weak-field warp drive, testing the energy conditions to first and second order of the non-relativistic warp-bubble velocity. We are primarily interested in a secondary feature of the warp drive that has not previously been remarked upon, if it could be built, the warp drive would be an example of a "reaction-less drive". For both the Alcubierre and Natario warp drives we find that the occurrence of significant energy condition violations is not just a high-speed effect, but that the violations persist even at arbitrarily low speeds.

An interesting feature of this construction is that it is now meaningful to place a finite mass spaceship at the center of the warp bubble, and compare the warp field energy with the mass-energy of the spaceship. There is no hope of doing this in Alcubierre's original version of the warp-field, since by definition the point in the center of the warp bubble moves on a geodesic and is "massless". That is, in Alcubierre's original formalism and in the Natario formalism the spaceship is always treated as a test particle, while in the linearized theory we can treat the spaceship as a finite mass object. For both the Alcubierre and Natario warp drives we find that even at low speeds the net (negative) energy stored in the warp fields must be a significant fraction of the mass of the spaceship.

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DeletedDeleteda particle at the rest in empty space when a Natario Warp Drive approaches is carried out by the Natario Warp Drive itself according to the geodesics equations for Eulerian observers exactly like in the Alcubierre Warp Drive as prediced by Monigal et al ..the particle is trapped inside the Warp Field

see http://arxiv.org/pdf/gr-qc/0110086v3.pdf pg 2 but for those unfamiliatized with the Euler-Lagrange equation for geodesics and how Professor Natario arrived at his result see the Advanced General Relativity Course of Professor Poisson at University of Guelph Ontario Canada http://www.physics.uoguelph.ca/poisson/research/agr.pdf at pg 21

Monigal Lewis and Byrne are entirely correct

see pg 10 of http://arxiv.org/pdf/1202.5708.pdf

a ship when dropping out of Warp will release these trapped particles and these will emit gamma rays.....

the ship must drop out of Warp outside a planetery system and must complete the journey at sub-light speed

the difference is that while in the Alcubierre Warp Drive the crew are not shielded against Doppler Blueshifts

in the Natario Warp Drive the crew have protection see the http://hal.archives-ouvertes.fr/INSMI/hal-00599657/fr/

section on Horizons and Doppler Blueshifts

in order to low the negative energy ensity requirements for the Warp Drive Spacetime i recommend

http://hal.archives-ouvertes.fr/INSMI/hal-00599640/fr/

but i am happy because i went to Google to check arXiv:1202.5708 and Google shows my RG post in the fourth position

if Monigal have curiousity to check Google for his work then Monigal already know about me

http://www.google.com/#hl=pt-BR&gs_nf=1&pq=eric%20poisson%20general%20relativity&cp=15&gs_id=1t&xhr=t&q=arXiv%3A1202.5708&pf=p&sclient=psy-ab&oq=arXiv:1202.5708&aq=f&aqi=&aql=&gs_l=&pbx=1&bav=on.2,or.r_gc.r_pw.r_qf.,cf.osb&fp=109fb21fd35f3dff&biw=1024&bih=681

the math is terminated...now the most difficult part to TeX in LaTeX and unfortunately i am a "lazy boy"

Deletedhttp://hal.inria.fr/docs/00/59/96/40/PDF/GeneRoddenberry5.pdf

http://hal.inria.fr/docs/00/59/96/57/PDF/Natario_Warp_Drive.pdf

DeletedLong distance space travel could create the ultimate 'killer entrance', devastating your destination and anything around the arriving spacecraft, according to calculations by Geraint Lewis and colleagues from the University of Sydney. The Alcubierre warp drive is a theoretical tool that would allow spacecraft to travel long distances in space rapidly by deforming the space-time continuum in a bubble around the spaceship.

Miguel Alcubierre, a Mexican physicist, proposed this warp drive in 1994 as a way to travel faster than light, overcoming the limit on particles travelling at such speeds posed by Einstein's theory of special relativity ."When the spacecraft decelerates to stop at its destination, the particles collected at the front of the spacecraft are released with such high-energy that they would destroy anything they came in contact with. During the journey the particles picked up and included inside the bubble could threaten the safety of people travelling in the spacecraft," said Geraint Lewis of the University of Sydney School of Physics.

