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| {{other uses|Faster than the speed of light (disambiguation)}}
| | Weight problem is just bad for wellness it will have a bad impact on earning power. Simply 10% increase in body mass index , a measure of weight relative to height, may cut a man's real earnings by 3.3% plus a woman's by 1.8%, Economists mentioned on wednesday.<br><br>People following the 3 day cardiac diet might probably feel hunger pangs and have lower energy degrees. This is especially true by the third day. But, keep in your mind that the diet is of limited duration and we should be fine unless we have stamina based physical feats to perform.<br><br>Examples 1 plus 2 show that an exponent of 3 is much more realistic than 2 for estimating the weight of a person for a provided height. With all due modesty, I propose the Larry Index (LI) as a reasonable compromise, plus because a realistic alternative to Ancel Keys' BMI.<br><br>A lot of folks have benefited from the [http://safedietplans.com/bmi-calculator bmi calculator] over the past few years nonetheless, there are more accurate alternatives available today. If you are not certain what method is ideal for the current condition, then we should consult a wellness expert for right guidance.<br><br>How do we recognize when you child is really obese or obese? You physician may assist we determine whether the child meets the criteria for medical obesity, although you may be able to determine at home whether the child meets the criteria to be greatly overweight or obese..<br><br>This means which the query of the ideal weight range for athletic women inside their 40's is a tough nut to crack. The body is a body, no matter what age you may be plus regardless of what amount of physical activity we do. Ladies, if you need to have the body of the 21-year-old, we can do it.<br><br>So, this would require time management. There are a great deal of exercise programs available even online for you to do and accomplish. It's all as much as we. If in case as of the moment you do not have the time to do it, then maybe doing a small adjustment in a daily escapades would be a advantageous start. |
| {{synthesis|date=September 2011}}
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| '''Faster-than-light''' (also '''superluminal''' or '''FTL''') [[Superluminal communication|communications]] and [[interstellar travel|travel]] refer to the propagation of [[information]] or [[matter]] faster than the [[speed of light]]. | |
| Under the [[special theory of relativity]], a particle (that has [[Mass in special relativity|rest mass]]) with subluminal velocity needs infinite energy to accelerate to the speed of light, although special relativity does not forbid the existence of particles that travel faster than light at all times ([[tachyon]]s).
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| On the other hand, what some physicists refer to as "apparent" or "effective" FTL<ref>
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| {{cite journal
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| | last = Gonzalez-Diaz | first = P. F.
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| | year = 2000
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| | title = Warp drive space-time
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| | url = http://omnis.if.ufrj.br/~mbr/warp/etc/PRD62_44005.pdf
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| | journal = [[Physical Review D]]
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| | volume = 62 | issue = 4 | page = 044005
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| | arxiv=gr-qc/9907026
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| | doi = 10.1103/PhysRevD.62.044005
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| | bibcode = 2000PhRvD..62d4005G
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| }}</ref><ref>
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| {{cite arXiv
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| |last1=Loup |first1=F.
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| |last2=Waite |first2=D.
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| |last3=Halerewicz |first3=E. Jr.
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| |year=2001
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| |title=Reduced total energy requirements for a modified Alcubierre warp drive spacetime
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| |class=gr-qc
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| |eprint=gr-qc/0107097
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| }}</ref><ref>
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| {{cite journal
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| |last1=Visser |first=M.
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| |last2=Bassett |first2=B.
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| |last3=Liberati |first3=S.
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| |year=2000
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| |title=Superluminal censorship
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| |journal=[[Nuclear Physics B: Proceedings Supplement]]
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| |volume=88 |pages=267–270
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| |arxiv=gr-qc/9810026
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| |bibcode = 2000NuPhS..88..267V
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| |doi=10.1016/S0920-5632(00)00782-9
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| }}</ref><ref>
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| {{cite journal
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| |last1=Visser |first=M.
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| |last2=Bassett |first2=B.
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| |last3=Liberati |first3=S.
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| |year=1999
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| |title=Perturbative superluminal censorship and the null energy condition
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| |journal=[[AIP Conference Proceedings]]
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| |volume=493 |pages=301–305
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| |arxiv=gr-qc/9908023
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| |doi=10.1063/1.1301601
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| |isbn=1-56396-905-X | |
| }}</ref> depends on the hypothesis that unusually distorted regions of [[spacetime]] might permit matter to reach distant locations in less time than light could in normal or undistorted spacetime. Although according to current theories matter is still required to travel subluminally with respect to the locally distorted spacetime region, ''apparent'' FTL is not excluded by [[general relativity]].
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| Examples of FTL proposals are the [[Alcubierre drive]] and the [[Wormhole#Traversable wormholes|traversable wormhole]], although their physical plausibility is uncertain.
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| ==FTL travel of non-information==
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| In the context of this article, FTL is the transmission of information or matter faster than ''c'', a constant equal to the [[speed of light]] in a vacuum, which is 299,792,458 meters per second (by definition) or about 186,282.4 miles per second. This is not quite the same as traveling faster than light, since:
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| * Some processes propagate faster than ''c'', but cannot carry information (see examples in the sections immediately following).
