Faster-than-light

For other uses, see Faster than the speed of light (disam-biguation).

Faster-than-light (also superluminal or FTL)communication and travel refer to the propagation ofinformation or matter faster than the speed of light.Under the special theory of relativity, a particle (that hasrest mass) with subluminal velocity needs innite energyto accelerate to the speed of light, although specialrelativity does not forbid the existence of particles thattravel faster than light at all times (tachyons).On the other hand, what some physicists refer to as ap-parent or eective FTL[1][2][3][4] depends on the hy-pothesis that unusually distorted regions of spacetimemight permit matter to reach distant locations in less timethan light could in normal or undistorted spacetime. Al-though according to current theories matter is still re-quired to travel subluminally with respect to the locallydistorted spacetime region, apparent FTL is not excludedby general relativity.Examples of FTL proposals are the Alcubierre drive andthe traversable wormhole, although their physical plausi-bility is uncertain.

1 FTL travel of non-informationIn the context of this article, FTL is the transmission ofinformation or matter faster than c, a constant equal to thespeed of light in a vacuum, which is 299,792,458 m/s (bydenition) or about 186,282.4 miles per second. This isnot quite the same as traveling faster than light, since:

Some processes propagate faster than c, but cannotcarry information (see examples in the sections im-mediately following).

Light travels at speed c/n when not in a vacuum buttravelling through a medium with refractive index =n (causing refraction), and in some materials otherparticles can travel faster than c/n (but still slowerthan c), leading to Cherenkov radiation (see phasevelocity below).

Neither of these phenomena violates special relativity orcreates problems with causality, and thus neither qualiesas FTL as described here.In the following examples, certain inuences may appearto travel faster than light, but they do not convey energy or

information faster than light, so they do not violate specialrelativity.

1.1 Daily sky motion

For an Earthbound observer, objects in the sky completeone revolution around the Earth in 1 day. Proxima Cen-tauri, which is the nearest star outside the solar system,is about 4 light-years away.[5] On a geostationary viewProxima Centauri has a speed many times greater thanc as the rim speed of an object moving in a circle is aproduct of the radius and angular speed.[5] It is also pos-sible on a geostatic view for objects such as comets tovary their speed from subluminal to superluminal and viceversa simply because the distance from the Earth varies.Cometsmay have orbits which take them out tomore than1000 AU.[6] The circumference of a circle with a radiusof 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.

1.2 Light spots and shadows

If a laser is swept across a distant object, the spot of laserlight can easily be made to move across the object ata speed greater than c.[7] Similarly, a shadow projectedonto a distant object can be made to move across the ob-ject faster than c.[7] In neither case does the light travelfrom the source to the object faster than c, nor does anyinformation travel faster than light.[7][8][9]

1.3 Apparent FTL propagation of staticeld eects

Main article: Static eld

Since there is no retardation (or aberration) of the ap-parent position of the source of a gravitational or electricstatic eld when the source moves with constant veloc-ity, the static eld eect may seem at rst glance tobe transmitted faster than the speed of light. How-ever, uniform motion of the static source may be re-moved with a change in reference frame, causing the di-rection of the static eld to change immediately, at alldistances. This is not a change of position which prop-agates, and thus this change cannot be used to transmitinformation from the source. No information or matter

1

2 1 FTL TRAVEL OF NON-INFORMATION

can be FTL-transmitted or propagated from source to re-ceiver/observer by an electromagnetic eld.

1.4 Closing speedsThe rate at which two objects in motion in a single frameof reference get closer together is called the mutual orclosing speed. This may approach twice the speed oflight, as in the case of two particles travelling at closeto the speed of light in opposite directions with respect tothe reference frame.Imagine two fast-moving particles approaching eachother from opposite sides of a particle accelerator of thecollider type. The closing speed would be the rate atwhich the distance between the two particles is decreas-ing. From the point of view of an observer standing atrest relative to the accelerator, this rate will be slightlyless than twice the speed of light.Special relativity does not prohibit this. It tells us thatit is wrong to use Galilean relativity to compute the ve-locity of one of the particles, as would be measured byan observer traveling alongside the other particle. Thatis, special relativity gives the right formula for computingsuch relative velocity.It is instructive to compute the relative velocity of parti-cles moving at v and -v in accelerator frame, which cor-responds to the closing speed of 2v > c. Expressing thespeeds in units of c, = v/c:

rel = +

1 + 2=

2

1 + 2 1:

1.5 Proper speedsIf a spaceship travels to a planet one light-year (as mea-sured in the Earths rest frame) away from Earth at highspeed, the time taken to reach that planet could be lessthan one year as measured by the travellers clock (al-though it will always be more than one year as measuredby a clock on Earth). The value obtained by dividingthe distance traveled, as determined in the Earths frame,by the time taken, measured by the travellers clock, isknown as a proper speed or a proper velocity. There isno limit on the value of a proper speed as a proper speeddoes not represent a speed measured in a single inertialframe. A light signal that left the Earth at the same timeas the traveller would always get to the destination beforethe traveller.

1.6 How far can one travel from the Earth?Since one might not travel faster than light, one mightconclude that a human can never travel further from theearth than 40 light-years if the traveler is active between

the age of 20 and 60. A traveler would then never be ableto reach more than the very few star systems which existwithin the limit of 20-40 light-years from the Earth. Thisis a mistaken conclusion: because of time dilation, thetraveler can travel thousands of light-years during their40 active years. If the spaceship accelerates at a constant1 g (in its own changing frame of reference), it will, after354 days, reach speeds a little under the speed of light(for an observer on Earth), and time dilation will increasetheir lifespan to thousands of Earth years, seen from thereference system of the Solar System, but the travelerssubjective lifespan will not thereby change. If the travelerreturns to the Earth, they will land thousands of years intothe future. Their speed will not be seen as higher than thespeed of light by observers on Earth, and the traveler willnot measure their speed as being higher than the speed oflight, but will see a length contraction of the universe intheir direction of travel. And as the traveler turns aroundto return, the Earth will seem to experience much moretime than the traveler does. So, although their (ordinary)speed cannot exceed c, the four-velocity (distance as seenby Earth divided by their proper, i.e. subjective, time) canbe much greater than c. This is seen in statistical studiesof muons traveling much further than c times their half-life (at rest), if traveling close to c.[10]

1.7 Phase velocities above cThe phase velocity of an electromagnetic wave, whentraveling through a medium, can routinely exceed c, thevacuum velocity of light. For example, this occurs inmost glasses at X-ray frequencies.[11] However, the phasevelocity of a wave corresponds to the propagation speedof a theoretical single-frequency (purely monochromatic)component of the wave at that frequency. Such a wavecomponent must be innite in extent and of constant am-plitude (otherwise it is not truly monochromatic), and socannot convey any information.[12] Thus a phase velocityabove c does not imply the propagation of signals with avelocity above c.[13]

1.8 Group velocities above cThe group velocity of a wave (e.g., a light beam) may alsoexceed c in some circumstances. In such cases, whichtypically at the same time involve rapid attenuation of theintensity, the maximum of the envelope of a pulse maytravel with a velocity above c. However, even this sit-uation does not imply the propagation of signals with avelocity above c,[14] even though one may be tempted toassociate pulse maxima with signals. The latter associa-tion has been shown to be misleading, basically becausethe information on the arrival of a pulse can be obtainedbefore the pulse maximum arrives. For example, if somemechanism allows the full transmission of the leading partof a pulse while strongly attenuating the pulse maximumand everything behind (distortion), the pulse maximum

1.10 Astronomical observations 3

is eectively shifted forward in time, while the informa-tion on the pulse does not come faster than c without thiseect.[15]

1.9 Universal expansion

{History of the Universe

Age of the Universe

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Free Electrons Scatter Light

Earliest Time Visible with Light

Density Waves

Gravitational Waves

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Cosm

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Waves Imprint Characteristic Polarization Signals