"It sounds like it's straight from science fiction, and in a way it is, as the Alcubierre warp drive is a theoretical solution to the problem of travelling the huge distances in space in a reasonable amount of time," said Lewis. "But unlike science fiction, the Alcubierre warp drive completely obeys Einstein's general theory of relativity."

"All innovations start with theory, however, so these calculations contribute to our understanding of how such speeds could be achieved. Our team decided to consider what would happen to particles and radiation that a spacecraft, travelling in a bubble created by the Alcubierre warp drive, would come across as it travelled through space," explained Lewis.

"What we've shown is that when this spacecraft decelerated to arrive at its destination, it would release high energy particles which would destroy anything near the spacecraft's landing spot."While scientists have examined how it's theoretically possible to create a bubble around a spacecraft with the Alcubierre warp drive compressing space-time in front of the bubble and expanding it behind the bubble, there has been little consideration of how this high-speed bubble would interact with particles of matter and light.

"Our calculations show that particles that come in contact with the warp bubble can get caught up and congregate in front of the spacecraft, and some particles even enter the warp bubble," added Lewis.

"Interestingly, the energy burst released upon arriving at the destination does not have an upper limit. You can just keep on traveling for longer and longer distances and the energy that will be released will continue to increase - one of the odd effects of General Relativity," obseerved team researcher, Brendan McMonigal. "Even for very short journeys the energy released is so large that you would completely obliterate anything in front of you. It seems that human exploration of the universe will have to wait until we've worked out how to avoid the destructive deceleration of a spacecraft in an Alcubierre warp drive bubble."

Kenneth Ricci· Adelphi Technology Inc.Deletedi assume from visiting your researchgate.net profile that since you are a nuclear physicist you are aware of the Lorentz Transformationf of Special Relativity where if v>c then the factoer sqrt(1-v^2 /c^2) would becomes immaginary etc

i assume that you are not aware of General Relativity so i would recommend as an introductory lecture on Warp Drives the following arXiv work

http://arxiv.org/abs/0710.4474

abstract

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The General Theory of Relativity has been an extremely successful theory, with a well established experimental footing, at least for weak gravitational fields. Its predictions range from the existence of black holes, gravitational radiation to the cosmological models, predicting a primordial beginning, namely the big-bang. All these solutions have been obtained by first considering a plausible distribution of matter, and through the Einstein field equation, the spacetime metric of the geometry is determined. However, one may solve the Einstein field equation in the reverse direction, namely, one first considers an interesting and exotic spacetime metric, then finds the matter source responsible for the respective geometry. In this manner, it was found that some of these solutions possess a peculiar property, namely 'exotic matter,' involving a stress-energy tensor that violates the null energy condition. These geometries also allow closed timelike curves, with the respective causality violations. These solutions are primarily useful as 'gedanken-experiments' and as a theoretician's probe of the foundations of general relativity, and include traversable wormholes and superluminal 'warp drive' spacetimes. Thus, one may be tempted to denote these geometries as 'exotic' solutions of the Einstein field equation, as they violate the energy conditions and generate closed timelike curves. In this article, in addition to extensively exploring interesting features, in particular, the physical properties and characteristics of these 'exotic spacetimes,' we also analyze other non-trivial general relativistic geometries which generate closed timelike curves.

-------------------------------

in order to get acquaintance with General Relativity i would recommend these ones

http://arxiv.org/abs/gr-qc/9712019

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These notes represent approximately one semester's worth of lectures on introductory general relativity for beginning graduate students in physics. Topics include manifolds, Riemannian geometry, Einstein's equations, and three applications: gravitational radiation, black holes, and cosmology.

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Advanced general relativity

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These are suitable for a one-semester course at the graduate level. They were designed for the course PHYS*7840 at the University of Guelph. Use them at your own peril.

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http://www.physics.uoguelph.ca/poisson/research/agr.pdf

Kenneth Ricci· Adelphi Technology Inc.I have indeed studied General Relativity. Thank you for the references.

In assuming that warp drive does NOT entail backward time travel

( we are all aware that forward time travel is possible since we are doing it right now,

and forward time travel with time dilation is possible since particles in linear accelerators

are measured doing it right now, therefore, accelerated forward time travel is clearly possible)

-- you are assuming that warp drive permits faster than light travel from Point A to Point B,

but does NOT permit slightly slower than light velocities. Because as you know from special

relativity, if you can travel from Point A to Point B faster than light, then accelerate back from

Point B toward Point A at a slightly-below-light-speed rate, the shift in reference frame allows

you to arrive back at Point A at an earlier time than when you left Point A.