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| * Light travels at speed ''c/n'' when not in a vacuum but [[time-of-flight|travelling]] through a medium with [[refractive index]] = ''n'' (causing [[refraction]]), and in some materials other particles can travel faster than ''c/n'' (but still slower than ''c''), leading to [[Cherenkov radiation]] (see phase velocity below).
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| Neither of these phenomena violates [[special relativity]] or creates problems with [[causality]], and thus neither qualifies as ''FTL'' as described here.
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| 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.
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| ===Daily sky motion===
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| For an earthbound observer, objects in the sky complete one revolution around the Earth in 1 day. [[Proxima Centauri]], which is the nearest star outside the [[solar system]], is about 4 [[light-year]]s away.<ref name="A2 Student Book">See Salters Horners ''Advanced Physics A2 Student Book'', Oxford etc. (Heinemann) 2001, pp. 302 and 303</ref> On a [[geostationary]] view Proxima Centauri has a speed many times greater than ''c'' as the rim speed of an object moving in a circle is a product of the radius and angular speed.<ref name="A2 Student Book" /> It is also possible on a geostatic view 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 1000 [[Astronomical unit|AU]].<ref>see http://www.oarval.org/furthest.htm</ref> 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.
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| ===Light spots and shadows===
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| If a laser is swept across a distant object, the spot of laser light can easily be made to move across the object at a speed greater than ''c''.<ref name="Gibbs" /> Similarly, a shadow projected onto a distant object can be made to move across the object faster than ''c''.<ref name="Gibbs">{{cite journal |last=Gibbs |first=Philip |year=1997 |url=http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html |title=Is Faster-Than-Light Travel or Communication Possible? |publisher=University of California, Riverside |accessdate=20 August 2008 |postscript=<!--None--> }}</ref> In neither case does the light travel from the source to the object faster than ''c'', nor does any information travel faster than light.<ref name="Gibbs" /><ref>{{cite book |title=Four Decades of Scientific Explanation |first1=Wesley C. |last1=Salmon |publisher=University of Pittsburgh Pre |year=2006 |isbn=0-8229-5926-7 |page=107 |url=http://books.google.com/books?id=FHqOXCd06e8C }}, [http://books.google.com/books?id=FHqOXCd06e8C&pg=PA107 Extract of page 107]</ref><ref>{{cite book |title=The Wonderful World of Relativity: A Precise Guide for the General Reader |first1=Andrew |last1=Steane |publisher=Oxford University Press |year=2012 |isbn=0-19-969461-3 |page=180 |url=http://books.google.com/books?id=4m14K1PpJwMC }}, [http://books.google.com/books?id=4m14K1PpJwMC&pg=PA180 Extract of page 180]</ref>
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| ===Apparent FTL propagation of static field effects===
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| {{main|Static field}}
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| Since there is no "retardation" (or [[aberration of light|aberration]]) of the apparent position of the source of a [[gravitation]]al or [[electric]] [[static field]] when the source moves with constant velocity, the static field "effect" may seem at first glance to be "transmitted" faster than the speed of light. However, uniform motion of the static source may be removed with a change in reference frame, causing the direction of the static field to change immediately, at all distances. This is not a change of position which "propagates", and thus this change cannot be used to transmit information from the source. No information or matter can be FTL-transmitted or propagated from source to receiver/observer by an electromagnetic field.
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| ===Closing speeds===
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| 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.
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| Imagine two fast-moving particles approaching each other from opposite sides of a [[particle accelerator]] of 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.
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| [[Special relativity]] does not prohibit this. It tells us that it is wrong to use [[Galilean relativity]] to 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 [[velocity-addition formula|right formula]] for computing such [[relative velocity]].
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| It is instructive to compute the relative velocity of particles moving at ''v'' and -''v'' in accelerator frame, which corresponds to the closing speed of 2''v'' > ''c''. Expressing the speeds in units of ''c'', β = ''v''/''c'':
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| :<math>\beta_{rel} = { \beta + \beta \over 1 + \beta ^2 } = { 2\beta \over 1 + \beta^2 } \leq 1.</math>
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| ===Proper speeds===
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| 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 a [[proper 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.
