Wikipedia

Faster-than-light

(Redirected fromFaster Than Light)
For other uses, seeFaster-than-light (disambiguation).

Faster-than-light(superluminalorsupercausal)travelandcommunicationare the conjectural propagation ofmatterorinformationfaster than thespeed of light(c). Thespecial theory of relativityimplies that only particles with zerorest mass(i.e.,photons) may travelatthe speed of light, and that nothing may travel faster.

Because the sphere travels faster than light, the observer sees nothing until it has already passed. Then, two images appear: one of the sphere arriving (on the right) and one of it departing (on the left).

Particles whose speed exceeds that of light (tachyons) have been hypothesized, but their existence would violatecausalityand would implytime travel.Thescientific consensusis that they do not exist.

According to all observations and current scientific theories, matter travels atslower-than-light(subluminal) speed with respect to the locally distorted spacetime region. Speculative faster-than-light concepts include theAlcubierre drive,Krasnikov tubes,traversable wormholes,andquantum tunneling.[1][2]Some of these proposals find loopholes around general relativity, such as by expanding or contracting space to make the object appear to be travelling greater thanc.Such proposals are still widely believed to be impossible as they still violate current understandings of causality, and they all require fanciful mechanisms to work (such as requiringexotic matter).

Superluminal travel of non-information

edit
Main article:Superluminal motion

In the context of this article, "faster-than-light" means the transmission of information or matter faster thanc,a constant equal to thespeed of lightin vacuum, which is 299,792,458 m/s (by definition of the metre)[3]or about 186,282.397 miles per second. This is not quite the same as traveling faster than light, since:

  • Some processes propagate faster thanc,but cannot carry information (see examples in the sections immediately following).
  • In some materials where light travels at speedc/n(wherenis therefractive index) other particles can travel faster thanc/n(but still slower thanc), leading toCherenkov radiation(seephase velocity below).

Neither of these phenomena violatesspecial relativityor creates problems withcausality,and thus neither qualifies as faster-than-light as described here.

In the following examples, certain influences may appear to travel faster than light, but they do not convey energy or information faster than light, so they do not violate special relativity.

Daily sky motion

edit

For an earth-bound observer, objects in the sky complete one revolution around the Earth in one day.Proxima Centauri,the nearest star outside theSolar System,is about four and a halflight-yearsaway.[4]In this frame of reference, in which Proxima Centauri is perceived to be moving in a circular trajectory with a radius of four light years, it could be described as having a speed many times greater thancas the rim speed of an object moving in a circle is a product of the radius and angular speed.[4]It is also possible on ageostaticview, for objects such as comets to vary their speed from subluminal to superluminal and vice versa simply because the distance from the Earth varies. Comets may have orbits which take them out to more than 1000AU.[5]The circumference of a circle with a radius of 1000 AU is greater than one light day. In other words, a comet at such a distance is superluminal in a geostatic, and therefore non-inertial, frame.

Light spots and shadows

edit

If a laser beam is swept across a distant object, the spot of laser light can seem to move across the object at a speed greater thanc.[6]Similarly, a shadow projected onto a distant object seems to move across the object faster thanc.[6]In neither case does the light travel from the source to the object faster thanc,nor does any information travel faster than light. No object is moving in these examples. For comparison, consider water squirting out of a garden hose as it is swung side to side: water does not instantly follow the direction of the hose.[6][7][8]

Closing speeds

edit

The rate at which two objects in motion in a single frame of reference get closer together is called the mutual or closing speed. This may approach twice the speed of light, as in the case of two particles travelling at close to the speed of light in opposite directions with respect to the reference frame.

Imagine two fast-moving particles approaching each other from opposite sides of aparticle acceleratorof the collider type. The closing speed would be the rate at which the distance between the two particles is decreasing. From the point of view of an observer standing at rest relative to the accelerator, this rate will be slightly less than twice the speed of light.

Special relativitydoes not prohibit this. It tells us that it is wrong to useGalilean relativityto compute the velocity of one of the particles, as would be measured by an observer traveling alongside the other particle. That is, special relativity gives the correctvelocity-addition formulafor computing suchrelative velocity.

It is instructive to compute the relative velocity of particles moving atvand −vin accelerator frame, which corresponds to the closing speed of 2v>c.Expressing the speeds in units ofc,β=v/c:

Proper speeds

edit

If a spaceship travels to a planet one light-year (as measured in the Earth's rest frame) away from Earth at high speed, the time taken to reach that planet could be less than one year as measured by the traveller's clock (although it will always be more than one year as measured by a clock on Earth). The value obtained by dividing the distance traveled, as determined in the Earth's frame, by the time taken, measured by the traveller's clock, is known as a proper speed or aproper velocity.There is no limit on the value of a proper speed as a proper speed does not represent a speed measured in a single inertial frame. A light signal that left the Earth at the same time as the traveller would always get to the destination before the traveller would.

Phase velocities abovec

edit

Thephase velocityof anelectromagnetic wave,when traveling through a medium, can routinely exceedc,the vacuum velocity of light. For example, this occurs in most glasses atX-rayfrequencies.[9]However, the phase velocity of a wave corresponds to the propagation speed of a theoretical single-frequency (purelymonochromatic) component of the wave at that frequency. Such a wave component must be infinite in extent and of constant amplitude (otherwise it is not truly monochromatic), and so cannot convey any information.[10] Thus a phase velocity abovecdoes not imply the propagation ofsignalswith a velocity abovec.[11]

Group velocities abovec

edit

Thegroup velocityof a wave may also exceedcin some circumstances.[12][13]In such cases, which typically at the same time involve rapid attenuation of the intensity, the maximum of the envelope of a pulse may travel with a velocity abovec.However, even this situation does not imply the propagation ofsignalswith a velocity abovec,[14]even though one may be tempted to associate pulse maxima with signals. The latter association has been shown to be misleading, because the information on the arrival of a pulse can be obtained before the pulse maximum arrives. For example, if some mechanism allows the full transmission of the leading part of a pulse while strongly attenuating the pulse maximum and everything behind (distortion), the pulse maximum is effectively shifted forward in time, while the information on the pulse does not come faster thancwithout this effect.[15]However, group velocitycan exceedcin some parts of aGaussian beamin vacuum (without attenuation). Thediffractioncauses the peak of the pulse to propagate faster, while overall power does not.[16]

Cosmic expansion

edit

According toHubble's law,theexpansion of the universecauses distant galaxies to recede from us faster than the speed of light. However, the recession speed associated withHubble's law,defined as the rate of increase inproper distanceper interval ofcosmological time,is not a velocity in a relativistic sense. Moreover, ingeneral relativity,velocity is a local notion, and there is not even a unique definition for the relative velocity of a cosmologically distant object.[17]Faster-than-light cosmological recession speeds are entirely acoordinateeffect.