Since particle beams are indeed already being produced at slightly slower-than-light

velocities in hundreds of linear accelerators around the world, it is a straight-forward matter

to show that, if a warp drive will be invented in the future, a slightly-slower-than-light particle

beam could then easily be used to send a message (consisting of pulses of protons, which

would be observed on earth as pulses of cosmic rays from the upper atmosphere) back to

earth, arriving at a time earlier than the original ship with warp drive left Point A (earth).

It also seems very likely to me that a civilization capable of building a warp drive would be

capable of building an impulse drive capable of near-light-speed (slightly slower than light)

travel. In this case, it is clear that backwards time travel will be possible. A space-time diagram

illustrating this problem can be seen here:

http://en.wikipedia.org/wiki/Minkowski_diagram#Speed_of_light_and_causality

The equations to derive backward time travel, and how backward time travel is an immediate

consequence of faster-than-light-travel plus the reference frame shift accompanying slightly

slower-than-light-travel, were derived for me in a freshman physics class at MIT in 1989, and

are frequently presented in university mechanics lectures on Special Relativity. Stephen Hawking,

as noted here

http://www.hawking.org.uk/space-and-time-warps.html

that faster-than-light travel would immediately entail the possibility of backward time travel and hence,

will probably not ever be invented since we do not currently see any evidence of travelers or messages

from the future.

Rob CarrollKenneth Ricci· Adelphi Technology Inc.When I saw that your topic heading was "Warp Drive Fact Or Fiction?" I assumed that you wanted to discuss the mathematical, physical, and perhaps philosophical arguments on both sides of the question. It is not obvious from the theoretical solutions of the Einstein equations that time travel or warp drive should be impossible in physical space; on the other hand, it is also not obvious that these solutions can occur in *real* space (the universe we live in) because real space has more properties than simply the Einstein metric-- it has, for example, also quantum foam and probably some form of quantum vacuum energy that may prevent or enable such exotic solutions of the Einstein equations to endure or not to endure (to evanesce, as Stephen Hawking would put it) in the real spacetime of our universe.

Since I thought that you were encouraging such a debate, I thought it would be relevant to begin with one of the strongest arguments why warp drive is unlikely to exist (not impossible; a physicist can never say impossible)--that is the argument given by Stephen Hawking, an acknowledged expert in General Relativity, and many others like him (including my freshman physics professor at MIT in 1989) who study relativity. They point out correctly that if you could get from A to B in space outside the "light-cone" (faster than light could get from A to B) then, IN NORMAL MINKOWSKI SPACETIME, it is a straightforward technological matter to send messages back in time to point A. I did not expect any of the experts here in General Relativity to challenge that basic and well-known property of spacetime and the Minkowski metric. Instead I expected a discussion on the various ways to resolve this paradox that could make it possible to travel faster than light but preventing time travel.

Or a discussion of the consequences of the time travel that may result when warp drive is used.

Perhaps I offended by beginning my statement with the comment "Fiction." As if I knew that were the one and only answer. That was meant to be only one "point of view," not intended as a dismissal or criticism of your work. If you wish I will delete that offensive comment, leaving my other comments which are simply technical discussions of the state of the art in relativity understanding (and a couple links to Hawking's and other related work).

Let me propose a possible solution to the apparent paradox, the kind of answer I was looking for in this discussion:

It may be that the creation of such a "warp drive" will generate a space-time "wake" --much like the wave behind a boat passing through water or the shockwave of an aircraft moving faster than the speed of sound. If there is a space-time "wake" it may have wave-like properties-- it would be expected to propagate through the nearly Minkowski (Special Relativity-like) spacetime that occupies most of our universe in the form of a very strong gravitational wave for example. If we were to fly in our space ship Enterprise, using your warp drive, from Earth to the star Vega for example (25 light years away) and we chose a space warping factor of 250 that allowed us to reach Vega in 0.1 years according to our on-board clocks, we would be 24.9 light years "outside of the light cone" in conventional relativity terms. If the space between Vega and Earth is Minkowski-like (relatively small gravitational/Einstein field perturbations) then it would certainly be possible for a person on Vega, at the moment of our arrival, to send a near-relativistic proton beam back to earth that would arrive at earth before the time at which our space ship left earth. This is a well-known problem presented in many undergraduate physics courses on Special Relativity: we could learn about our arrival on Vega before we actually left earth.