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| ===How far can one travel from the Earth?===
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| Since one might not travel faster than light, one might conclude that a human can never travel further from the earth than 40 light-years if the traveler is active between the age of 20 and 60. A traveler would then never be able to reach more than the very few star systems which exist within the limit of 20-40 light-years from the Earth. This is a mistaken conclusion: because of [[time dilation]], the traveler can travel thousands of light-years during their 40 active years. If the spaceship accelerates at a constant 1 g (in its own changing frame of reference), it will, after 354 days, reach speeds a little under the [[speed of light]] (for an observer on Earth), and [[time dilation]] will increase their lifespan to thousands of Earth years, seen from the reference system of the [[Solar System]], but the traveler's subjective lifespan will not thereby change. If the traveler returns to the Earth, they will land thousands of years into the future. Their speed will not be seen as higher than the speed of light by observers on Earth, and the traveler will not measure their speed as being higher than the [[speed of light]], but will see a length contraction of the universe in their direction of travel. And as the traveler turns around to return, the Earth will seem to experience much more time than the traveler does. So, although their (ordinary) speed cannot exceed ''c'', the [[four-velocity]] (distance as seen by Earth divided by their proper, i.e. subjective, time) can be much greater than ''c''. This is seen in statistical studies of [[muon]]s traveling much further than ''c'' times their [[half-life]] (at rest), if traveling close to ''c''.<ref>[http://library.thinkquest.org/C0116043/specialtheorytext.htm Special Theory of Relativity<!-- Bot generated title -->]</ref>
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| ===Phase velocities above ''c''===
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| The [[phase velocity]] of an [[electromagnetic wave]], when traveling through a medium, can routinely exceed ''c'', the vacuum velocity of light. For example, this occurs in most glasses at [[X-ray]] frequencies.<ref>{{cite book |first=Eugene |last=Hecht |year=1987 |title=Optics |edition=2nd |publisher=Addison Wesley |isbn=0-201-11609-X |page=62 }}</ref> However, the phase velocity of a wave corresponds to the propagation speed of a theoretical single-frequency (purely [[monochromatic]]) 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.<ref>{{cite journal |first=Arnold |last=Sommerfeld |year=1907 |title=[[s:An Objection Against the Theory of Relativity and its Removal|An Objection Against the Theory of Relativity and its Removal]] |journal=Physikalische Zeitschrift |volume=8 |issue=23 |pages=841–842 }}</ref>
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| Thus a phase velocity above ''c'' does not imply the propagation of [[signal (information theory)|signals]] with a velocity above ''c''.<ref name="phase">{{cite web |title=MathPages - Phase, Group, and Signal Velocity |url=http://www.mathpages.com/home/kmath210/kmath210.htm |accessdate=2007-04-30 }}</ref>
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| ===Group velocities above ''c''===
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| The [[group velocity]] of a wave (e.g., a light beam) may also exceed ''c'' in some circumstances. 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 above ''c''. However, even this situation does not imply the propagation of [[signal (information theory)|signals]] with a velocity above ''c'',<ref>Brillouin, Léon; ''Wave Propagation and Group Velocity'', Academic Press, 1960</ref> even though one may be tempted to associate pulse maxima with signals. The latter association has been shown to be misleading, basically 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 than ''c'' without this effect.<ref>Withayachumnankul, W.; et al.; [http://www.eleceng.adelaide.edu.au/personal/dabbott/publications/PIE_withayachumnankul2010.pdf "A systemized view of superluminal wave propagation,"] ''[[Proceedings of the IEEE]]'', Vol. 98, No. 10, pp. 1775-1786, 2010</ref>
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| ===Universal expansion===
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| The expansion of the [[universe]] causes distant galaxies to recede from us faster than the speed of light, if [[comoving distance]] and cosmological time are used to calculate the speeds of these galaxies. However, in [[general relativity]], velocity is a local notion, so velocity calculated using comoving coordinates does not have any simple relation to velocity calculated locally.<ref>{{cite web |url=http://www.astro.ucla.edu/~wright/cosmo_02.htm#MD |title=Cosmology Tutorial - Part 2 |publisher=Astro.ucla.edu |date=2009-06-12 |accessdate=2011-09-26 }}</ref> (See ''[[Comoving distance#Uses of the proper distance|comoving distance]]'' for a discussion of different notions of 'velocity' in cosmology.) Rules that apply to relative velocities in special relativity, such as the rule that relative velocities cannot increase past the speed of light, do not apply to relative velocities in comoving coordinates, which are often described in terms of the "expansion of space" between galaxies. This expansion rate is thought to have been at its peak during the [[inflationary epoch]] thought to have occurred in a tiny fraction of the second after the [[Big Bang]] (models suggest the period would have been from around 10<sup>−36</sup> seconds after the Big Bang to around 10<sup>−33</sup> seconds), when the universe may have rapidly expanded by a factor of around 10<sup>20</sup> to 10<sup>30</sup>.<ref>{{cite web |url=http://hyperphysics.phy-astr.gsu.edu/hbase/astro/planck.html#c5 |title=Inflationary Period from HyperPhysics |publisher=Hyperphysics.phy-astr.gsu.edu |accessdate=2011-09-26 }}</ref>
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| There are many galaxies visible in telescopes with [[red shift]] numbers of 1.4 or higher. All of these are currently traveling away from us at speeds greater than the speed of light. Because the [[Hubble's law#Interpretation|Hubble parameter]] is 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.<ref>[http://curious.astro.cornell.edu/question.php?number=575 Is the universe expanding faster than the speed of light?] (see the last two paragraphs)</ref><ref name="ly93">{{cite web |last=Lineweaver |first=Charles |coauthors=Davis, Tamara M. |year=2005 |url=http://space.mit.edu/~kcooksey/teaching/AY5/MisconceptionsabouttheBigBang_ScientificAmerican.pdf |title=Misconceptions about the Big Bang |publisher=Scientific American |accessdate=2008-11-06 }}</ref> However, because [[Accelerating universe|the expansion of the universe is accelerating]], it is projected that most galaxies will eventually cross a type of cosmological [[event horizon]] where any light they emit past that point will never be able to reach us at any time in the infinite future,<ref>{{cite journal |last=Loeb |first=Abraham |title=The Long-Term Future of Extragalactic Astronomy |journal=Physical Review D |volume=65 |issue=4 |year=2002 |doi=10.1103/PhysRevD.65.047301 |arxiv=astro-ph /0107568 |bibcode=2002PhRvD..65d7301L }}</ref> 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 in [[Comoving distance#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.<ref name="ly93" />