0 1032 s 1 s 0.01 s 3 min 380,000 yrs 13.8 Billion yrs

Quan

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History of the universe - gravitational waves are hypothesizedto arise from cosmic ination, a faster-than-light expansion justafter the Big Bang (17 March 2014).[16][17][18]

The expansion of the universe causes distant galaxies torecede from us faster than the speed of light, if properdistance and cosmological time are used to calculate thespeeds of these galaxies. However, in general relativ-ity, velocity is a local notion, so velocity calculated usingcomoving coordinates does not have any simple relationto velocity calculated locally.[19] (See comoving distancefor a discussion of dierent notions of 'velocity' in cos-mology.) Rules that apply to relative velocities in spe-cial relativity, such as the rule that relative velocities can-not increase past the speed of light, do not apply to rela-tive velocities in comoving coordinates, which are oftendescribed in terms of the expansion of space betweengalaxies. This expansion rate is thought to have been atits peak during the inationary epoch thought to have oc-curred in a tiny fraction of the second after the Big Bang(models suggest the period would have been from around1036 seconds after the Big Bang to around 1033 sec-onds), when the universe may have rapidly expanded bya factor of around 1020 to 1030.[20]

There are many galaxies visible in telescopes with redshift numbers of 1.4 or higher. All of these are currentlytraveling away from us at speeds greater than the speed oflight. Because the Hubble parameter is decreasing withtime, there can actually be cases where a galaxy that isreceding from us faster than light does manage to emita signal which reaches us eventually.[21][22] However, be-cause the expansion of the universe is accelerating, it isprojected that most galaxies will eventually cross a typeof cosmological event horizon where any light they emitpast that point will never be able to reach us at any timein the innite future,[23] because the light never reaches

a point where its peculiar velocity towards us exceedsthe expansion velocity away from us (these two notionsof velocity are also discussed in Comoving distance#Usesof the proper distance). The current distance to this cos-mological event horizon is about 16 billion light-years,meaning that a signal from an event happening at presentwould eventually be able to reach us in the future if theevent was less than 16 billion light-years away, but thesignal would never reach us if the event was more than 16billion light-years away.[22]

1.10 Astronomical observations

Apparent superluminal motion is observed in manyradio galaxies, blazars, quasars and recently also inmicroquasars. The eect was predicted before it was ob-served by Martin Rees and can be explained as an opticalillusion caused by the object partly moving in the direc-tion of the observer,[24] when the speed calculations as-sume it does not. The phenomenon does not contradictthe theory of special relativity. Interestingly, correctedcalculations show these objects have velocities close tothe speed of light (relative to our reference frame). Theyare the rst examples of large amounts of mass movingat close to the speed of light.[25] Earth-bound laborato-ries have only been able to accelerate small numbers ofelementary particles to such speeds.

1.11 Quantum mechanics

Certain phenomena in quantum mechanics, such asquantum entanglement, might give the supercial im-pression of allowing communication of information fasterthan light. According to the no-communication theoremthese phenomena do not allow true communication; theyonly let two observers in dierent locations see the samesystem simultaneously, without any way of controllingwhat either sees. Wavefunction collapse can be viewedas an epiphenomenon of quantum decoherence, which inturn is nothing more than an eect of the underlying localtime evolution of the wavefunction of a system and all ofits environment. Since the underlying behaviour doesn'tviolate local causality or allow FTL it follows that nei-ther does the additional eect of wavefunction collapse,whether real or apparent.The uncertainty principle implies that individual photonsmay travel for short distances at speeds somewhat faster(or slower) than c, even in a vacuum; this possibility mustbe taken into account when enumerating Feynman dia-grams for a particle interaction.[26] However, it was shownin 2011 that a single photon may not travel faster thanc.[27] In quantum mechanics, virtual particles may travelfaster than light, and this phenomenon is related to the factthat static eld eects (which are mediated by virtual par-ticles in quantum terms) may travel faster than light (seesection on static elds above). However, macroscopically

4 1 FTL TRAVEL OF NON-INFORMATION

these uctuations average out, so that photons do travel instraight lines over long (i.e., non-quantum) distances, andthey do travel at the speed of light on average. There-fore, this does not imply the possibility of superluminalinformation transmission.There have been various reports in the popular press ofexperiments on faster-than-light transmission in opticsmost often in the context of a kind of quantum tunnellingphenomenon. Usually, such reports deal with a phase ve-locity or group velocity faster than the vacuum velocity oflight. However, as stated above, a superluminal phase ve-locity cannot be used for faster-than-light transmission ofinformation. There has sometimes been confusion con-cerning the latter point. Additionally a channel that per-mits such propagation cannot be laid out faster than thespeed of light.Quantum teleportation transmits quantum information atwhatever speed is used to transmit the same amount ofclassical information, likely the speed of light. This quan-tum information may theoretically be used in ways thatclassical information can not, such as in quantum com-putations involving quantum information only availableto the recipient.

1.11.1 Hartman eect

Main article: Hartman eect

The Hartman eect is the tunnelling eect through a bar-rier where the tunnelling time tends to a constant for largebarriers.[28] This was rst described by Thomas Hartmanin 1962.[29] This could, for instance, be the gap betweentwo prisms. When the prisms are in contact, the lightpasses straight through, but when there is a gap, the light isrefracted. There is a nonzero probability that the photonwill tunnel across the gap rather than follow the refractedpath. For large gaps between the prisms the tunnellingtime approaches a constant and thus the photons appearto have crossed with a superluminal speed.[30]

However, an analysis by Herbert G. Winful from the Uni-versity of Michigan suggests that the Hartman eect can-not actually be used to violate relativity by transmittingsignals faster than c, because the tunnelling time shouldnot be linked to a velocity since evanescent waves do notpropagate.[31] The evanescent waves in the Hartman ef-fect are due to virtual particles and a non-propagatingstatic eld, as mentioned in the sections above for gravityand electromagnetism.

1.11.2 Casimir eect

Main article: Casimir eect

In physics, the Casimir eect or Casimir-Polder force isa physical force exerted between separate objects due to

resonance of vacuum energy in the intervening space be-tween the objects. This is sometimes described in termsof virtual particles interacting with the objects, owing tothe mathematical form of one possible way of calculat-ing the strength of the eect. Because the strength ofthe force falls o rapidly with distance, it is only measur-able when the distance between the objects is extremelysmall. Because the eect is due to virtual particles me-diating a static eld eect, it is subject to the commentsabout static elds discussed above.

1.11.3 EPR Paradox

Main article: EPR paradox

The EPR paradox refers to a famous thought experimentof Einstein, Podolski and Rosen that was realized exper-imentally for the rst time by Alain Aspect in 1981 and1982 in the Aspect experiment. In this experiment, themeasurement of the state of one of the quantum systemsof an entangled pair apparently instantaneously forces theother system (which may be distant) to be measured inthe complementary state. However, no information canbe transmitted this way; the answer to whether or not themeasurement actually aects the other quantum systemcomes down to which interpretation of quantummechan-ics one subscribes to.An experiment performed in 1997 by Nicolas Gisin at theUniversity of Geneva has demonstrated non-local quan-tum correlations between particles separated by over 10kilometers.[32] But as noted earlier, the non-local corre-lations seen in entanglement cannot actually be used totransmit classical information faster than light, so thatrelativistic causality is preserved; see no-communicationtheorem for further information. A 2008 quantumphysics experiment also performed by Nicolas Gisin andhis colleagues in Geneva, Switzerland has determinedthat in any hypothetical non-local hidden-variables the-ory the speed of the quantum non-local connection (whatEinstein called spooky action at a distance) is at least10,000 times the speed of light.[33]