But with the enormous mass-energy required to operate a warp-drive, perhaps the space between earth and Vega would no longer be "Minkowski-like." Perhaps the propagating gravitational wake of our spaceship enterprise carries with it a wake of time-dilation, such that any proton beam, or even a living being (like ourselves) sent back from Vega to earth at a near-relativistic speed would have to cross this space-time wake and may suffer a very sudden time-dilation, (we would probably get motion sickness as well, ha, ha!) making it impossible to reach earth before we left earth. One possible solution to Stephen Hawking's conundrum then is to say that moving the enormous mass-energies necessary to produce the space warp that gets us from here to there faster than light, also fundamentally alters the geometry of space over that path, and any paths sufficiently nearby (within the "light-cone" of our entire journey from earth to Vega), such that it is impossible to retrace the path without encountering a severe time dilation and gravitational wake that prevents backward time travel.

We all know that accelerated FORWARD time travel is possible, because particles are doing it every day at CERN and the world's other accelerators. Perhaps warp drive AND backward time travel are both possible, and the reason we have not seen any travelers from the future is because they realize that, if they tried to visit earth in the past, they would destroy earth from the energy release of this enormous gravitational wake. That is another possible answer.

All of these are possible solutions to a problem that I think is non-trivial and very important to your field: can faster-than-light travel exist without also enabling backward time travel? I think it is an open question, and I also think (but here I am speculating, not trying to PROVE anything) that it is unlikely for warp drive to actually happen in the spacetime of our universe, except perhaps on the very small scale (on the Planck scale for example, it probably happens all the time.)

Finally: If you tell me to do so I will remove my post where I said "fiction." It would be kindly if you also removed posts that personally attack me. I want to be your good colleague, not your enemy or an annoyance to you. We should keep this discussion cordial and professional.

Thank you,

-Ken

Tapio Ala-Nissila· Aalto UniversityLouis Brassard·into another thread

http://www.researchgate.net/topic/W1P-Warp_One_Project/post/Alcubierre_Warp_Drive_concept_on_Wikipedia

Raul Alvarez· Universidad Nacional Autónoma de MéxicoGreetings

Raúl

Kenneth Ricci· Adelphi Technology Inc.Deletedhttp://hal.archives-ouvertes.fr/hal-00711861/en/

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Warp Drives are solutions of the Einstein field equations that allows superluminal travel within the framework of General Relativity. There are at the present moment two known solutions: The Alcubierre warp drive discovered in $1994$ and the Natario warp drive discovered in $2001$. Recently McMonigal,Lewis and O'Byrne presented an important analysis for the Alcubierre warp drive:A warp drive ship at superluminal speeds in interstellar space would trap in the warp bubble all the particles and radiations the ship encounters in its pathway and these trapped bodies would achieve immense energies due to the bubble superluminal speed.As far the ship goes by in interstellar space, more and more particles and radiations are trapped in the bubble generating in front of it a blanket with extremely large amounts of positive energy. The physical consequences of having this blanket of positive energies with enormous magnitudes in front of the negative energy of the warp bubble are still unknown. When the ship finishes the trip it stops suddenly releasing in a highly energetic burst all the trapped particles and radiations contained in the blanket damaging severely the destination point. In this work,we reproduce the same analysis for the Natario warp drive however using different mathematical arguments more accessible to beginners or intermediate students and we arrived exactly to the same conclusions. While in a long-term future some of the physical problems associated to the warp drive science(negative energy,Horizons) seems to have solutions(better shape functions for the negative energy problem and a theory that encompasses both General Relativity and non local quantum entanglements of Quantum Mechanics for the Horizons problem) and we discuss these solutions in our work,the analysis of McMonigal,Lewis and O'Byrne although entirely correct do not have a foreseeable solution and remains the most serious obstacle against the warp drive as a physical reality

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Deletedthanks for the contributions to the debate

warp drives are difficult to be build and the analysis of McMonigal Lewis and O´Byrne makes everything worst and unfortunately they are correct.....i verified their calculations by myself

but i believe that a solution will appear....