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| ===Astronomical observations===
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| Apparent [[superluminal motion]] is observed in many [[Active galaxy|radio galaxies]], [[blazar]]s, [[quasar]]s and recently also in [[microquasar]]s. The effect was predicted before it was observed by [[Martin Rees]]{{clarify|Was it predicted by Rees or observed by Rees?|date=March 2012}} and can be explained as an [[optical illusion]] caused by the object partly moving in the direction of the observer,<ref>{{cite journal |last1=Rees |first1=Martin J. |title=Appearance of relativistically expanding radio sources |journal=Nature |volume=211 |issue=5048 |year=1966 |page=468 |bibcode=1966Natur.211..468R |doi = 10.1038/211468a0 }}</ref> when the speed calculations assume it does not. The phenomenon does not contradict the theory of [[special relativity]]. Interestingly, 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.<ref>{{cite journal |last1=Blandford |first1=Roger D. |authorlink=Roger Blandford |last2=McKee |first2=C. F. |last3=Rees |first3=Martin J. |title=Super-luminal expansion in extragalactic radio sources |journal=Nature |volume=267 |page=211 |issue=5608 |year=1977 |doi=10.1038/267211a0 |bibcode=1977Natur.267..211B }}</ref> Earth-bound laboratories have only been able to accelerate small numbers of elementary particles to such speeds.
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| ===Quantum mechanics===
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| Certain phenomena in [[quantum mechanics]], such as [[quantum entanglement]], might give the superficial impression of allowing communication information faster than light. According to the [[no-communication theorem]] these 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 collapse]] can be viewed as an [[epiphenomenon]] of quantum decoherence, which in turn is nothing more than an effect of the underlying local time evolution of the wavefunction of a system and ''all'' of its environment. Since the ''underlying'' behaviour doesn't violate local causality or allow FTL it follows that neither does the additional effect of wavefunction collapse, whether real ''or'' apparent.
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| The [[uncertainty principle]] implies that individual photons may travel for short distances at speeds somewhat faster (or slower) than ''c'', even in a vacuum; this possibility must be taken into account when enumerating [[Feynman diagram]]s for a particle interaction.<ref>{{cite book |last=Feynman |title=QED |chapter=Chapter 3 |page=89 |isbn=981-256-914-6 }}</ref> It has since been proven that a single photon may not travel faster than ''c''.<ref>{{cite web |last=Zhang |first=Shanchao |title=Single photons obey the speed limits |url=http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.106.243602 |work=Physics |publisher=American Physical Society |accessdate=25 July 2011 }}</ref> In quantum mechanics, [[virtual particle]]s may travel faster than light, and this phenomenon is related to the fact that static field effects (which are mediated by virtual particles in quantum terms) may travel faster than light (see section on static fields above). However, macroscopically these fluctuations average out, so that photons do travel in straight lines over long (i.e., non-quantum) distances, and they do travel at the speed of light on average. Therefore, this does not imply the possibility of superluminal information transmission.
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| 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 of [[quantum tunnelling]] phenomenon. Usually, such reports deal with a [[phase velocity]] or [[group velocity]] faster than the vacuum velocity of light.{{citation needed|date=September 2011}} However, as stated above, a superluminal ''phase velocity'' cannot be used for faster-than-light transmission of information. There has sometimes been confusion concerning the latter point. Additionally a channel that permits such propagation cannot be laid out faster than the speed of light.{{citation needed|date=September 2011}}
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| [[Quantum teleportation]] transmits quantum information at whatever speed is used to transmit the same amount of classical information, likely the speed of light. This quantum information may theoretically be used in ways that classical information can not, such as in quantum computations involving quantum information only available to the recipient.
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| ====Hartman effect====
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| {{Main|Hartman effect}}
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| The Hartman effect is the tunnelling effect through a barrier where the tunnelling time tends to a constant for large barriers.<ref>Martinez, J. C.; and Polatdemir, E.; "Origin of the Hartman effect", ''Physics Letters A'', Vol. 351, Iss. 1-2, 20 February 2006, pp. 31-36</ref> This was first described by [[Thomas Hartman (scientist)|Thomas Hartman]] in 1962.<ref>Hartman, Thomas E.; "Tunneling of a wave packet", ''Journal of Applied Physics'' 33, 3427 (1962)</ref> 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 nonzero probability that the photon will tunnel across the gap rather than follow the refracted path. For large gaps between the prisms the tunnelling time approaches a constant and thus the photons appear to have crossed with a superluminal speed.<ref name="nimtz1" />
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| However, an analysis by Herbert G. Winful from the University of Michigan suggests that the Hartman effect cannot actually be used to violate relativity by transmitting signals faster than ''c'', because the tunnelling time "should not be linked to a velocity since evanescent waves do not propagate".<ref>Winful, Herbert G.; [http://sitemaker.umich.edu/herbert.winful/files/physics_reports_review_article__2006_.pdf "Tunneling time, the Hartman effect, and superluminality: A proposed resolution of an old paradox"], ''Physics Reports'', Vol. 436, Iss. 1-2, December 2006, pp. 1-69</ref> 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.