There are many galaxies visible in telescopes withredshiftnumbers of 1.4 or higher. All of these have cosmological recession speeds greater than the speed of light. Because theHubble parameteris decreasing with time, there can actually be cases where a galaxy that is receding from us faster than light does manage to emit a signal which reaches us eventually.[18][19][20]

However, becausethe expansion of the universe is accelerating,it is projected that most galaxies will eventually cross a type of cosmologicalevent horizonwhere any light they emit past that point will never be able to reach us at any time in the infinite future,[21]because the light never reaches a point where its "peculiar velocity" towards us exceeds the expansion velocity away from us (these two notions of velocity are also discussed inComoving and proper distances#Uses of the proper distance). The current distance to this cosmological event horizon is about 16 billion light-years, meaning that a signal from an event happening at present would eventually be able to reach us in the future if the event was less than 16 billion light-years away, but the signal would never reach us if the event was more than 16 billion light-years away.[19]

Astronomical observations

edit

Apparentsuperluminal motionis observed in manyradio galaxies,blazars,quasars,and recently also inmicroquasars.The effect was predicted before it was observed byMartin Rees[clarification needed]and can be explained as anoptical illusioncaused by the object partly moving in the direction of the observer,[22]when the speed calculations assume it does not. The phenomenon does not contradict the theory ofspecial relativity.Corrected calculations show these objects have velocities close to the speed of light (relative to our reference frame). They are the first examples of large amounts of mass moving at close to the speed of light.[23]Earth-bound laboratories have only been able to accelerate small numbers of elementary particles to such speeds.

Quantum mechanics

edit

Certain phenomena inquantum mechanics,such asquantum entanglement,might give the superficial impression of allowing communication of information faster than light. According to theno-communication theoremthese phenomena do not allow true communication; they only let two observers in different locations see the same system simultaneously, without any way of controlling what either sees.Wavefunction collapsecan be viewed as anepiphenomenonof quantum decoherence, which in turn is nothing more than an effect of the underlying local time evolution of the wavefunction of a system andallof its environment. Since the underlying behavior does not violate local causality or allow FTL communication, it follows that neither does the additional effect of wavefunction collapse, whether realorapparent.

Theuncertainty principleimplies that individual photons may travel for short distances at speeds somewhat faster (or slower) thanc,even in vacuum; this possibility must be taken into account when enumeratingFeynman diagramsfor a particle interaction.[24]However, it was shown in 2011 that a single photon may not travel faster thanc.[25]

There have been various reports in the popular press of experiments on faster-than-light transmission in optics — most often in the context of a kind ofquantum tunnellingphenomenon. Usually, such reports deal with aphase velocityorgroup velocityfaster than the vacuum velocity of light.[26][27]However, as stated above, a superluminal phase velocity cannot be used for faster-than-light transmission of information[28][29]

Hartman effect

edit
Main article:Hartman effect

The Hartman effect is the tunneling effect through a barrier where the tunneling time tends to a constant for large barriers.[30][31]This could, for instance, be the gap between two prisms. When the prisms are in contact, the light passes straight through, but when there is a gap, the light is refracted. There is a non-zero probability that the photon will tunnel across the gap rather than follow the refracted path.

However, it has been claimed that the Hartman effect cannot actually be used to violate relativity by transmitting signals faster thanc,also because the tunnelling time "should not be linked to a velocity since evanescent waves do not propagate".[32]The evanescent waves in the Hartman effect are due to virtual particles and a non-propagating static field, as mentioned in the sections above for gravity and electromagnetism.

Casimir effect

edit
Main article:Casimir effect

In physics, theCasimir–Polder forceis a physical force exerted between separate objects due to resonance ofvacuum energyin the intervening space between the objects. This is sometimes described in terms of virtual particles interacting with the objects, owing to the mathematical form of one possible way of calculating the strength of the effect. Because the strength of the force falls off rapidly with distance, it is only measurable when the distance between the objects is extremely small. Because the effect is due to virtual particles mediating a static field effect, it is subject to the comments about static fields discussed above.

EPR paradox

edit
Main article:EPR paradox

The EPR paradox refers to a famousthought experimentofAlbert Einstein,Boris PodolskyandNathan Rosenthat was realized experimentally for the first time byAlain Aspectin 1981 and 1982 in theAspect experiment.In this experiment, the two measurements of anentangledstate are correlated even when the measurements are distant from the source and each other. However, no information can be transmitted this way; the answer to whether or not the measurement actually affects the other quantum system comes down to whichinterpretation of quantum mechanicsone subscribes to.