Deletedhttp://hal.archives-ouvertes.fr/INSMI/hal-00711861/fr/

Deletedhere is the answer from the arXiv author Brendan Monigal (well i think he dont mind if i paste here the text of the email of course i will not place here the email adress since it can be botained from arXiv)

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Hi Fernando,

Thankyou for contacting us, we are very pleased to hear that your results agree with ours. I have read your paper, and think it is most promising.

We succeeded in getting published in Physical Review D (http://prd.aps.org/abstract/PRD/v85/i6/e064024), and wish you the best of luck getting published there as well.

Cheers

Brendan

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i am thinking to do like they did..submit to Physical Review D however i think i will not get the same luck of them

because I am a non native English speaker and PRD is more exigent than arXiv in English grammar….they like “Cambridge” or “Oxford style” and I cannot pay a reviewer….i gave up to send from arXiv because I was constantly rejected because my English is not according to “Cornell University Standards” moderators of arXiv said to me

France created HAL because there are French,German,Italian,Polish or Russian scientists that are not willing to take a course of English Literature to write like William Shapespeare or that do not want to pay a professional reviewer

HAL is moderated like arXiv but do not restrain English style….after all HAL is French…

http://hal.archives-ouvertes.fr/index.php?halsid=dlmr3vt6mvmgjnphs96jdtgna0&action_todo=home

http://hal.archives-ouvertes.fr/index.php?langue=fr&halsid=dlmr3vt6mvmgjnphs96jdtgna0

Deletedthe main one from University of Sidney

http://sydney.edu.au/news/science/397.html?newsstoryid=8790

the others

http://www.buzzbox.com/news/2012-03-01/alcubierre-warp-drive:physics/?clusterId=9087509

http://www.messagetoeagle.com/alcubierrewarpdrive.php

http://www.theregister.co.uk/2012/03/04/killer_warp_drive/

http://www.pakalertpress.com/2012/03/13/alcubierre-warp-drive-a-doomsday-weapon/

http://www.popsci.com/technology/article/2012-03/pro-tip-flying-faster-speed-light-could-have-devastating-consequences

Deletedbut i used mathematical arguments....those who are coming here with "Quantum" or "Minkowsky" or "Hawking" against the warp drive i recommend to read all my publications on RG

because chatty style is not my style..those that are not familiarized with the theory study it first

a guy that wants to post against the warp drive study the paper arXiv:1202.5708 and please use mathematical arguments..... like i did in HAL-00711861

browse my RG publications.....a guy wrote a comment about my answer to arXiv:1202.5708

here is my reply

dear Graham...Star Trek is for the future but i believe it will come

it is the force behind me...remember that the submarine was science fiction 200 years ago....Jules Verne wrote 20.000 submarine leagues under the sea.....now we have nuclear submarines....and every captain of a submarine...every "skipper" (US Navy) that reads Jules Verne speak about how impressive were the details about Nautilus and Captain Nemo...written in mid XIX Century

now it is the Warp Drive that is trying to pass from science fiction...to science fact..many issues from science to engineered needs to be worked out.....but i am confident that one day a future version of Captain Jean-Luc Picard will say "engage"

thanks for your sweet compliment Graham

i would invite the guys that wrot

Deletedhttp://hal.archives-ouvertes.fr/hal-00732757/en/

here is the abstract

Warp Drives are solutions of the Einstein Field Equations that allows superluminal travel within the framework of General Relativity. There are at the present moment two known solutions: The Alcubierre warp drive discovered in $1994$ and the Natario warp drive discovered in $2001$. However as stated by both Alcubierre and Natario themselves the warp drive violates all the known energy conditions because the stress energy momentum tensor(the right side of the Einstein Field Equations) for the Einstein tensor $G_{00}$ is negative implying in a negative energy density. While from a classical point of view the negative energy is forbidden the Quantum Field Theory allows the existence of very small amounts of it being the Casimir effect a good example as stated by Alcubierre himself.The major drawback concerning negative energies for the warp drive are the so-called Quantum Inequalities(QI) that restricts the time we can observe the negative energy density.This time is known as the sampling time.Ford and Pfenning computed the QI for the Alcubierre warp drive and concluded that the negative energy in the Alcubierre warp drive can only exists for a sampling time of approximately $10^{-10}$ seconds rendering the warp drive impossible for an interstellar trip for example a given star at $20$ light years away with a speed of $200$ times faster than light because such a trip would require months not $10^{-10}$ seconds. We repeated the QI analysis of Ford and Pfenning for the Natario warp drive and because the Natario warp drive have a very different distribution of negative energy when compared to its Alcubierre counterpart this affects the QI analysis.We arrived at a sampling time that can last longer than $10^{-10}$ seconds enough to sustain a warp bubble for the interstellar travel mentioned above.We also computed the total negative energy requirements for the Natario warp drive and we arrived at a comfortable result.This leads us to conclude that the Natario warp drive is a valid solution of the Einstein Field Equations of General Relativity physically accessible for interstellar spaceflight. We also discuss Horizons and infinite Doppler blueshifts.