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| ====Casimir effect====
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| In physics, the [[Casimir effect]] or Casimir-Polder force is a physical force exerted between separate objects due to resonance of [[vacuum energy]] in 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.
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| ====EPR Paradox====
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| The [[EPR paradox]] refers to a famous [[thought experiment]] of Einstein, Podolski and Rosen that was realized experimentally for the first time by [[Alain Aspect]] in 1981 and 1982 in the [[Aspect experiment]]. In this experiment, the measurement of the state of one of the quantum systems of an [[quantum entanglement|entangled]] pair apparently instantaneously forces the other system (which may be distant) to be measured in the complementary state. 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 which [[Interpretations of quantum mechanics|interpretation of quantum mechanics]] one subscribes to.
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| An experiment performed in 1997 by Nicolas Gisin at the University of Geneva has demonstrated non-local quantum correlations between particles separated by over 10 kilometers.<ref>{{cite web|url=http://www.quantumphil.org/history.htm |title=History |publisher=Quantumphil.org |accessdate=2011-09-26 }}</ref> 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; see [[no-communication theorem]] for further information. A 2008 quantum physics experiment also performed by Nicolas Gisin and his colleagues in [[Geneva, Switzerland]] has determined that in any hypothetical [[Hidden variable theory#Non-local hidden-variable theory|non-local hidden-variables theory]] the speed of the ''quantum non-local connection'' (what Einstein called "spooky action at a distance") is at least 10,000 times the speed of light.<ref>{{cite journal |author1=Salart |author2=Baas |author3=Branciard |author4=Gisin |author5=Zbinden |doi=10.1038/nature07121 |journal=Nature |volume=454 |title=Testing spooky action at a distance |issue=7206 |pages=861–864 |year=2008 |arxiv=0808.3316 |bibcode=2008Natur.454..861S |pmid=18704081 }}</ref>
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| ====Delayed choice quantum eraser====
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| {{Main|Delayed choice quantum eraser}}
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| [[Delayed choice quantum eraser]] (an experiment of [[Marlan Scully]]) is a version of the EPR paradox in which the observation or not of interference after the passage of a photon through a [[double slit experiment]] depends 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,<ref>{{cite web |url=http://www.bottomlayer.com/bottom/kim-scully/kim-scully-web.htm |title=Delayed Choice Quantum Eraser |publisher=Bottomlayer.com |date=2002-09-04 |accessdate=2011-09-26 }}</ref> 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 can't 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 FTL or backwards-in-time manner.<ref>Scientific American : Delayed-Choice Experiments http://www.scientificamerican.com/article.cfm?id=quantum-eraser-delayed-choice-experiments</ref><ref>The Reference Frame: Delayed Choice Quantum Eraser http://motls.blogspot.com/2010/11/delayed-choice-quantum-eraser.html</ref>
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| ==FTL communication possibility==
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| Faster-than-light communication is, by [[Einstein]]'s [[theory of relativity]], equivalent to [[time travel]]. According to Einstein's theory of [[special relativity]], what we measure as the [[speed of light]] in a vacuum is actually the fundamental physical constant ''c''. This means that all [[inertial]] observers, regardless of their relative [[velocity]], will always measure zero-mass particles such as [[photon]]s traveling at ''c'' in a 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 by [[Poincaré transformation]]s. These transformations have important implications:
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| * The relativistic momentum of a [[mass]]ive particle would increase with speed in such a way that at the speed of light an object would have infinite momentum.
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| * To accelerate an object of non-zero [[Mass in special relativity|rest mass]] to ''c'' would require infinite time with any finite acceleration, or infinite acceleration for a finite amount of time.
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| * Either way, such acceleration requires infinite energy.
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| * Some observers with sub-light relative motion will disagree about which occurs first of any two events that are separated by a [[Spacetime interval|space-like interval]].<ref>Einstein, Albert, ''Relativity:the special and the general theory'', Methuen & Co, 1927, pp. 25-27</ref> 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,{{Citation needed|date=March 2013}} or need to assume the speculative hypothesis of possible Lorentz violations at a presently unobserved scale (for instance the Planck scale).{{Citation needed|date=March 2013}} Therefore any theory which permits "true" FTL also has to cope with [[time travel]] and all its associated paradoxes,<ref>{{cite journal |first=J. Richard |last=Gott |title=Time Travel in Einstein's Universe |year=2002 |pages=pp. 82–83}}</ref> or else to assume the [[Lorentz invariance]] to be a symmetry of thermodynamical statistical nature (hence a symmetry broken at some presently unobserved scale).
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| * In special relativity the coordinate speed of light is only guaranteed to be ''c'' in an [[inertial frame of reference|inertial frame]], in a non-inertial frame the coordinate speed may be different from ''c'';<ref>Petkov, Vesselin; ''Relativity and the Nature of Spacetime'', [http://books.google.com/books?id=AzfFo6A94WEC&lpg=PR1&pg=PA219#v=onepage&q&f=false p. 219]</ref> in general relativity no coordinate system on a large region of curved spacetime is "inertial", so it's permissible to use a global coordinate system where objects travel faster than ''c'', 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 be ''c'' in this frame,<ref>Raine, Derek J.; Thomas, Edwin George; and Thomas, E. G.; ''An Introduction to the Science of Cosmology'', [http://books.google.com/books?id=RK8qDGKSTPwC&lpg=PR1&pg=PA94#v=onepage&q&f=false p. 94]</ref> with massive objects moving through this local neighborhood always having a speed less than ''c'' in the local inertial frame.