An experiment performed in 1997 byNicolas Gisinhas demonstrated quantum correlations between particles separated by over 10 kilometers.[33]But as noted earlier, the non-local correlations seen in entanglement cannot actually be used to transmit classical information faster than light, so that relativistic causality is preserved. The situation is akin to sharing a synchronized coin flip, where the second person to flip their coin will always see the opposite of what the first person sees, but neither has any way of knowing whether they were the first or second flipper, without communicating classically. SeeNo-communication theoremfor further information. A 2008 quantum physics experiment also performed by Nicolas Gisin and his colleagues has determined that in any hypotheticalnon-local hidden-variable theory,the speed of thequantum non-local connection(what Einstein called "spooky action at a distance" ) is at least 10,000 times the speed of light.[34]

Delayed choice quantum eraser

edit
Main article:Delayed-choice quantum eraser

Thedelayed-choice quantum eraseris a version of the EPR paradox in which the observation (or not) of interference after the passage of a photon through adouble slit experimentdepends on the conditions of observation of a second photon entangled with the first. The characteristic of this experiment is that the observation of the second photon can take place at a later time than the observation of the first photon,[35]which may give the impression that the measurement of the later photons "retroactively" determines whether the earlier photons show interference or not, although the interference pattern can only be seen by correlating the measurements of both members of every pair and so it cannot be observed until both photons have been measured, ensuring that an experimenter watching only the photons going through the slit does not obtain information about the other photons in an faster-than-light or backwards-in-time manner.[36][37]

Superluminal communication

edit
Main article:Superluminal communication

Faster-than-light communication is, according to relativity, equivalent totime travel.What we measure as thespeed of lightin vacuum (or near vacuum) is actually the fundamental physical constantc.This means that allinertialand, for the coordinate speed of light, non-inertial observers, regardless of their relativevelocity,will always measure zero-mass particles such asphotonstraveling atcin vacuum. This result means that measurements of time and velocity in different frames are no longer related simply by constant shifts, but are instead related byPoincaré transformations.These transformations have important implications:

  • The relativistic momentum of amassiveparticle would increase with speed in such a way that at the speed of light an object would have infinite momentum.
  • To accelerate an object of non-zerorest masstocwould require infinite time with any finite acceleration, or infinite acceleration for a finite amount of time.
  • Either way, such acceleration requires infinite energy.
  • Some observers with sub-light relative motion will disagree about which occurs first of any two events that are separated by aspace-like interval.[38]In other words, any travel that is faster-than-light will be seen as traveling backwards in time in some other, equally valid, frames of reference,[39]or need to assume the speculative hypothesis of possible Lorentz violations at a presently unobserved scale (for instance the Planck scale).[citation needed]Therefore, any theory which permits "true" FTL also has to cope withtime traveland all its associated paradoxes,[40]or else to assume theLorentz invarianceto be a symmetry of thermodynamical statistical nature (hence a symmetry broken at some presently unobserved scale).
  • In special relativity the coordinate speed of light is only guaranteed to becin aninertial frame;in a non-inertial frame the coordinate speed may be different fromc.[41]In general relativity no coordinate system on a large region of curved spacetime is "inertial", so it is permissible to use a global coordinate system where objects travel faster thanc,but in the local neighborhood of any point in curved spacetime we can define a "local inertial frame" and the local speed of light will becin this frame,[42]with massive objects moving through this local neighborhood always having a speed less thancin the local inertial frame.

Justifications

edit

Casimir vacuum and quantum tunnelling

edit

Special relativitypostulates that the speed of light in vacuum is invariant ininertial frames.That is, it will be the same from any frame of reference moving at a constant speed. The equations do not specify any particular value for the speed of light, which is an experimentally determined quantity for a fixed unit of length. Since 1983, theSIunit of length (themeter) has been defined using thespeed of light.

The experimental determination has been made in vacuum. However, the vacuum we know is not the only possible vacuum which can exist. The vacuum has energy associated with it, called simply thevacuum energy,which could perhaps be altered in certain cases.[43]When vacuum energy is lowered, light itself has been predicted to go faster than the standard valuec.This is known as theScharnhorst effect.Such a vacuum can be produced by bringing two perfectly smooth metal plates together at near atomic diameter spacing. It is called aCasimir vacuum.Calculations imply that light will go faster in such a vacuum by a minuscule amount: a photon traveling between two plates that are 1 micrometer apart would increase the photon's speed by only about one part in 1036.[44]Accordingly, there has as yet been no experimental verification of the prediction. A recent analysis[45]argued that the Scharnhorst effect cannot be used to send information backwards in time with a single set of plates since the plates' rest frame would define a "preferred frame"for FTL signaling. However, with multiple pairs of plates in motion relative to one another the authors noted that they had no arguments that could" guarantee the total absence of causality violations ", and invoked Hawking's speculativechronology protection conjecturewhich suggests that feedback loops of virtual particles would create "uncontrollable singularities in the renormalized quantum stress-energy" on the boundary of any potential time machine, and thus would require a theory of quantum gravity to fully analyze. Other authors argue that Scharnhorst's original analysis, which seemed to show the possibility of faster-than-csignals, involved approximations which may be incorrect, so that it is not clear whether this effect could actually increase signal speed at all.[46]

It was later claimed by Eckleet al.that particle tunneling does indeed occur in zero real time.[47]Their tests involved tunneling electrons, where the group argued a relativistic prediction for tunneling time should be 500–600 attoseconds (anattosecondis one quintillionth (10−18) of a second). All that could be measured was 24 attoseconds, which is the limit of the test accuracy. Again, though, other physicists believe that tunneling experiments in which particles appear to spend anomalously short times inside the barrier are in fact fully compatible with relativity, although there is disagreement about whether the explanation involves reshaping of the wave packet or other effects.[48][49][50]

Give up (absolute) relativity

edit

Because of the strong empirical support forspecial relativity,any modifications to it must necessarily be quite subtle and difficult to measure. The best-known attempt isdoubly special relativity,which posits that thePlanck lengthis also the same in all reference frames, and is associated with the work ofGiovanni Amelino-CameliaandJoão Magueijo.[51][52] There are speculative theories that claim inertia is produced by the combined mass of the universe (e.g.,Mach's principle), which implies that the rest frame of the universe might bepreferredby conventional measurements of natural law. If confirmed, this would implyspecial relativityis an approximation to a more general theory, but since the relevant comparison would (by definition) be outside theobservable universe,it is difficult to imagine (much less construct) experiments to test this hypothesis. Despite this difficulty, such experiments have been proposed.[53]