Deletedhttp://hal.archives-ouvertes.fr/INSMI/hal-00732757/fr/

Deletedthis uses the Planck Scale

http://hal.archives-ouvertes.fr/hal-00734603/en/

Warp Drives are solutions of the Einstein Field Equations that allows superluminal travel within the framework of General Relativity. There are at the present moment two known solutions: The Alcubierre warp drive discovered in $1994$ and the Natario warp drive discovered in $2001$. However as stated by both Alcubierre and Natario themselves the warp drive violates all the known energy conditions because the stress energy momentum tensor(the right side of the Einstein Field Equations) for the Einstein tensor $G_{00}$ is negative implying in a negative energy density. While from a classical point of view the negative energy is forbidden the Quantum Field Theory allows the existence of very small amounts of it being the Casimir effect a good example as stated by Alcubierre himself.The major drawback concerning negative energies for the warp drive are the so-called Quantum Inequalities(QI) that restricts the time we can observe the negative energy density.This time is known as the sampling time.Ford and Pfenning computed the QI for the Alcubierre warp drive using a Planck Length Scale shape function and concluded that the negative energy in the Alcubierre warp drive can only exists for a sampling time of approximately $10^{-33}$ seconds rendering the warp drive impossible for an interstellar trip for example a given star at $20$ light years away with a speed of $200$ times faster than light because such a trip would require months not $10^{-33}$ seconds. We repeated the QI analysis of Ford and Pfenning for the Natario warp drive using the same Planck Length Scale but with a shape function that although different from the function choosed by Ford and Pfenning it obeys Natario requirements and because the Natario warp drive have a very different distribution of negative energy when compared to its Alcubierre counterpart this affects the QI analysis.We arrived at a sampling time that can last longer than $10^{-33}$ seconds enough to sustain a warp bubble for the interstellar travel mentioned above.We also computed the total negative energy requirements for the Natario warp drive and we arrived at a comfortable result.This leads us to conclude that the Natario warp drive is a valid solution of the Einstein Field Equations of General Relativity physically accessible for interstellar spaceflight. We also discuss Horizons and infinite Doppler blueshifts.

Deletedhttp://hal.archives-ouvertes.fr/INSMI/hal-00734603/fr/

Deletedtitle:

The Analysis of Harold White applied to the Natario Warp Drive Spacetime. From $10$ times the mass of the Universe to the mass of the Mount Everest

abstract

Warp Drives are solutions of the Einstein Field Equations that allows superluminal travel within the framework of General Relativity. There are at the present moment two known solutions: The Alcubierre warp drive discovered in $1994$ and the Natario warp drive discovered in $2001$. However as stated by both Alcubierre and Natario themselves the warp drive violates all the known energy conditions because the stress energy momentum tensor is negative implying in a negative energy density. While from a classical point of view the negative energy is forbidden the Quantum Field Theory allows the existence of very small amounts of it being the Casimir effect a good example as stated by Alcubierre himself.The major drawback concerning negative energies for the warp drive is the huge amount of negative energy able to sustain the warp bubble.Ford and Pfenning computed the amount of negative energy needed to maintain an Alcubierre warp drive and they arrived at the result of $10$ times the mass of the entire Universe for a stable warp drive configuration rendering the warp drive impossible.However Harold White manipulating the parameter $@$ in the original shape function that defines the Alcubierre spacetime demonstrated that it is possible to low these energy density requirements.We repeat here the Harold White analysis for the Natario spacetime and we arrive at similar conclusions.From $10$ times the mass of the Universe we also manipulated the parameter $@$ in the original shape function that defines the Natario spacetime and we arrived at a result of $10$ billion tons of negative mass to maintain a warp drive moving with a speed $200$ times faster than light.Our result is still a huge number about the weight of the Everest Mountain but at least it is better than the original Ford-Pfenning result of $10$ times the mass of the Universe.The main reason of this work is to demonstrate that Harold White point of view is entirely correct.