1.11.4 Delayed choice quantum eraser

Main article: Delayed choice quantum eraser

Delayed choice quantum eraser (an experiment ofMarlanScully) is a version of the EPR paradox in which the ob-servation or not of interference after the passage of a pho-ton through a double slit experiment depends on the con-ditions of observation of a second photon entangled withthe rst. The characteristic of this experiment is thatthe observation of the second photon can take place ata later time than the observation of the rst photon,[34]which may give the impression that the measurement ofthe later photons retroactively determines whether the

5earlier photons show interference or not, although theinterference pattern can only be seen by correlating themeasurements of both members of every pair and so itcan't be observed until both photons have been measured,ensuring that an experimenter watching only the pho-tons going through the slit does not obtain informationabout the other photons in an FTL or backwards-in-timemanner.[35][36]

2 FTL communication possibilityFaster-than-light communication is, by Einstein's theoryof relativity, equivalent to time travel. According to Ein-steins theory of special relativity, what we measure asthe speed of light in a vacuum is actually the fundamen-tal physical constant c. This means that all inertial ob-servers, regardless of their relative velocity, will alwaysmeasure zero-mass particles such as photons traveling atc in a vacuum. This result means that measurements oftime and velocity in dierent frames are no longer re-lated simply by constant shifts, but are instead relatedby Poincar transformations. These transformations haveimportant implications:

The relativistic momentum of a massive particlewould increase with speed in such a way that at thespeed of light an object would have innite momen-tum.

To accelerate an object of non-zero rest mass to cwould require innite time with any nite acceler-ation, or innite acceleration for a nite amount oftime.

Either way, such acceleration requires innite en-ergy.

Some observers with sub-light relative motion willdisagree about which occurs rst of any two eventsthat are separated by a space-like interval.[37] Inother words, any travel that is faster-than-light willbe seen as traveling backwards in time in someother, equally valid, frames of reference,[38] or needto assume the speculative hypothesis of possibleLorentz violations at a presently unobserved scale(for instance the Planck scale). Therefore any theorywhich permits true FTL also has to cope with timetravel and all its associated paradoxes,[39] or else toassume the Lorentz invariance to be a symmetry ofthermodynamical statistical nature (hence a symme-try broken at some presently unobserved scale).

In special relativity the coordinate speed of light isonly guaranteed to be c in an inertial frame, in a non-inertial frame the coordinate speed may be dierentfrom c;[40] in general relativity no coordinate systemon a large region of curved spacetime is inertial,so its permissible to use a global coordinate system

where objects travel faster than c, but in the localneighborhood of any point in curved spacetime wecan dene a local inertial frame and the local speedof light will be c in this frame,[41] with massive ob-jects moving through this local neighborhood alwayshaving a speed less than c in the local inertial frame.

3 Justications

3.1 Faster light (Casimir vacuum andquantum tunnelling)

Raymond Y. Chiao was rst to measure the quantum tun-nelling time, which was found to be between 1.5 to 1.7times the speed of light.Einsteins equations of special relativity postulate that thespeed of light in a vacuum is invariant in inertial frames.That is, it will be the same from any frame of referencemoving at a constant speed. The equations do not specifyany particular value for the speed of the light, which isan experimentally determined quantity for a xed unit oflength. Since 1983, the SI unit of length (the meter) hasbeen dened using the speed of light.The experimental determination has been made in vac-uum. However, the vacuum we know is not the only pos-sible vacuum which can exist. The vacuum has energyassociated with it, unsurprisingly called the vacuum en-ergy. This vacuum energy can perhaps be changed in cer-tain cases.[42] When vacuum energy is lowered, light itselfhas been predicted to go faster than the standard valuec. This is known as the Scharnhorst eect. Such a vac-uum can be produced by bringing two perfectly smoothmetal plates together at near atomic diameter spacing. Itis called a Casimir vacuum. Calculations imply that lightwill go faster in such a vacuum by a minuscule amount: aphoton traveling between two plates that are 1 microme-ter apart would increase the photons speed by only aboutone part in 1036.[43] Accordingly there has as yet beenno experimental verication of the prediction. A recentanalysis[44] argued that the Scharnhorst eect cannot beused to send information backwards in time with a sin-gle set of plates since the plates rest frame would de-ne a preferred frame for FTL signalling. However,with multiple pairs of plates in motion relative to oneanother the authors noted that they had no argumentsthat could guarantee the total absence of causality vi-olations, and invoked Hawkings speculative chronologyprotection conjecture which suggests that feedback loopsof virtual particles would create uncontrollable singu-larities in the renormalized quantum stress-energy onthe boundary of any potential time machine, and thuswould require a theory of quantum gravity to fully ana-lyze. Other authors argue that Scharnhorsts original anal-ysis which seemed to show the possibility of faster-than-csignals involved approximations which may be incorrect,

6 3 JUSTIFICATIONS

so that it is not clear whether this eect could actuallyincrease signal speed at all.[45]

The physicists Gnter Nimtz and Alfons Stahlhofen, ofthe University of Cologne, claim to have violated rela-tivity experimentally by transmitting photons faster thanthe speed of light.[30] They say they have conductedan experiment in which microwave photonsrelativelylow energy packets of lighttravelled instantaneouslybetween a pair of prisms that had been moved up to3 ft (1 m) apart. Their experiment involved an op-tical phenomenon known as evanescent modes, andthey claim that since evanescent modes have an imagi-nary wave number, they represent a mathematical anal-ogy to quantum tunnelling.[30] Nimtz has also claimedthat evanescent modes are not fully describable by theMaxwell equations and quantum mechanics have to betaken into consideration.[46] Other scientists such as Her-bert G. Winful and Robert Helling have argued that infact there is nothing quantum-mechanical about Nimtzsexperiments, and that the results can be fully predicted bythe equations of classical electromagnetism (Maxwellsequations).[47][48]

Nimtz told New Scientist magazine: For the time being,this is the only violation of special relativity that I knowof. However, other physicists say that this phenomenondoes not allow information to be transmitted faster thanlight. Aephraim Steinberg, a quantum optics expert atthe University of Toronto, Canada, uses the analogy of atrain traveling from Chicago to New York, but droppingo train cars at each station along the way, so that thecenter of the ever shrinking main train moves forward ateach stop; in this way, the speed of the center of the trainexceeds the speed of any of the individual cars.[49]

Herbert G. Winful argues that the train analogy is a vari-ant of the reshaping argument for superluminal tunnel-ing velocities, but he goes on to say that this argumentis not actually supported by experiment or simulations,which actually show that the transmitted pulse has thesame length and shape as the incident pulse.[47] Instead,Winful argues that the group delay in tunneling is not ac-tually the transit time for the pulse (whose spatial lengthmust be greater than the barrier length in order for itsspectrum to be narrow enough to allow tunneling), butis instead the lifetime of the energy stored in a standingwave which forms inside the barrier. Since the storedenergy in the barrier is less than the energy stored in abarrier-free region of the same length due to destructiveinterference, the group delay for the energy to escape thebarrier region is shorter than it would be in free space,which according to Winful is the explanation for appar-ently superluminal tunneling.[50][51]

A number of authors have published papers disputingNimtzs claim that Einstein causality is violated by hisexperiments, and there are many other papers in the lit-erature discussing why quantum tunneling is not thoughtto violate causality.[52]

It was later claimed by the Keller group in Switzerlandthat particle tunneling does indeed occur in zero realtime. Their tests involved tunneling electrons, wherethe group argued a relativistic prediction for tunnelingtime should be 500-600 attoseconds (an attosecond is onequintillionth (1018) of a second). All that could be mea-sured was 24 attoseconds, which is the limit of the testaccuracy.[53] Again, though, other physicists believe thattunneling experiments in which particles appear to spendanomalously short times inside the barrier are in fact fullycompatible with relativity, although there is disagreementabout whether the explanation involves reshaping of thewave packet or other eects.[50][51][54]

3.2 Give up (absolute) relativity

Because of the strong empirical support for special rel-ativity, any modications to it must necessarily be quitesubtle and dicult to measure. The best-known attemptis doubly special relativity, which posits that the Plancklength is also the same in all reference frames, and isassociated with the work of Giovanni Amelino-Cameliaand Joo Magueijo. One consequence of this theory is avariable speed of light, where photon speed would varywith energy, and some zero-mass particles might possi-bly travel faster than c. However, even if this theory isaccurate, it is still very unclear whether it would allow in-formation to be communicated, and appears not in anycase to allow massive particles to exceed c.There are speculative theories that claim inertia is pro-duced by the combined mass of the universe (e.g., Machsprinciple), which implies that the rest frame of the uni-verse might be preferred by conventional measurementsof natural law. If conrmed, this would imply special rel-ativity is an approximation to a more general theory, butsince the relevant comparison would (by denition) beoutside the observable universe, it is dicult to imagine(much less construct) experiments to test this hypothesis.