Spacetime distortion

edit

Although the theory ofspecial relativityforbids objects to have a relative velocity greater than light speed, andgeneral relativityreduces to special relativity in a local sense (in small regions of spacetime where curvature is negligible), general relativity does allow the space between distant objects to expand in such a way that they have a "recession velocity"which exceeds the speed of light, and it is thought that galaxies which are at a distance of more than about 14 billion light-years from us today have a recession velocity which is faster than light.[19]Miguel Alcubierretheorized that it would be possible to create awarp drive,in which a ship would be enclosed in a "warp bubble" where the space at the front of the bubble is rapidly contracting and the space at the back is rapidly expanding, with the result that the bubble can reach a distant destination much faster than a light beam moving outside the bubble, but without objects inside the bubble locally traveling faster than light.[54]However,several objectionsraised against the Alcubierre drive appear to rule out the possibility of actually using it in any practical fashion. Another possibility predicted by general relativity is thetraversable wormhole,which could create a shortcut between arbitrarily distant points in space. As with the Alcubierre drive, travelers moving through the wormhole would notlocallymove faster than light travelling through the wormhole alongside them, but they would be able to reach their destination (and return to their starting location) faster than light traveling outside the wormhole.

Gerald Cleaver and Richard Obousy, a professor and student ofBaylor University,theorized that manipulating the extra spatial dimensions ofstring theoryaround a spaceship with an extremely large amount of energy would create a "bubble" that could cause the ship to travel faster than the speed of light. To create this bubble, the physicists believe manipulating the 10th spatial dimension would alter thedark energyin three large spatial dimensions: height, width and length. Cleaver said positive dark energy is currently responsible for speeding up the expansion rate of our universe as time moves on.[55]

Lorentz symmetry violation

edit
Main articles:Modern searches for Lorentz violationandStandard-Model Extension

The possibility that Lorentz symmetry may be violated has been seriously considered in the last two decades, particularly after the development of a realistic effective field theory that describes this possible violation, the so-calledStandard-Model Extension.[56][57][58]This general framework has allowed experimental searches by ultra-high energy cosmic-ray experiments[59]and a wide variety of experiments in gravity, electrons, protons, neutrons, neutrinos, mesons, and photons.[60] The breaking of rotation and boost invariance causes direction dependence in the theory as well as unconventional energy dependence that introduces novel effects, includingLorentz-violating neutrino oscillationsand modifications to the dispersion relations of different particle species, which naturally could make particles move faster than light.

In some models of broken Lorentz symmetry, it is postulated that the symmetry is still built into the most fundamental laws of physics, but thatspontaneous symmetry breakingof Lorentz invariance[61]shortly after theBig Bangcould have left a "relic field" throughout the universe which causes particles to behave differently depending on their velocity relative to the field;[62]however, there are also some models where Lorentz symmetry is broken in a more fundamental way. If Lorentz symmetry can cease to be a fundamental symmetry at the Planck scale or at some other fundamental scale, it is conceivable that particles with a critical speed different from the speed of light be the ultimate constituents of matter.

In current models of Lorentz symmetry violation, the phenomenological parameters are expected to be energy-dependent. Therefore, as widely recognized,[63][64]existing low-energy bounds cannot be applied to high-energy phenomena; however, many searches for Lorentz violation at high energies have been carried out using theStandard-Model Extension.[60] Lorentz symmetry violation is expected to become stronger as one gets closer to the fundamental scale.

Superfluid theories of physical vacuum

edit
Main article:Superfluid vacuum theory

In this approach, the physicalvacuumis viewed as a quantumsuperfluidwhich is essentially non-relativistic, whereasLorentz symmetryis not an exact symmetry of nature but rather the approximate description valid only for the small fluctuations of the superfluid background.[65]Within the framework of the approach, a theory was proposed in which the physical vacuum is conjectured to be aquantum Bose liquidwhose ground-statewavefunctionis described by thelogarithmic Schrödinger equation.It was shown that therelativistic gravitational interactionarises as the small-amplitudecollective excitationmode[66]whereas relativisticelementary particlescan be described by theparticle-like modesin the limit of low momenta.[67]The important fact is that at very high velocities the behavior of the particle-like modes becomes distinct from therelativisticone – they can reach thespeed of light limitat finite energy; also, faster-than-light propagation is possible without requiring moving objects to haveimaginary mass.[68][69]

FTL neutrino flight results

edit

MINOS experiment

edit
Main article:MINOS

In 2007 theMINOScollaboration reported results measuring the flight-time of 3GeVneutrinosyielding a speed exceeding that of light by 1.8-sigma significance.[70]However, those measurements were considered to be statistically consistent with neutrinos traveling at the speed of light.[71]After the detectors for the project were upgraded in 2012, MINOS corrected their initial result and found agreement with the speed of light. Further measurements are going to be conducted.[72]

OPERA neutrino anomaly

edit
Main article:Faster-than-light neutrino anomaly

On September 22, 2011, a preprint[73]from theOPERA Collaborationindicated detection of 17 and 28 GeV muon neutrinos, sent 730 kilometers (454 miles) fromCERNnearGeneva, Switzerlandto theGran Sasso National Laboratoryin Italy, traveling faster than light by a relative amount of2.48×10−5(approximately 1 in 40,000), a statistic with 6.0-sigma significance.[74]On 17 November 2011, a second follow-up experiment by OPERA scientists confirmed their initial results.[75][76]However, scientists were skeptical about the results of these experiments, the significance of which was disputed.[77]In March 2012, theICARUS collaborationfailed to reproduce the OPERA results with their equipment, detecting neutrino travel time from CERN to the Gran Sasso National Laboratory indistinguishable from the speed of light.[78]Later the OPERA team reported two flaws in their equipment set-up that had caused errors far outside their originalconfidence interval:afiber-optic cableattached improperly, which caused the apparently faster-than-light measurements, and a clock oscillator ticking too fast.[79]