available at HAL

http://hal.archives-ouvertes.fr/hal-00736930/en/

Deletedhttp://hal.archives-ouvertes.fr/INSMI/hal-00736930/fr/

Deletedalthough destinated to all Sciencies and not only Physics it contains inteesting features of the warp drive

https://www.researchgate.net/post/Open_Letter_to_ReseacrhGate

Deletedhttp://hal.archives-ouvertes.fr/hal-00827161/en/

Hyper Fast Interstellar Travel Within General Relativity:The Alcubierre and Natario Warp Drive Spacetimes:From Science Fiction to Science Fact

Warp Drives are solutions of the Einstein Field Equations that allows superluminal travel within the framework of General Relativity.There are at the present moment two known solutions: The Alcubierre warp drive discovered in $1994$ and the Natario warp drive discovered in $2001$.The warp drive seems to be very attractive because allows interstellar space travel at arbitrarily large speeds avoiding the light speed limit,time dilatation and mass increase paradoxes of Einstein Special Relativity.This is an introductory article without mathematics written for the general public outlining a brief resume of the "status quo" of the warp drive science from an Historical perspective.We cover the $3$ major obstacles raised by modern science against the physical integrity of the warp drive as a dynamical spacetime that can carry a ship at faster than light speeds.We show using a clear and accessible language that the Natario warp drive emerges as a "winner" against all the $3$ obstacles and can be regarded as a valid candidate for faster than light space travel.Our goal in writing a non-technical paper on this subject is to captive the interest of potential common readers that might would appreciate this subject avoiding the details of complex mathematical explanations.

Graham Allan Partis· University of Southern QueenslandSome of the stuff I am into may have some applications to do with FTL, but you seem to have the warpdrive aspects well in hand.

Deleteddid you liked the work????

it was the most difficult i ever wrote....trasmit the entire warp drive idea to common readers without a single equation

DeletedThe Analysis of Harold White applied to the Natario Warp Drive Spacetime. From $10$ times the mass of the Universe to arbitrary low levels of negative energy density using a continuous Natario shape function with power factors.Warp Drives with two warped regions

Warp Drives are solutions of the Einstein Field Equations that allows superluminal travel within the framework of General Relativity. There are at the present moment two known solutions: The Alcubierre warp drive discovered in $1994$ and the Natario warp drive discovered in $2001$. However as stated by both Alcubierre and Natario themselves the warp drive violates all the known energy conditions because the stress energy momentum tensor is negative implying in a negative energy density. While from a classical point of view the negative energy is forbidden the Quantum Field Theory allows the existence of very small amounts of it being the Casimir effect a good example as stated by Alcubierre himself.The major drawback concerning negative energies for the warp drive is the huge amount of negative energy able to sustain the warp bubble.Ford and Pfenning computed the amount of negative energy needed to maintain an Alcubierre warp drive and they arrived at the result of $10$ times the mass of the entire Universe for a stable warp drive configuration rendering the warp drive impossible.However Harold White manipulating the parameter $@$ in the original shape function that defines the Alcubierre spacetime demonstrated that it is possible to low these energy density requirements.We repeat here the Harold White analysis for the Natario spacetime and we arrive at similar conclusions.From $10$ times the mass of the Universe we also manipulated the parameter $@$ in the original shape function that defines the Natario spacetime and we arrived at arbitrary low results.We demonstrate in this work that both Alcubierre and Natario warp drives have two warped regions and not only one.We also discuss Horizons and Doppler Blueshifts.The main reason of this work is to demonstrate that Harold White point of view is entirely correct.

Deletedhttp://hal.archives-ouvertes.fr/INSMI/hal-00844801/fr/

Graham Allan Partis· University of Southern QueenslandI assume you have read Kip Thorne's work.

Can you help by adding an answer?