3.3 Space-time distortion

Although the theory of special relativity forbids objectsto have a relative velocity greater than light speed, andgeneral relativity reduces to special relativity in a localsense (in small regions of spacetime where curvature isnegligible), general relativity does allow the space be-tween distant objects to expand in such a way that theyhave a "recession velocity" which exceeds the speed oflight, and it is thought that galaxies which are at a dis-tance of more than about 14 billion light-years from us to-day have a recession velocity which is faster than light.[55]Miguel Alcubierre theorized that it would be possible tocreate an Alcubierre drive, in which a ship would be en-closed in a warp bubble where the space at the frontof the bubble is rapidly contracting and the space at theback is rapidly expanding, with the result that the bub-

3.7 Superuid theories of physical vacuum 7

ble can reach a distant destination much faster than alight beam moving outside the bubble, but without ob-jects inside the bubble locally traveling faster than light.However, several objections raised against the Alcubierredrive appear to rule out the possibility of actually usingit in any practical fashion. Another possibility predictedby general relativity is the traversable wormhole, whichcould create a shortcut between arbitrarily distant pointsin space. As with the Alcubierre drive, travelers movingthrough the wormhole would not locallymove faster thanlight which travels through the wormhole alongside them,but they would be able to reach their destination (and re-turn to their starting location) faster than light travelingoutside the wormhole.Dr. Gerald Cleaver, associate professor of physics atBaylor University, and Richard Obousy, a Baylor grad-uate student, theorize that by manipulating the extra spa-tial dimensions of string theory around a spaceship withan extremely large amount of energy, it would create abubble that could cause the ship to travel faster than thespeed of light. To create this bubble, the physicists be-lieve manipulating the 10th spatial dimension would alterthe dark energy in three large spatial dimensions: height,width and length. Cleaver said positive dark energy iscurrently responsible for speeding up the expansion rateof our universe as time moves on.[56]

3.4 Heim theoryIn 1977, a paper on Heim theory theorized that it may bepossible to travel faster than light by using magnetic eldsto enter a higher-dimensional space.[57]

3.5 MiHsC/Quantised inertiaA new theory has been proposed that Modies inertiaby assuming it is due to Unruh radiation subject to aHubble scale Casimir eect (MiHsC, or quantised in-ertia). MiHsC predicts a minimum possible accelerationeven at light speed, implying that this speed can be ex-ceeded. [58]

3.6 Lorentz symmetry violationMain articles: Modern searches for Lorentz violationand Standard-Model Extension

The possibility that Lorentz symmetry may be violatedhas been seriously considered in the last two decades, par-ticularly after the development of a realistic eective eldtheory that describes this possible violation, the so-calledStandard-Model Extension.[59][60][61] This general frame-work has allowed experimental searches by ultra-high en-ergy cosmic-ray experiments[62] and a wide variety of ex-periments in gravity, electrons, protons, neutrons, neutri-

nos, mesons, and photons.[63] The breaking of rotationand boost invariance causes direction dependence in thetheory as well as unconventional energy dependence thatintroduces novel eects, including Lorentz-violating neu-trino oscillations and modications to the dispersion rela-tions of dierent particle species, which naturally couldmake particles move faster than light.In some models of broken Lorentz symmetry, it is pos-tulated that the symmetry is still built into the most fun-damental laws of physics, but that spontaneous symme-try breaking of Lorentz invariance[64] shortly after theBig Bang could have left a relic eld throughout theuniverse which causes particles to behave dierently de-pending on their velocity relative to the eld;[65] however,there are also some models where Lorentz symmetry isbroken in a more fundamental way. If Lorentz symmetrycan cease to be a fundamental symmetry at Planck scaleor at some other fundamental scale, it is conceivable thatparticles with a critical speed dierent from the speed oflight be the ultimate constituents of matter.In current models of Lorentz symmetry violation, thephenomenological parameters are expected to be energy-dependent. Therefore, as widely recognized,[66][67] exist-ing low-energy bounds cannot be applied to high-energyphenomena; however, many searches for Lorentz vio-lation at high energies have been carried out using theStandard-Model Extension.[63] Lorentz symmetry viola-tion is expected to become stronger as one gets closer tothe fundamental scale.Another recent theory (see EPR paradox above) result-ing from the analysis of an EPR communication set up,has the simple device based on removing the eective re-tarded time terms in the Lorentz transform to yield a pre-ferred absolute reference frame.[68][69] This frame can-not be used to do physics (i.e., compute the inuence oflight-speed limited signals) but it provides an objective,absolute frame all could agree upon, if superluminal com-munication is possible. If this sounds indulgent, it allowssimultaneity, absolute space and time and a determinis-tic universe (along with decoherence theory) whilst thestatus-quo permits time travel/causality paradoxes, sub-jectivity in the measurement process and multiple uni-verses.

3.7 Superuid theories of physical vacuumMain article: Superuid vacuum

In this approach the physical vacuum is viewed as thequantum superuid which is essentially non-relativisticwhereas the Lorentz symmetry is not an exact sym-metry of nature but rather the approximate descrip-tion valid only for the small uctuations of the super-uid background.[70] Within the framework of the ap-proach a theory was proposed in which the physicalvacuum is conjectured to be the quantum Bose liquid

8 6 GENERAL RELATIVITY

whose ground-state wavefunction is described by thelogarithmic Schrdinger equation. It was shown that therelativistic gravitational interaction arises as the small-amplitude collective excitation mode[71] whereas rela-tivistic elementary particles can be described by theparticle-like modes in the limit of low momenta.[72] Theimportant fact is that at very high velocities the behav-ior of the particle-like modes becomes distinct from therelativistic one - they can reach the speed of light limit atnite energy; also the faster-than-light propagation is pos-sible without requiring moving objects to have imaginarymass.[73][74]

4 Time of ight of neutrinos

4.1 MINOS experiment

Main article: MINOS

In 2007MINOS collaboration reported results measuringthe ight-time of 3 GeV neutrinos yielding a speed ex-ceeding that of light by 1.8-sigma signicance.[75] How-ever, those measurements were considered to be statis-tically consistent with neutrinos traveling at the speed oflight.[76] After the detectors for the project were upgradedin 2012, MINOS corrected their initial result and foundagreement with the speed of light. Further measurementsare going to be conducted.[77]

4.2 OPERA neutrino anomaly

Main article: Faster-than-light neutrino anomaly

On September 22, 2011, a paper[78] from the OPERACollaboration indicated detection of 17 and 28 GeVmuon neutrinos, sent 730 kilometers (454 miles) fromCERN near Geneva, Switzerland to the Gran Sasso Na-tional Laboratory in Italy, traveling faster than light bya factor of 2.48105 (approximately 1 in 40,000), astatistic with 6.0-sigma signicance.[79] On 18 Novem-ber 2011, a second follow-up experiment by OPERAscientists conrmed their initial results.[80][81] However,scientists were skeptical about the results of these ex-periments, the signicance of which was disputed.[82] InMarch 2012, the ICARUS collaboration failed to repro-duce the OPERA results with their equipment, detect-ing neutrino travel time from CERN to the Gran SassoNational Laboratory indistinguishable from the speed oflight.[83] Later the OPERA team reported two aws intheir equipment set-up that had caused errors far outsidetheir original condence interval: a ber optic cable at-tached improperly, which caused the apparently faster-than-light measurements, and a clock oscillator tickingtoo fast.[84]