Tachyons

edit
Main article:Tachyon

In special relativity, it is impossible to accelerate an objecttothe speed of light, or for a massive object to moveatthe speed of light. However, it might be possible for an object to exist whichalwaysmoves faster than light. The hypotheticalelementary particleswith this property are called tachyons or tachyonic particles. Attemptsto quantize themfailed to produce faster-than-light particles, and instead illustrated that their presence leads to an instability.[80][81]

Various theorists have suggested that theneutrinomight have a tachyonic nature,[82][83][84][85]while others have disputed the possibility.[86]

General relativity

edit

General relativitywas developed afterspecial relativityto include concepts likegravity.It maintains the principle that no object can accelerate to the speed of light in the reference frame of any coincident observer.[citation needed]However, it permits distortions inspacetimethat allow an object to move faster than light from the point of view of a distant observer.[citation needed]One suchdistortionis theAlcubierre drive,which can be thought of as producing a ripple inspacetimethat carries an object along with it. Another possible system is thewormhole,which connects two distant locations as though by a shortcut. Both distortions would need to create a very strong curvature in a highly localized region of space-time and their gravity fields would be immense. To counteract the unstable nature, and prevent the distortions from collapsing under their own 'weight', one would need to introduce hypotheticalexotic matteror negative energy.

General relativity also recognizes that any means of faster-than-lighttravelcould also be used fortime travel.This raises problems withcausality.Many physicists believe that the above phenomena are impossible and that future theories ofgravitywill prohibit them. One theory states that stable wormholes are possible, but that any attempt to use a network of wormholes to violate causality would result in their decay.[citation needed]Instring theory,Eric G. Gimon andPetr Hořavahave argued[87]that in asupersymmetricfive-dimensionalGödel universe,quantum corrections to general relativity effectively cut off regions of spacetime with causality-violating closed timelike curves. In particular, in the quantum theory a smeared supertube is present that cuts the spacetime in such a way that, although in the full spacetime a closed timelike curve passed through every point, no complete curves exist on the interior region bounded by the tube.

edit
See also:Space travel in science fiction

FTL travel is a commonplot deviceinscience fiction.[88]