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| ==Justifications==
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| ===Faster light (Casimir vacuum and quantum tunnelling)===
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| [[Raymond Y. Chiao]] was first to measure the quantum tunnelling time, which was found to be between 1.5 to 1.7 times the speed of light.
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| Einstein's equations of [[special relativity]] postulate that the speed of light in a vacuum is invariant in [[inertial 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 the light, which is an experimentally determined quantity for a fixed unit of length. Since 1983, the [[International System of Units|SI]] unit of length (the [[meter]]) has been defined using the [[speed of light]].
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| 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, unsurprisingly called the [[vacuum energy]]. This vacuum energy can perhaps be changed in certain cases.<ref>{{cite web |title=What is the 'zero-point energy' (or 'vacuum energy') in quantum physics? Is it really possible that we could harness this energy? |url=http://www.scientificamerican.com/article.cfm?id=follow-up-what-is-the-zer |publisher=Scientific American |date=1997-08-18 |accessdate=2009-05-27 }}</ref> When vacuum energy is lowered, light itself has been predicted to go faster than the standard value ''c''. This is known as the [[Scharnhorst effect]]. Such a vacuum can be produced by bringing two perfectly smooth metal plates together at near atomic diameter spacing. It is called a [[Casimir effect#Vacuum energy|Casimir 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 10<sup>36</sup>.<ref>{{cite web |author=Scharnhorst, Klaus |title=Secret of the vacuum: Speedier light |date=1990-05-12 |accessdate=2009-05-27 |url= http://www.nat.vu.nl/~scharnh/m16scine.htm }}</ref> Accordingly there has as yet been no experimental verification of the prediction. A recent analysis<ref name="lib">{{cite journal |title=Faster-than-c signals, special relativity, and causality |author=Visser, Matt |coauthors=Liberati, Stefano; and Sonego, Sebastiano |date=2001-07-27 |pages=167–185 |volume=298 |doi=10.1006/aphy.2002.6233 |journal=Annals of Physics |arxiv=gr-qc/0107091 |bibcode=2002AnPhy.298..167L }}</ref> 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 signalling. 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 speculative [[chronology protection conjecture]] which 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-''c'' signals involved approximations which may be incorrect, so that it is not clear whether this effect could actually increase signal speed at all.<ref>{{cite journal |author1=Fearn, Heidi |doi=10.1134/S1054660X07050155 |journal=LaserPhys. |volume=17 |title=Can Light Signals Travel Faster than ''c'' in Nontrivial Vacuua in Flat space-time? Relativistic Causality II |issue=5 |pages=695–699 |year=2007 |arxiv=0706.0553 |bibcode=2007LaPhy..17..695F }}</ref>
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| The physicists [[Günter Nimtz]] and Alfons Stahlhofen, of the [[University of Cologne]], claim to have violated relativity experimentally by transmitting photons faster than the speed of light.<ref name="nimtz1">{{cite arXiv |eprint=0708.0681 |author1=Nimtz, Günter |author2=Stahlhofen, Alfons |title=Macroscopic violation of special relativity |class=quant-ph |year=2007 }}</ref> They say they have conducted an experiment in which microwave photons—relatively low energy packets of light—travelled "instantaneously" between a pair of prisms that had been moved up to {{convert|3|ft|0|abbr=on}} apart. Their experiment involved an optical phenomenon known as [[Evanescent wave|"evanescent modes"]], and they claim that since evanescent modes have an imaginary wave number, they represent a "mathematical analogy" to [[quantum tunnelling]].<ref name="nimtz1" /> Nimtz has also claimed that "evanescent modes are not fully describable by the [[Maxwell's equations|Maxwell equations]] and quantum mechanics have to be taken into consideration."<ref>Nimtz, Günter; [http://cdsweb.cern.ch/record/547324/files/0204043.pdf?version=1 ''Superluminal Tunneling Devices''], 2001</ref> Other scientists such as Herbert G. Winful and Robert Helling have argued that in fact there is nothing quantum-mechanical about Nimtz's experiments, and that the results can be fully predicted by the equations of [[classical electromagnetism]] (Maxwell's equations).<ref name="winful">{{cite arXiv |title=Comment on "Macroscopic violation of special relativity" by Nimtz and Stahlhofen |eprint=0709.2736 |author=Winful, Herbert G. |date=2007-09-18 |class=quant-ph }}</ref><ref>[http://www.atdotde.de/ Helling, Robert C.]; [http://atdotde.blogspot.com/2005/09/faster-than-light-or-not.html "Faster than light or not"] (blog)</ref>
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| Nimtz told ''[[New Scientist]]'' magazine: "For the time being, this is the only violation of special relativity that I know of." However, other physicists say that this phenomenon does not allow information to be transmitted faster than light. Aephraim Steinberg, a quantum optics expert at the [[University of Toronto]], Canada, uses the analogy of a train traveling from Chicago to New York, but dropping off train cars at each station along the way, so that the center of the ever shrinking main train moves forward at each stop; in this way, the speed of the center of the train exceeds the speed of any of the individual cars.<ref name="nimtz">{{cite news |last=Anderson |first=Mark |title=Light seems to defy its own speed limit |magazine=[[New Scientist]] |volume=195 |issue=2617 |page=10 |date=18–24 August 2007 |url=http://www.eurekalert.org/pub_releases/2007-08/ns-lst081607.php |postscript=<!--None--> }}</ref>