5 Tachyons

Main article: Tachyon

In special relativity, it is impossible to accelerate an ob-ject to the speed of light, or for a massive object to moveat the speed of light. However, it might be possible foran object to exist which always moves faster than light.The hypothetical elementary particles with this propertyare called tachyonic particles. Attempts to quantize themfailed to produce faster-than-light particles, and insteadillustrated that their presence leads to an instability.[85][86]

Various theorists have suggested that the neutrino mighthave a tachyonic nature,[87][88][89][90][91] while others havedisputed the possibility.[92]

6 General relativity

General relativity was developed after special relativityto include concepts like gravity. It maintains the princi-ple that no object can accelerate to the speed of light inthe reference frame of any coincident observer. How-ever, it permits distortions in spacetime that allow an ob-ject to move faster than light from the point of view of adistant observer. One such distortion is the Alcubierredrive, which can be thought of as producing a ripplein spacetime that carries an object along with it. An-other possible system is the wormhole, which connectstwo distant locations as though by a shortcut. Both dis-tortions would need to create a very strong curvature ina highly localized region of space-time and their grav-ity elds would be immense. To counteract the unstablenature, and prevent the distortions from collapsing undertheir own 'weight', one would need to introduce hypothet-ical exotic matter or negative energy.General relativity also recognizes that any means offaster-than-light travel could also be used for time travel.This raises problems with causality. Many physicists be-lieve that the above phenomena are impossible and thatfuture theories of gravity will prohibit them. One the-ory states that stable wormholes are possible, but thatany attempt to use a network of wormholes to violatecausality would result in their decay. In string theory,Eric G. Gimon and Petr Hoava have argued[93] thatin a supersymmetric ve-dimensional Gdel universe,quantum corrections to general relativity eectively cuto regions of spacetime with causality-violating closedtimelike curves. In particular, in the quantum theory asmeared supertube is present that cuts the spacetime insuch a way that, although in the full spacetime a closedtimelike curve passed through every point, no completecurves exist on the interior region bounded by the tube.

97 Variable speed of lightMain article: Variable speed of light

In conventional physics, the speed of light in a vacuum isassumed to be a constant. However, theories exist whichpostulate that the speed of light is not a constant. Theinterpretation of this statement is as follows.The speed of light is a dimensional quantity and so, as hasbeen emphasized in this context by JooMagueijo, it can-not be measured.[94] Measurable quantities in physics are,without exception, dimensionless, although they are oftenconstructed as ratios of dimensional quantities. For ex-ample, when the height of a mountain is measured, whatis really measured is the ratio of its height to the lengthof a meter stick. The conventional SI system of unitsis based on seven basic dimensional quantities, namelydistance, mass, time, electric current, thermodynamictemperature, amount of substance, and luminous inten-sity.[95] These units are dened to be independent and socannot be described in terms of each other. As an al-ternative to using a particular system of units, one canreduce all measurements to dimensionless quantities ex-pressed in terms of ratios between the quantities be-ing measured and various fundamental constants such asNewtons constant, the speed of light and Plancks con-stant; physicists can dene at least 26 dimensionless con-stants which can be expressed in terms of these sorts ofratios and which are currently thought to be independentof one another.[96] Bymanipulating the basic dimensionalconstants one can also construct the Planck time, Plancklength and Planck energy which make a good system ofunits for expressing dimensional measurements, knownas Planck units.Magueijos proposal used a dierent set of units, a choicewhich he justies with the claim that some equations willbe simpler in these new units. In the new units he xesthe ne structure constant, a quantity which some peo-ple, using units in which the speed of light is xed, haveclaimed is time-dependent. Thus in the system of unitsin which the ne structure constant is xed, the observa-tional claim is that the speed of light is time-dependent.While it may bemathematically possible to construct sucha system, it is not clear what additional explanatory poweror physical insight such a systemwould provide, assumingthat it does indeed accord with existing empirical data.

8 See alsoMain pages: Category:Faster-than-light travel andCategory:Faster-than-light communication

Science ction

9 Notes[1] Gonzalez-Diaz, P. F. (2000). Warp drive space-

time. Physical Review D 62 (4): 044005. arXiv:gr-qc/9907026. Bibcode:2000PhRvD..62d4005G.doi:10.1103/PhysRevD.62.044005.

[2] Loup, F.; Waite, D.; Halerewicz, E. Jr. (2001). Reducedtotal energy requirements for a modied Alcubierre warpdrive spacetime. arXiv:0107097 [gr-qc].

[3] Visser, M.; Bassett, B.; Liberati, S. (2000). Super-luminal censorship. Nuclear Physics B: ProceedingsSupplement 88: 267270. arXiv:gr-qc/9810026.Bibcode:2000NuPhS..88..267V. doi:10.1016/S0920-5632(00)00782-9.

[4] Visser, M.; Bassett, B.; Liberati, S. (1999). Perturbativesuperluminal censorship and the null energy condition.AIP Conference Proceedings 493: 301305. arXiv:gr-qc/9908023. doi:10.1063/1.1301601. ISBN 1-56396-905-X.

[5] See Salters Horners Advanced Physics A2 Student Book,Oxford etc. (Heinemann) 2001, pp. 302 and 303

[6] see http://www.oarval.org/furthest.htm

[7] Gibbs, Philip (1997). Is Faster-Than-Light Travel orCommunication Possible?". University of California,Riverside. Retrieved 20 August 2008.

[8] Salmon, Wesley C. (2006). Four Decades of Scientic Ex-planation. University of Pittsburgh Pre. p. 107. ISBN0-8229-5926-7., Extract of page 107

[9] Steane, Andrew (2012). The Wonderful World of Rela-tivity: A Precise Guide for the General Reader. OxfordUniversity Press. p. 180. ISBN 0-19-969461-3., Extractof page 180

[10] Special Theory of Relativity

[11] Hecht, Eugene (1987). Optics (2nd ed.). AddisonWesley.p. 62. ISBN 0-201-11609-X.

[12] Sommerfeld, Arnold (1907). "An Objection Against theTheory of Relativity and its Removal". PhysikalischeZeitschrift 8 (23): 841842.

[13] MathPages - Phase, Group, and Signal Velocity. Re-trieved 2007-04-30.

[14] Brillouin, Lon; Wave Propagation and Group Velocity,Academic Press, 1960

[15] Withayachumnankul, W.; et al.; A systemized view ofsuperluminal wave propagation, Proceedings of the IEEE,Vol. 98, No. 10, pp. 1775-1786, 2010

[16] Sta (17 March 2014). BICEP2 2014 Results Release.National Science Foundation. Retrieved 18 March 2014.

[17] Clavin, Whitney (17 March 2014). NASA TechnologyViews Birth of the Universe. NASA. Retrieved 17 March2014.

10 9 NOTES

[18] Overbye, Dennis (17 March 2014). Detection of Wavesin Space Buttresses Landmark Theory of Big Bang. NewYork Times. Retrieved 17 March 2014.

[19] Cosmology Tutorial - Part 2. Astro.ucla.edu. 2009-06-12. Retrieved 2011-09-26.

[20] Inationary Period from HyperPhysics.Hyperphysics.phy-astr.gsu.edu. Retrieved 2011-09-26.

[21] Is the universe expanding faster than the speed of light?(see the last two paragraphs)

[22] Lineweaver, Charles; Davis, Tamara M. (2005).Misconceptions about the Big Bang. ScienticAmerican. Retrieved 2008-11-06.