See also

edit

Notes

edit
  1. ^"Quantum-tunnelling time is measured using ultracold atoms".Physics World.22 July 2020.
  2. ^"Quanta Magazine".20 October 2020.
  3. ^"The 17th Conférence Générale des Poids et Mesures (CGPM): Definition of the metre".bipm.org.Archived fromthe originalon May 27, 2020.RetrievedJuly 5,2020.
  4. ^ab University of York Science Education Group (2001).Salter Horners Advanced Physics A2 Student Book.Heinemann. pp. 302–303.ISBN978-0435628925.
  5. ^ "The Furthest Object in the Solar System".Information Leaflet No. 55.Royal Greenwich Observatory. 15 April 1996.
  6. ^abc Gibbs, P. (1997)."Is Faster-Than-Light Travel or Communication Possible?".The Original Usenet Physics FAQ.Retrieved20 August2008.
  7. ^ Salmon, W. C. (2006).Four Decades of Scientific Explanation.University of Pittsburgh Press.p. 107.ISBN978-0-8229-5926-7.
  8. ^ Steane, A. (2012).The Wonderful World of Relativity: A Precise Guide for the General Reader.Oxford University Press.p. 180.ISBN978-0-19-969461-7.
  9. ^ Hecht, E. (1987).Optics(2nd ed.).Addison Wesley.p. 62.ISBN978-0-201-11609-0.
  10. ^ Sommerfeld, A. (1907)."An Objection Against the Theory of Relativity and its Removal".Physikalische Zeitschrift.8(23): 841–842.
  11. ^ Weber, J. (1954)."Phase, Group, and Signal Velocity".American Journal of Physics.22(9): 618.Bibcode:1954AmJPh..22..618W.doi:10.1119/1.1933858.Retrieved2007-04-30.
  12. ^ Wang, L. J.; Kuzmich, A.; Dogariu, A. (2000). "Gain-assisted superluminal light propagation".Nature.406(6793): 277–279.Bibcode:2000Natur.406..277W.doi:10.1038/35018520.PMID10917523.S2CID4358601.
  13. ^ Bowlan, P.; Valtna-Lukner, H.; Lõhmus, M.; Piksarv, P.; Saari, P.; Trebino, R. (2009). "Measurement of the spatiotemporal electric field of ultrashort superluminal Bessel-X pulses".Optics and Photonics News.20(12): 42.Bibcode:2009OptPN..20...42M.doi:10.1364/OPN.20.12.000042.S2CID122056218.
  14. ^ Brillouin, L. (1960).Wave Propagation and Group Velocity.Academic Press.
  15. ^ Withayachumnankul, W.; Fischer, B. M.; Ferguson, B.; Davis, B. R.; Abbott, D. (2010)."A Systemized View of Superluminal Wave Propagation"(PDF).Proceedings of the IEEE.98(10): 1775–1786.doi:10.1109/JPROC.2010.2052910.S2CID15100571.
  16. ^ Horváth, Z. L.; Vinkó, J.; Bor, Zs.; von der Linde, D. (1996)."Acceleration of femtosecond pulses to superluminal velocities by Gouy phase shift"(PDF).Applied Physics B.63(5): 481–484.Bibcode:1996ApPhB..63..481H.doi:10.1007/BF01828944.S2CID54757568.Archived(PDF)from the original on 2003-04-03.
  17. ^ Wright, E. L. (12 June 2009)."Cosmology Tutorial – Part 2".Ned Wright's Cosmology Tutorial.UCLA.Retrieved2011-09-26.
  18. ^See the last two paragraphs inRothstein, D. (10 September 2003)."Is the universe expanding faster than the speed of light?".Ask an Astronomer.
  19. ^abc Lineweaver, C.; Davis, T. M. (March 2005)."Misconceptions about the Big Bang"(PDF).Scientific American.pp. 36–45.Archived(PDF)from the original on 2006-05-27.Retrieved2008-11-06.
  20. ^ Davis, T. M.; Lineweaver, C. H. (2004). "Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the universe".Publications of the Astronomical Society of Australia.21(1): 97–109.arXiv:astro-ph/0310808.Bibcode:2004PASA...21...97D.doi:10.1071/AS03040.S2CID13068122.
  21. ^ Loeb, A. (2002). "The Long-Term Future of Extragalactic Astronomy".Physical Review D.65(4): 047301.arXiv:astro-ph/0107568.Bibcode:2002PhRvD..65d7301L.doi:10.1103/PhysRevD.65.047301.S2CID1791226.
  22. ^ Rees, M. J. (1966). "Appearance of relativistically expanding radio sources".Nature.211(5048): 468–470.Bibcode:1966Natur.211..468R.doi:10.1038/211468a0.S2CID41065207.
  23. ^ Blandford, R. D.;McKee, C. F.; Rees, M. J. (1977). "Super-luminal expansion in extragalactic radio sources".Nature.267(5608): 211–216.Bibcode:1977Natur.267..211B.doi:10.1038/267211a0.S2CID4260167.
  24. ^ Grozin, A. (2007).Lectures on QED and QCD.World Scientific.p.89.ISBN978-981-256-914-1.
  25. ^ Zhang, S.; Chen, J. F.; Liu, C.; Loy, M. M. T.; Wong, G. K. L.; Du, S. (2011)."Optical Precursor of a Single Photon"(PDF).Physical Review Letters.106(24): 243602.Bibcode:2011PhRvL.106x3602Z.doi:10.1103/PhysRevLett.106.243602.PMID21770570.Archived(PDF)from the original on 2019-12-05.
  26. ^ Kåhre, J. (2012).The Mathematical Theory of Information(Illustrated ed.).Springer Science & Business Media.p. 425.ISBN978-1-4615-0975-2.
  27. ^ Steinberg, A. M. (1994).When Can Light Go Faster Than Light?(Thesis).University of California, Berkeley.p. 100.Bibcode:1994PhDT.......314S.
  28. ^ Chubb, J.; Eskandarian, A.; Harizanov, V. (2016).Logic and Algebraic Structures in Quantum Computing(Illustrated ed.).Cambridge University Press.p. 61.ISBN978-1-107-03339-9.
  29. ^ Ehlers, J.; Lämmerzahl, C. (2006).Special Relativity: Will it Survive the Next 101 Years?(Illustrated ed.). Springer. p. 506.ISBN978-3-540-34523-7.
  30. ^ Martinez, J. C.; Polatdemir, E. (2006). "Origin of the Hartman effect".Physics Letters A.351(1–2): 31–36.Bibcode:2006PhLA..351...31M.doi:10.1016/j.physleta.2005.10.076.
  31. ^ Hartman, T. E. (1962). "Tunneling of a Wave Packet".Journal of Applied Physics.33(12): 3427–3433.Bibcode:1962JAP....33.3427H.doi:10.1063/1.1702424.
  32. ^ Winful, H. G. (2006). "Tunneling time, the Hartman effect, and superluminality: A proposed resolution of an old paradox".Physics Reports.436(1–2): 1–69.Bibcode:2006PhR...436....1W.doi:10.1016/j.physrep.2006.09.002.
  33. ^ Suarez, A. (26 February 2015)."History".Center for Quantum Philosophy.Retrieved2017-06-07.
  34. ^ Salart, D.; Baas, A.; Branciard, C.; Gisin, N.; Zbinden, H. (2008). "Testing spooky action at a distance".Nature.454(7206): 861–864.arXiv:0808.3316.Bibcode:2008Natur.454..861S.doi:10.1038/nature07121.PMID18704081.S2CID4401216.