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| Herbert G. Winful argues that the train analogy is a variant of the "reshaping argument" for superluminal tunneling velocities, but he goes on to say that this argument is not actually supported by experiment or simulations, which actually show that the transmitted pulse has the same length and shape as the incident pulse.<ref name="winful" /> Instead, Winful argues that the [[Group velocity|group delay]] in tunneling is not actually the transit time for the pulse (whose spatial length must be greater than the barrier length in order for its spectrum to be narrow enough to allow tunneling), but is instead the lifetime of the energy stored in a [[standing wave]] which forms inside the barrier. Since the stored energy in the barrier is less than the energy stored in a barrier-free region of the same length due to destructive interference, the group delay for the energy to escape the barrier region is shorter than it would be in free space, which according to Winful is the explanation for apparently superluminal tunneling.<ref name="WinfulHartman">{{cite journal |last=Winful |first=Herbert G. |title=Tunneling time, the Hartman effect, and superluminality: A proposed resolution of an old paradox |journal=Physics Reports |volume=436 |issue=1–2 |pages=1–69 |date=December 2006 |url=http://sitemaker.umich.edu/herbert.winful/files/physics_reports_review_article__2006_.pdf |doi=10.1016/j.physrep.2006.09.002 |bibcode=2006PhR...436....1W }}</ref><ref name="WinfulArticle">For a summary of Herbert G. Winful's explanation for apparently superluminal tunneling time which does not involve reshaping, see http://spie.org/x18001.xml?ArticleID=x18001</ref>
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| A number of authors have published papers disputing Nimtz's claim that Einstein causality is violated by his experiments, and there are many other papers in the literature discussing why quantum tunneling is not thought to violate causality.<ref>A number of papers are listed at [http://www.aei.mpg.de/~mpoessel/Physik/FTL/tunnelingftl.html Literature on Faster-than-light tunneling experiments]</ref>
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| It was later claimed by the Keller group in Switzerland that particle tunneling does indeed occur in zero real time. Their tests involved tunneling electrons, where the group argued a relativistic prediction for tunneling time should be 500-600 attoseconds (an [[attosecond]] is one quintillionth (10<sup>−18</sup>) of a second). All that could be measured was 24 attoseconds, which is the limit of the test accuracy.<ref name="Eckle">Eckle, P.; et al., "Attosecond Ionization and Tunneling Delay Time Measurements in Helium", Science, 322 (2008) 1525</ref> 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.<ref name="WinfulHartman" /><ref name="WinfulArticle" /><ref name="Sokolovski">{{cite journal |last=Sokolovski |first=D. |title=Why does relativity allow quantum tunneling to 'take no time'? |journal=[[Proceedings of the Royal Society]] A |volume=460 |issue=2042 |pages=499–506 |date=8 February 2004 |url=http://rspa.royalsocietypublishing.org/content/460/2042/499.full.pdf |doi=10.1098/rspa.2003.1222 |bibcode=2004RSPSA.460..499S }}</ref>
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| ===Give up (absolute) relativity===
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| Because of the strong empirical support for [[special relativity]], any modifications to it must necessarily be quite subtle and difficult to measure. The best-known attempt is [[doubly special relativity]], which posits that the [[Planck length]] is also the same in all reference frames, and is associated with the work of [[Giovanni Amelino-Camelia]] and [[João Magueijo]]. One consequence of this theory is a [[variable speed of light]], where photon speed would vary with energy, and some zero-mass particles might possibly travel faster than ''c''.{{citation needed|date=February 2007}} However, even if this theory is accurate, it is still very unclear whether it would allow information to be communicated, and appears not in any case to allow massive particles to exceed ''c''.
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| 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 be ''preferred'' by conventional measurements of natural law. If confirmed, this would imply [[special relativity]] is an approximation to a more general theory, but since the relevant comparison would (by definition) be outside the [[observable universe]], it is difficult to imagine (much less construct) experiments to test this hypothesis.
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| ===Space-time distortion===
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| Although the theory of [[special relativity]] forbids objects to have a relative velocity greater than light speed, and [[general relativity]] reduces 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.<ref name="misconceptions">{{cite news |author=Lineweaver, Charles H.; and Davis, Tamara M. |title=Misconceptions about the Big Bang |publisher=Scientific American |date=March 2005 |url=http://www.sciam.com/article.cfm?id=misconceptions-about-the-2005-03 }}</ref> [[Miguel Alcubierre]] [http://www.iop.org/EJ/abstract/0264-9381/11/5/001 theorized] that it would be possible to create an [[Alcubierre 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. However, [[Alcubierre drive#Difficulties|several objections]] raised 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 the [[wormhole#Traversable wormholes|traversable wormhole]], which could create a shortcut between arbitrarily distant points in space. As with the Alcubierre drive, travelers moving through the wormhole would not ''locally'' move faster than light which travels 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.