[23] Loeb, Abraham (2002). The Long-Term Future of Extragalactic Astronomy.Physical Review D 65 (4). arXiv:astro-ph/0107568. Bibcode:2002PhRvD..65d7301L.doi:10.1103/PhysRevD.65.047301.

[24] Rees, Martin J. (1966). Appearance of relativisticallyexpanding radio sources. Nature 211 (5048): 468.Bibcode:1966Natur.211..468R. doi:10.1038/211468a0.

[25] Blandford, Roger D.; McKee, C. F.; Rees, Mar-tin J. (1977). Super-luminal expansion in extra-galactic radio sources. Nature 267 (5608): 211.Bibcode:1977Natur.267..211B. doi:10.1038/267211a0.

[26] Feynman. Chapter 3. QED. p. 89. ISBN 981-256-914-6.

[27] Zhang, Shanchao. Single photons obey the speed limits.Physics. American Physical Society. Archived from theoriginal on 2013-05-14. Retrieved 25 July 2011.

[28] Martinez, J. C.; and Polatdemir, E.; Origin of the Hart-man eect, Physics Letters A, Vol. 351, Iss. 1-2, 20February 2006, pp. 31-36

[29] Hartman, Thomas E.; Tunneling of a wave packet, Jour-nal of Applied Physics 33, 3427 (1962)

[30] Nimtz, Gnter; Stahlhofen, Alfons (2007). Macroscopicviolation of special relativity. arXiv:0708.0681 [quant-ph].

[31] Winful, Herbert G.; Tunneling time, the Hartman ef-fect, and superluminality: A proposed resolution of an oldparadox, Physics Reports, Vol. 436, Iss. 1-2, December2006, pp. 1-69

[32] History. Quantumphil.org. Retrieved 2011-09-26.

[33] Salart; Baas; Branciard; Gisin; Zbinden (2008). Testingspooky action at a distance. Nature 454 (7206): 861864. arXiv:0808.3316. Bibcode:2008Natur.454..861S.doi:10.1038/nature07121. PMID 18704081.

[34] Delayed Choice Quantum Eraser. Bottomlayer.com.2002-09-04. Retrieved 2011-09-26.

[35] Scientic American : Delayed-Choice Experimentshttp://www.scientificamerican.com/article.cfm?id=quantum-eraser-delayed-choice-experiments

[36] The Reference Frame: Delayed Choice Quan-tum Eraser http://motls.blogspot.com/2010/11/delayed-choice-quantum-eraser.html

[37] Einstein, Albert, Relativity:the special and the general the-ory, Methuen & Co, 1927, pp. 25-27

[38] Odenwald, Sten. Special & General Relativity Questionsand Answers: If we could travel faster than light, could wego back in time?". NASA Astronomy Cafe. Retrieved 7April 2014.

[39] Gott, J. Richard (2002). Time Travel in Einsteins Uni-verse. pp. pp. 8283.

[40] Petkov, Vesselin; Relativity and the Nature of Spacetime,p. 219

[41] Raine, Derek J.; Thomas, Edwin George; and Thomas, E.G.; An Introduction to the Science of Cosmology, p. 94

[42] What is the 'zero-point energy' (or 'vacuum energy') inquantum physics? Is it really possible that we could har-ness this energy?". Scientic American. 1997-08-18. Re-trieved 2009-05-27.

[43] Scharnhorst, Klaus (1990-05-12). Secret of the vacuum:Speedier light. Retrieved 2009-05-27.

[44] Visser, Matt; Liberati, Stefano; Sonego, Sebastiano(2001-07-27). Faster-than-c signals, special relativ-ity, and causality. Annals of Physics 298: 167185.arXiv:gr-qc/0107091. Bibcode:2002AnPhy.298..167L.doi:10.1006/aphy.2002.6233.

[45] Fearn, Heidi (2007). Can Light Signals Travel Fasterthan c in Nontrivial Vacuua in Flat space-time? Rel-ativistic Causality II. LaserPhys. 17 (5): 695699. arXiv:0706.0553. Bibcode:2007LaPhy..17..695F.doi:10.1134/S1054660X07050155.

[46] Nimtz, Gnter; Superluminal Tunneling Devices, 2001

[47] Winful, Herbert G. (2007-09-18). Comment on Macro-scopic violation of special relativity by Nimtz andStahlhofen. arXiv:0709.2736 [quant-ph].

[48] Helling, Robert C.; Faster than light or not (blog)

[49] Anderson, Mark (1824 August 2007). Light seems todefy its own speed limit. New Scientist 195 (2617). p.10.

[50] Winful, Herbert G. (December 2006). Tunnelingtime, the Hartman eect, and superluminality: A pro-posed resolution of an old paradox. Physics Re-ports 436 (12): 169. Bibcode:2006PhR...436....1W.doi:10.1016/j.physrep.2006.09.002.

[51] For a summary of Herbert G. Winfuls explanationfor apparently superluminal tunneling time which doesnot involve reshaping, see http://spie.org/x18001.xml?ArticleID=x18001

[52] A number of papers are listed at Literature on Faster-than-light tunneling experiments

11

[53] Eckle, P.; et al., Attosecond Ionization and Tunnel-ing Delay Time Measurements in Helium, Science, 322(2008) 1525

[54] Sokolovski, D. (8 February 2004). Why doesrelativity allow quantum tunneling to 'take notime'?". Proceedings of the Royal Society A 460(2042): 499506. Bibcode:2004RSPSA.460..499S.doi:10.1098/rspa.2003.1222.

[55] Lineweaver, Charles H.; and Davis, Tamara M. (March2005). Misconceptions about the Big Bang. ScienticAmerican.

[56] Traveling Faster Than the Speed of Light: A New IdeaThat Could Make It Happen Newswise, retrieved on 24August 2008.

[57] Heim, Burkhard (1977). Vorschlag eines Weges einereinheitlichen Beschreibung der Elementarteilchen [Rec-ommendation of a Way to a Unied Description of Ele-mentary Particles]". Zeitschrift fr Naturforschung 32a:233243. Bibcode:1977ZNatA..32..233H.

[58] McCulloch, M. E. (2014). Physics from the edge: a newcosmological model for inertia. World Scientic. ISBN978-9814596251.

[59] Colladay, Don; Kosteleck, V. Alan (1997).CPT violation and the standard model. Phys-ical Review D 55 (11): 6760. arXiv:hep-ph/9703464. Bibcode:1997PhRvD..55.6760C.doi:10.1103/PhysRevD.55.6760.

[60] Colladay, Don; Kosteleck, V. Alan (1998).Lorentz-violating extension of the standardmodel. Physical Review D 58 (11). arXiv:hep-ph/9809521. Bibcode:1998PhRvD..58k6002C.doi:10.1103/PhysRevD.58.116002.

[61] Kosteleck, V. Alan (2004). Gravity,Lorentz violation, and the standard model.Physical Review D 69 (10). arXiv:hep-th/0312310. Bibcode:2004PhRvD..69j5009K.doi:10.1103/PhysRevD.69.105009.

[62] Gonzalez-Mestres, Luis (2009). AUGER-HiRes re-sults and models of Lorentz symmetry violation. Nu-clear Physics B: Proceedings Supplements 190: 191197. arXiv:0902.0994. Bibcode:2009NuPhS.190..191G.doi:10.1016/j.nuclphysbps.2009.03.088.

[63] Kosteleck, V. Alan; Russell, Neil (2011).Data tables for Lorentz and CPT viola-tion. Review of Modern Physics 83: 11.arXiv:0801.0287. Bibcode:2011RvMP...83...11K.doi:10.1103/RevModPhys.83.11.

[64] Kosteleck, V. Alan; and Samuel, S.; Spontaneous Break-ing of Lorentz Symmetry in String Theory, Physical ReviewD 39, 683 (1989)

[65] PhysicsWeb - Breaking Lorentz symmetry.Web.archive.org. 2004-04-05. Archived from theoriginal on 2004-04-05. Retrieved 2011-09-26.