  35. ^ Kim, Yoon-Ho; Yu, Rong; Kulik, Sergei P.; Shih, Yanhua; Scully, Marlan O. (2000). "Delayed" Choice "Quantum Eraser".Physical Review Letters.84(1): 1–5.arXiv:quant-ph/9903047.Bibcode:2000PhRvL..84....1K.doi:10.1103/PhysRevLett.84.1.PMID11015820.S2CID5099293.
  36. ^ Hillmer, R.;Kwiat, P.(16 April 2017)."Delayed-Choice Experiments".Scientific American.
  37. ^ Motl, L. (November 2010)."Delayed choice quantum eraser".The Reference Frame.
  38. ^ Einstein, A. (1927).Relativity:the special and the general theory.Methuen & Co. pp. 25–27.
  39. ^ Odenwald, S."If we could travel faster than light, could we go back in time?".NASA Astronomy Café.Retrieved7 April2014.
  40. ^ Gott, J. R. (2002).Time Travel in Einstein's Universe.Mariner Books.pp. 82–83.ISBN978-0618257355.
  41. ^ Petkov, V. (2009).Relativity and the Nature of Spacetime.Springer Science & Business Media.p. 219.ISBN978-3642019623.
  42. ^ Raine, D. J.; Thomas, E. G. (2001).An Introduction to the Science of Cosmology.CRC Press.p. 94.ISBN978-0750304054.
  43. ^"What is the 'zero-point energy' (or 'vacuum energy') in quantum physics? Is it really possible that we could harness this energy?".Scientific American.1997-08-18.Retrieved2009-05-27.
  44. ^Scharnhorst, Klaus (1990-05-12)."Secret of the vacuum: Speedier light".Vrije Universiteit Amsterdam.Retrieved2009-05-27.
  45. ^Liberati, Stefano; Sonego, Sebastiano; Visser, Matt (2002). "Faster-than-c Signals, Special Relativity, and Causality".Annals of Physics.298(1): 167–185.arXiv:gr-qc/0107091.Bibcode:2002AnPhy.298..167L.doi:10.1006/aphy.2002.6233.S2CID48166.
  46. ^Fearn, H. (2007). "Can light signals travel faster thancin nontrivial vacua in flat space-time? Relativistic causality II ".Laser Physics.17(5): 695–699.arXiv:0706.0553.Bibcode:2007LaPhy..17..695F.doi:10.1134/S1054660X07050155.ISSN1054-660X.S2CID61962.
  47. ^Eckle, P.; Pfeiffer, A. N.; Cirelli, C.; Staudte, A.; Dorner, R.; Muller, H. G.; Buttiker, M.; Keller, U. (5 December 2008). "Attosecond Ionization and Tunneling Delay Time Measurements in Helium".Science.322(5907): 1525–1529.Bibcode:2008Sci...322.1525E.doi:10.1126/science.1163439.PMID19056981.S2CID206515239.
  48. ^Winful, Herbert G. (December 2006)."Tunneling time, the Hartman effect, and superluminality: A proposed resolution of an old paradox"(PDF).Physics Reports.436(1–2): 1–69.Bibcode:2006PhR...436....1W.doi:10.1016/j.physrep.2006.09.002.Archived fromthe original(PDF)on 2011-12-18.Retrieved2010-06-08.
  49. ^For a summary of Herbert G. Winful's explanation for apparently superluminal tunneling time which does not involve reshaping, seeWinful, Herbert (2007). "New paradigm resolves old paradox of faster-than-light tunneling".SPIE Newsroom.doi:10.1117/2.1200711.0927.
  50. ^Sokolovski, D. (8 February 2004). "Why does relativity allow quantum tunneling to 'take no time'?".Proceedings of the Royal Society A.460(2042): 499–506.Bibcode:2004RSPSA.460..499S.doi:10.1098/rspa.2003.1222.S2CID122620657.
  51. ^Amelino-Camelia, Giovanni (1 November 2009). "Doubly-Special Relativity: Facts, Myths and Some Key Open Issues".Recent Developments in Theoretical Physics.Statistical Science and Interdisciplinary Research. Vol. 9. pp. 123–170.arXiv:1003.3942.doi:10.1142/9789814287333_0006.ISBN978-981-4287-32-6.S2CID118855372.
  52. ^Amelino-Camelia, Giovanni (1 July 2002). "Doubly Special Relativity".Nature.418(6893): 34–35.arXiv:gr-qc/0207049.Bibcode:2002Natur.418...34A.doi:10.1038/418034a.PMID12097897.S2CID16844423.
  53. ^Chang, Donald C. (March 22, 2017)."Is there a resting frame in the universe? A proposed experimental test based on a precise measurement of particle mass".The European Physical Journal Plus.132(3): 140.arXiv:1706.05252.Bibcode:2017EPJP..132..140C.doi:10.1140/epjp/i2017-11402-4.
  54. ^Alcubierre, Miguel (1 May 1994). "The warp drive: hyper-fast travel within general relativity".Classical and Quantum Gravity.11(5): L73–L77.arXiv:gr-qc/0009013.Bibcode:1994CQGra..11L..73A.CiteSeerX10.1.1.338.8690.doi:10.1088/0264-9381/11/5/001.S2CID4797900.
  55. ^"Traveling Faster Than the Speed of Light: A New Idea That Could Make It Happen".www.newswise.com.Retrieved2023-08-24.
  56. ^Colladay, Don; Kostelecký, V. Alan (1997). "CPT violation and the standard model".Physical Review D.55(11): 6760–6774.arXiv:hep-ph/9703464.Bibcode:1997PhRvD..55.6760C.doi:10.1103/PhysRevD.55.6760.S2CID7651433.
  57. ^Colladay, Don; Kostelecký, V. Alan (1998). "Lorentz-violating extension of the standard model".Physical Review D.58(11): 116002.arXiv:hep-ph/9809521.Bibcode:1998PhRvD..58k6002C.doi:10.1103/PhysRevD.58.116002.S2CID4013391.
  58. ^Kostelecký, V. Alan (2004). "Gravity, Lorentz violation, and the standard model".Physical Review D.69(10): 105009.arXiv:hep-th/0312310.Bibcode:2004PhRvD..69j5009K.doi:10.1103/PhysRevD.69.105009.S2CID55185765.
  59. ^Gonzalez-Mestres, Luis (2009). "AUGER-HiRes results and models of Lorentz symmetry violation".Nuclear Physics B - Proceedings Supplements.190:191–197.arXiv:0902.0994.Bibcode:2009NuPhS.190..191G.doi:10.1016/j.nuclphysbps.2009.03.088.S2CID14848782.
  60. ^abKostelecký, V. Alan; Russell, Neil (2011). "Data tables for Lorentz and CPT violation".Reviews of Modern Physics.83(1): 11–31.arXiv:0801.0287.Bibcode:2011RvMP...83...11K.doi:10.1103/RevModPhys.83.11.S2CID3236027.
  61. ^Kostelecký, V. A.; Samuel, S. (15 January 1989)."Spontaneous breaking of Lorentz symmetry in string theory"(PDF).Physical Review D.39(2): 683–685.Bibcode:1989PhRvD..39..683K.doi:10.1103/PhysRevD.39.683.hdl:2022/18649.PMID9959689.Archived(PDF)from the original on 2021-07-13.