[66] Mavromatos, Nick E.; Testing models for quantum gravity,CERN Courier, http://cerncourier.com/cws/article/cern/28696 (August 2002)

[67] Overbye, Dennis; Interpreting the Cosmic Rays, The NewYork Times, 31 December 2002

[68] Cornwall, Remi. Secure Quantum Communicationand Superluminal Signalling on the Bell Channel.arXiv:1106.2257.

[69] Cornwall, Remi. Is the Consequence of SuperluminalSignalling to Physics AbsoluteMotion through an Ether?".arXiv:1106.2258.

[70] Volovik, G. E. (2003). The Universe in a heliumdroplet. International Series of Monographs on Physics117: 1507.

[71] Zloshchastiev, Konstantin G. (2009). Spontaneous sym-metry breaking and mass generation as built-in phenom-ena in logarithmic nonlinear quantum theory. ActaPhysica Polonica B 42 (2): 261292. arXiv:0912.4139.doi:10.5506/APhysPolB.42.261.

[72] Avdeenkov, Alexander V.; Zloshchastiev, KonstantinG. (2011). Quantum Bose liquids with logarithmicnonlinearity: Self-sustainability and emergence of spatialextent. Journal of Physics B: Atomic, Molecular andOptical Physics 44 (19): 195303. arXiv:1108.0847.Bibcode:2011JPhB...44s5303A. doi:10.1088/0953-4075/44/19/195303.

[73] Zloshchastiev, Konstantin G.; Chakrabarti, Sandip K.;Zhuk, Alexander I.; Bisnovatyi-Kogan, Gennady S.(2010). Logarithmic nonlinearity in theories ofquantum gravity: Origin of time and observationalconsequences. AIP Conference Proceedings. p.112. arXiv:0906.4282. Bibcode:2010AIPC.1206..112Z.doi:10.1063/1.3292518.

[74] Zloshchastiev, Konstantin G. (2011). VacuumCherenkov eect in logarithmic nonlinear quan-tum theory. Physics Letters A 375 (24): 2305.arXiv:1003.0657. Bibcode:2011PhLA..375.2305Z.doi:10.1016/j.physleta.2011.05.012.

[75] Adamson, P.; Andreopoulos, C.; Arms, K.; Arm-strong, R.; Auty, D.; Avvakumov, S.; Ayres, D.;Baller, B. et al. (2007). Measurement of neu-trino velocity with the MINOS detectors andNuMI neutrino beam. Physical Review D 76 (7).arXiv:0706.0437. Bibcode:2007PhRvD..76g2005A.doi:10.1103/PhysRevD.76.072005.

[76] Overbye, Dennis (22 September 2011). Tiny neutrinosmay have broken cosmic speed limit. New York Times.That group found, although with less precision, that theneutrino speeds were consistent with the speed of light.

[77] MINOS reports new measurement of neutrino velocity.Fermilab today. June 8, 2012. Retrieved June 8, 2012.

[78] Adam; Agafonova; Aleksandrov; Altinok; AlvarezSanchez; Aoki; Ariga; Ariga et al. (2011). Measurementof the neutrino velocity with the OPERA detector in theCNGS beam. arXiv:1109.4897 [hep-ex].

12 11 EXTERNAL LINKS

[79] Cho, Adrian; Neutrinos Travel Faster Than Light, Accord-ing to One Experiment, ScienceNOW, 22 September 2011

[80] Overbye, Dennis (18 November 2011). Scientists ReportSecond Sighting of Faster-Than-Light Neutrinos. NewYork Times. Retrieved 2011-11-18.

[81] Adam, T.; et al.; (OPERA Collaboration) (17 Novem-ber 2011). Measurement of the neutrino veloc-ity with the OPERA detector in the CNGS beam.arXiv:1109.4897v2 [hep-ex].

[82] Reuters: Study rejects faster than light particle nding

[83] ICARUS collaboration (March 15, 2012). Measurementof the neutrino velocity with the ICARUS detector at theCNGS beam. arXiv:1203.3433.

[84] Strassler, M. (2012) OPERA: What Went Wrong prof-mattstrassler.com

[85] Randall, Lisa; Warped Passages: Unraveling the Myster-ies of the Universes Hidden Dimensions, p. 286: Peopleinitially thought of tachyons as particles travelling fasterthan the speed of light...But we now know that a tachyonindicates an instability in a theory that contains it. Regret-tably for science ction fans, tachyons are not real physicalparticles that appear in nature.

[86] Gates, S. James. Superstring Theory: The DNA of Re-ality.

[87] Chodos, A.; Hauser, A. I.; and Kosteleck, V. Alan; TheNeutrino As A Tachyon, Physics Letters B 150, 431 (1985)

[88] Chodos, Alan; Kosteleck, V. Alan; IUHET 280(1994). Nuclear Null Tests for Spacelike Neu-trinos. Physics Letters B 336 (34): 295302.arXiv:hep-ph/9409404. Bibcode:1994PhLB..336..295C.doi:10.1016/0370-2693(94)90535-5.

[89] Chodos, Alan; Kosteleck, V. Alan; Potting, R.; andGates, E.; Null experiments for neutrino masses, ModernPhysics Letters A7, 467 (1992)

[90] List of articles on the tachyonic neutrino idea (may be in-complete). InSPIRE database. Parity Violation and Neu-trino Mass Tsao Chang

[91] Chang, Taso; Parity Violation and Neutrino Mass, NuclearScience and Techniques, Vol. 13, No. 3 (2002) 129

[92] Hughes, R. J.; and Stephenson, G. J., Jr.; Against tachyonicneutrinos, Physics Letters B 244, 95-100 (1990)

[93] Gimon, Eric G.; Hoava, Petr (2004). Over-rotatingblack holes, Gdel holography and the hypertube.arXiv:hep-th/0405019 [hep-th].

[94] Magueijo, Joo; Albrecht, Andreas (1999). A timevarying speed of light as a solution to cosmologicalpuzzles. Physical Review D 59 (4). arXiv:astro-ph/9811018. Bibcode:1999PhRvD..59d3516A.doi:10.1103/PhysRevD.59.043516.

[95] SI base units.

[96] constants.

10 References Falla, D. F.; Floyd, M. J. (2002). Superlumi-nal motion in astronomy. European Journal ofPhysics 23: 6981. Bibcode:2002EJPh...23...69F.doi:10.1088/0143-0807/23/1/310.

Kaku, Michio (2008). Faster than Light. Physicsof the Impossible. Allen Lane. pp. 197215. ISBN978-0-7139-9992-1.

Nimtz, Gnter (2008). Zero Time Space. Wiley-VCH. ISBN 978-3-527-40735-4.

Cramer, J. G. (2009). Faster-than-Light Implica-tions of Quantum Entanglement and Nonlocality.In Millis, M. G.; et al. Frontiers of Propulsion Sci-ence. American Institute of Aeronautics and Astro-nautics. pp. 509529. ISBN 1-56347-956-7.

11 External links

11.1 Scientic links Measurement of the neutrino velocity with theOPERA detector in the CNGS beam

Encyclopedia of laser physics and technology onsuperluminal transmission, with more details onphase and group velocity, and on causality

July 22, 1997, The NewYork Times Company: Sig-nal Travels Farther and Faster Than Light Far Apart,2 Particles Respond Faster Than Light Archives

Markus Pssel: Faster-than-light (FTL) speeds intunneling experiments: an annotated bibliography

Alcubierre, Miguel; The Warp Drive: Hyper-FastTravel Within General Relativity, Classical andQuantum Gravity 11 (1994), L73L77

A systemized view of superluminal wave propaga-tion

Relativity and FTL Travel FAQ Usenet Physics FAQ: is FTL travel or communica-tion Possible?