  62. ^"PhysicsWeb – Breaking Lorentz symmetry".PhysicsWeb. 2004-04-05. Archived fromthe originalon 2004-04-05.Retrieved2011-09-26.
  63. ^Mavromatos, Nick E. (15 August 2002)."Testing models for quantum gravity".CERN Courier.
  64. ^Overbye, Dennis (2002-12-31)."Interpreting the Cosmic Rays".The New York Times.ISSN0362-4331.Retrieved2023-08-24.
  65. ^Volovik, G. E. (2003). "The Universe in a helium droplet".International Series of Monographs on Physics.117:1–507.
  66. ^Zloshchastiev, Konstantin G. (2011). "Spontaneous symmetry breaking and mass generation as built-in phenomena in logarithmic nonlinear quantum theory".Acta Physica Polonica B.42(2): 261–292.arXiv:0912.4139.Bibcode:2011AcPPB..42..261Z.doi:10.5506/APhysPolB.42.261.S2CID118152708.
  67. ^Avdeenkov, Alexander V.; Zloshchastiev, Konstantin G. (2011). "Quantum Bose liquids with logarithmic nonlinearity: Self-sustainability and emergence of spatial extent".Journal of Physics B: Atomic, Molecular and Optical Physics.44(19): 195303.arXiv:1108.0847.Bibcode:2011JPhB...44s5303A.doi:10.1088/0953-4075/44/19/195303.S2CID119248001.
  68. ^Zloshchastiev, Konstantin G.; Chakrabarti, Sandip K.; Zhuk, Alexander I.; Bisnovatyi-Kogan, Gennady S. (2010). "Logarithmic nonlinearity in theories of quantum gravity: Origin of time and observational consequences".American Institute of Physics Conference Series.AIP Conference Proceedings.1206:288–297.arXiv:0906.4282.Bibcode:2010AIPC.1206..112Z.doi:10.1063/1.3292518.
  69. ^Zloshchastiev, Konstantin G. (2011). "Vacuum Cherenkov effect in logarithmic nonlinear quantum theory".Physics Letters A.375(24): 2305–2308.arXiv:1003.0657.Bibcode:2011PhLA..375.2305Z.doi:10.1016/j.physleta.2011.05.012.S2CID118152360.
  70. ^Adamson, P.; Andreopoulos, C.; Arms, K.; Armstrong, R.; Auty, D.; Avvakumov, S.; Ayres, D.; Baller, B.; et al. (2007). "Measurement of neutrino velocity with the MINOS detectors and NuMI neutrino beam".Physical Review D.76(7): 072005.arXiv:0706.0437.Bibcode:2007PhRvD..76g2005A.doi:10.1103/PhysRevD.76.072005.S2CID14358300.
  71. ^Overbye, Dennis (22 September 2011)."Tiny neutrinos may have broken cosmic speed limit".The New York Times.Archivedfrom the original on 2022-01-02.That group found, although with less precision, that the neutrino speeds were consistent with the speed of light.
  72. ^"MINOS reports new measurement of neutrino velocity".Fermilab today. June 8, 2012.RetrievedJune 8,2012.
  73. ^Adam, T.; et al. (OPERA Collaboration) (22 September 2011). "Measurement of the neutrino velocity with the OPERA detector in the CNGS beam".arXiv:1109.4897v1[hep-ex].
  74. ^Cho, Adrian;Neutrinos Travel Faster Than Light, According to One Experiment,Science NOW, 22 September 2011
  75. ^Overbye, Dennis (18 November 2011)."Scientists Report Second Sighting of Faster-Than-Light Neutrinos".The New York Times.Archivedfrom the original on 2022-01-02.Retrieved2011-11-18.
  76. ^Adam, T.; et al. (OPERA Collaboration) (17 November 2011). "Measurement of the neutrino velocity with the OPERA detector in the CNGS beam".arXiv:1109.4897v2[hep-ex].
  77. ^"Study rejects" faster than light "particle finding".Reuters.2011-11-20.Retrieved2023-08-24.
  78. ^Antonello, M.; et al. (ICARUS Collaboration) (15 March 2012). "Measurement of the neutrino velocity with the ICARUS detector at the CNGS beam".Physics Letters B.713(1): 17–22.arXiv:1203.3433.Bibcode:2012PhLB..713...17A.doi:10.1016/j.physletb.2012.05.033.S2CID55397067.
  79. ^Strassler, M.(2012-04-02)."OPERA: What Went Wrong".Of Particular Significance.Retrieved2023-08-24.
  80. ^Randall, Lisa;Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions,p. 286: "People initially thought of tachyons as particles travelling faster than the speed of light...But we now know that a tachyon indicates an instability in a theory that contains it. Regrettably forscience fiction fans,tachyons are not real physical particles that appear in nature. "
  81. ^Gates, S.James;Nishino, Hitoshi (October 2000)."Will the real 4D, N=1 SG limit of superstring/M-theory please stand up?".Physics Letters B.492(1–2): 178–186.arXiv:hep-th/0008206.Bibcode:2000PhLB..492..178G.doi:10.1016/S0370-2693(00)01073-X.
  82. ^Chodos, A.; Hauser, A. I.; Alan Kostelecký, V. (1985). "The neutrino as a tachyon".Physics Letters B.150(6): 431–435.Bibcode:1985PhLB..150..431C.doi:10.1016/0370-2693(85)90460-5.hdl:2022/20737.
  83. ^Chodos, Alan; Alan Kostelecký, V.; IUHET 280 (1994). "Nuclear null tests for spacelike neutrinos".Physics Letters B.336(3–4): 295–302.arXiv:hep-ph/9409404.Bibcode:1994PhLB..336..295C.doi:10.1016/0370-2693(94)90535-5.S2CID16496246.{{cite journal}}:CS1 maint: numeric names: authors list (link)
  84. ^Chodos, A.; Kostelecký, V. A.; Potting, R.; Gates, Evalyn (1992). "Null experiments for neutrino masses".Modern Physics Letters A.7(6): 467–476.Bibcode:1992MPLA....7..467C.doi:10.1142/S0217732392000422.
  85. ^Chang, Tsao (2002). "Parity Violation and Neutrino Mass".Nuclear Science and Techniques.13:129–133.arXiv:hep-ph/0208239.Bibcode:2002hep.ph....8239C.
  86. ^Hughes, R. J.; Stephenson, G. J. (1990)."Against tachyonic neutrinos".Physics Letters B.244(1): 95–100.Bibcode:1990PhLB..244...95H.doi:10.1016/0370-2693(90)90275-B.
  87. ^Gimon, Eric G.; Hořava, Petr (2004). "Over-rotating black holes, Gödel holography and the hypertube".arXiv:hep-th/0405019.
  88. ^"Themes: Faster Than Light: SFE: Science Fiction Encyclopedia".www.sf-encyclopedia.com.Retrieved2021-09-01.

Further reading

edit
edit
Wikimedia Commons has media related toFaster-than-light travel.
Retrieved from "https://en.wikipedia.org/w/index.php?title=Faster-than-light&oldid=1259522109"