Superluminal Relativity, FTL and causality Superluminal velocity fusing with Einstein specialrelativity

Stimulated Generation of Superlumi-nal Light Pulses via Four-Wave Mixingdoi:10.1103/PhysRevLett.108.173902

11.2 Proposed FTL Methods links 13

11.2 Proposed FTL Methods links Conical and paraboloidal superluminal particle ac-celerators

Relativity and FTL (=Superluminal motion) TravelHomepage

14 12 TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES

12 Text and image sources, contributors, and licenses12.1 Text

Faster-than-light Source: http://en.wikipedia.org/wiki/Faster-than-light?oldid=638915786 Contributors: Vicki Rosenzweig, Bryan Derk-sen, The Anome, Toby Bartels, Roadrunner, DrBob, Rickyrab, Boud, Michael Hardy, Modster, Brian Sayrs, Alodyne, Ixfd64, 6birc, Sebas-tianHelm, Tregoweth, Jimfbleak, JWSchmidt, Bueller 007, Aarchiba, Glenn, Evercat, John K, Ec5618, PS4FA, Charles Matthews, Timwi,Gingekerr, WhisperToMe, Timc, Tpbradbury, Val42, Phys, Topbanana, Zack, Baclan, Pakaran, Drernie, AnthonyQBachler, Pingveno,X-Bahamut, Auric, Rasmus Faber, UtherSRG, Jheise, Alexwcovington, Giftlite, DocWatson42, Sim, Wolfkeeper, Geeoharee, Leyman,LeYaYa, Foot, Anville, Curps, Waltpohl, Revth, Siroxo, SWAdair, Antandrus, Superborsuk, Rattlesnake, Latitude0116, Elroch, Icairns,Urhixidur, TJSwoboda, MakeRocketGoNow, , M1ss1ontomars2k4, Eisnel, Guppynsoup, Eep, Geof, Real NC, Rich Farmbrough,Hydrox, Dbachmann, Kipton, JustinWick, El C, Jeroenr, Art LaPella, Bobo192, O18, Army1987, Bradkittenbrink, Cwolfsheep, Foobaz,Fritz freiheit, Anr, Photonique, Larry V, Nhandler, Dfeldmann, Danski14, Gary, Anthony Appleyard, LtNOWIS, RPaschotta, Hack-wrench, DariuszT, Axl, EvanTPeoples, Yipdw, Wtmitchell, Jwinius, Count Iblis, LukeSurl, Oleg Alexandrov, Feezo, Angr, Mindmatrix,BenWilson, Percy Snoodle, Oliphaunt, Mcy, Meeso, GregorB,Waldir, Christopher Thomas, Aarghdvaark, Ashmoo, Corambis, Drbogdan,Teque5, Rjwilmsi, Strait, Arabani, Loudenvier, Eyu100, Mike Peel, Palpatine, R.e.b., Latka, RexNL, Mark J, Fosnez, Intgr, Fresheneesz,Alphachimp, Diza, DVdm, Manscher, Roboto de Ajvol, The Rambling Man, Hellsheep, Hairy Dude, Hillman, Icarus3, The Final Dream,Ihope127, Cryptic, Member, Spike Wilbury, GenestealerUK, ErkDemon, Trovatore, Dugosz, Prickus, Sted, ArmadniGeneral, Jeme,Hanredrst74, WayneC, Zwobot, Rwalker, Kortoso, DeadEyeArrow, Bota47, Jeh, SamuelRiv, Light current, Paul Magnussen, Deville,Zzuuzz, Knotnic, Eliezerke, Th1rt3en, Petri Krohn, Jetman123, Sambc, Georey.landis, Nixer, Eaefremov, JeBurdges, Sinus, Rogerwilco, ArquiWHAT, KasugaHuang, Alextrevelian 006, Locke Cole, Children of the dragon, SmackBot, Tom Lougheed, dit, Timeshifter,Lainagier, Cuddlyopedia, Gilliam, Skizzik, Hraefen, Ati3414, Chris the speller, Ziiv, Wuyz, EncMstr, Sadads, Sbharris, Colonies Chris,Emurphy42, Javalenok, Scwlong, Ron g, Furby100, Brentonstrine, Nima Baghaei, Matthew, LeContexte, Akral, RolandR, Dreadstar,Gregwmay, Doogie2K, Nairebis, MIKQ, Sayden, Minutes, Rory096, Soap, Vampus, JorisvS, Joshua Scott, Shattered, RomanSpa, Ripe,Starfyredragon, Dingopup, Hypnosi, Dr.K., Sopholatre, Grapplequip, Autonova, JarahE, Hu12, Michaelbusch, Newone, Tetrahedron93,Amakuru, Buddy13, Rangi42, Jman1974, JRSpriggs, Firehawk1717, Gregory9, CmdrObot, Amalas, Einstein runner, Vyznev Xnebara,Rwammang, DeLarge, Green caterpillar, Skybon, Rotiro, Logicus, Icek, Cydebot, Rapierian, ANTIcarrot, TMaster, Michael C Price, Fcn,Dchristle, Ldussan, Arb, Gimmetrow, Thijs!bot, Epbr123, Barticus88, Mbell, Martin Hogbin, Keraunos, Headbomb, Second Quantiza-tion, Hcobb, CharlotteWebb, D.H, Alphius, Will Bradshaw, Noclevername, Navigatr85, AntiVandalBot, Fru1tbat, AllanLee, Tyco.skinner,Yellowdesk, Samuel Erau, JAnDbot, DarthVadre, Canjth, Pedro, Chrisempson, JNW, SHCarter, Kim Dent-Brown, Think outside thebox, Wormcast, Theroadislong, Suvadip 192, Seleucus, Animum, Lenoil, BatteryIncluded, Dirac66, Tercer, Yawe, MarxistRevolutionary,Kronnang Dunn, R'n'B, Fusion7, Randyis, Jatoo, Wiki Raja, J.delanoy, Captain panda, Kpvats, Justaperson117, Dispenser, Andywebby,Aiglard, Myrin1, M-le-mot-dit, Tparameter, Warut, Richard D. 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Tjiptono and Anonymous: 598

12.2 Images File:Ambox_question.svg Source: http://upload.wikimedia.org/wikipedia/commons/1/1b/Ambox_question.svg License: Public domain

Contributors: Based on Image:Ambox important.svg Original artist: Mysid, Dsmurat, penubag

File:Earth-moon.jpg Source: http://upload.wikimedia.org/wikipedia/commons/5/5c/Earth-moon.jpg License: Public domain Contribu-tors: NASA [1] Original artist: Apollo 8 crewmember Bill Anders

File:History_of_the_Universe.svg Source: http://upload.wikimedia.org/wikipedia/commons/d/db/History_of_the_Universe.svg Li-cense: CC BY-SA 3.0 Contributors: Own work Original artist: Yinweichen

File:Sf-userbox.png Source: http://upload.wikimedia.org/wikipedia/en/0/05/Sf-userbox.png License: CC-BY-SA-3.0 Contributors:I (Senix (talk)) created this work entirely by myself. Original artist:Senix (talk)

12.3 Content license 15

12.3 Content license Creative Commons Attribution-Share Alike 3.0

FTL travel of non-informationDaily sky motionLight spots and shadowsApparent FTL propagation of static field effectsClosing speedsProper speedsHow far can one travel from the Earth?Phase velocities above cGroup velocities above cUniversal expansionAstronomical observationsQuantum mechanicsHartman effectCasimir effectEPR ParadoxDelayed choice quantum eraser

FTL communication possibilityJustificationsFaster light (Casimir vacuum and quantum tunnelling)Give up (absolute) relativitySpace-time distortionHeim theoryMiHsC/Quantised inertiaLorentz symmetry violationSuperfluid theories of physical vacuum

Time of flight of neutrinosMINOS experimentOPERA neutrino anomaly

TachyonsGeneral relativityVariable speed of lightSee alsoNotesReferencesExternal linksScientific linksProposed FTL Methods links

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