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| Dr. Gerald Cleaver, associate professor of physics at [[Baylor University]], and Richard Obousy, a Baylor graduate student, theorize that by manipulating the extra spatial dimensions of [[string theory]] around a spaceship with an extremely large amount of energy, it 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 the [[dark energy]] in 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.<ref>[http://newswise.com/articles/view/543391/ Traveling Faster Than the Speed of Light: A New Idea That Could Make It Happen] Newswise, retrieved on 24 August 2008.</ref>
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| ===Heim theory===
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| In 1977, a paper on [[Heim theory]] theorized that it may be possible to travel faster than light by using magnetic fields to enter a higher-dimensional space.<ref>{{cite journal |author=Heim, Burkhard |title=Vorschlag eines Weges einer einheitlichen Beschreibung der Elementarteilchen [Recommendation of a Way to a Unified Description of Elementary Particles] |journal=Zeitschrift für Naturforschung |year=1977 |volume=32a |pages=233–243 |bibcode=1977ZNatA..32..233H }}</ref>
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| ===MiHsC/Quantised inertia===
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| A new theory has been proposed that '''M'''odifies '''i'''nertia by assuming it is due to [[Unruh effect|Unruh radiation]] subject to a '''H'''ubble '''s'''cale '''C'''asimir effect ('''MiHsC''', or quantised inertia). MiHsC predicts a minimum possible acceleration<ref>{{cite journal |author=McCulloch, M. E. |title=Minimum accelerations from quantised inertia |journal=EPL |year=2010 |volume=90 |page=29001 |bibcode=2010EL.....9029001M |doi=10.1209/0295-5075/90/29001 |arxiv=1004.3303 |issue=2 }}</ref> even at light speed, implying that this speed can be exceeded.
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| ===Lorentz symmetry violation===
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| {{Main|Modern searches for Lorentz violation|Standard-Model Extension}}
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| 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-called [[Standard-Model Extension]].<ref>{{cite journal |arxiv=hep-ph/9703464 |bibcode=1997PhRvD..55.6760C |doi=10.1103/PhysRevD.55.6760 |title=CPT violation and the standard model |year=1997 |last1=Colladay |first1=Don |last2=Kostelecký |first2=V. Alan |journal=Physical Review D |volume=55 |issue=11 |page=6760 }}</ref><ref>{{cite journal |arxiv=hep-ph/9809521 |bibcode=1998PhRvD..58k6002C |doi=10.1103/PhysRevD.58.116002 |title=Lorentz-violating extension of the standard model |year=1998 |last1=Colladay |first1=Don |last2=Kostelecký |first2=V. Alan |journal=Physical Review D |volume=58 |issue=11 }}</ref><ref>{{cite journal |arxiv=hep-th/0312310 |bibcode=2004PhRvD..69j5009K |doi=10.1103/PhysRevD.69.105009 |title=Gravity, Lorentz violation, and the standard model |year=2004 |last1=Kostelecký |first1=V. Alan |journal=Physical Review D |volume=69 |issue=10 }}</ref> This general framework has allowed experimental searches by ultra-high energy cosmic-ray experiments<ref name="Gonzalez-Mestres2009b">{{cite journal |author1=Gonzalez-Mestres, Luis |doi=10.1016/j.nuclphysbps.2009.03.088 |journal=Nuclear Physics B: Proceedings Supplements |volume=190 |title=AUGER-HiRes results and models of Lorentz symmetry violation |pages=191–197 |year=2009 |arxiv=0902.0994 |bibcode=2009NuPhS.190..191G }}</ref> and a wide variety of experiments in gravity, electrons, protons, neutrons, neutrinos, mesons, and photons.<ref name="autogenerated1">{{cite journal |arxiv=0801.0287 |bibcode=2011RvMP...83...11K |doi=10.1103/RevModPhys.83.11 |title=Data tables for Lorentz and CPT violation |year=2011 |last1=Kostelecký |first1=V. Alan |last2=Russell |first2=Neil |journal=Review of Modern Physics |volume=83 |page=11 }}</ref>
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| The breaking of rotation and boost invariance causes direction dependence in the theory as well as unconventional energy dependence that introduces novel effects, including [[Lorentz-violating neutrino oscillations]] and modifications to the dispersion relations of different particle species, which naturally could make particles move faster than light.
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| In some models of broken Lorentz symmetry, it is postulated that the symmetry is still built into the most fundamental laws of physics, but that [[spontaneous symmetry breaking]] of Lorentz invariance<ref>Kostelecký, V. Alan; and Samuel, S.; ''Spontaneous Breaking of Lorentz Symmetry in String Theory'', Physical Review D 39, 683 (1989)</ref> shortly after the [[Big Bang]] could have left a "relic field" throughout the universe which causes particles to behave differently depending on their velocity relative to the field;<ref>{{cite web |url=http://physicsweb.org/article/world/17/3/7 |archiveurl=http://web.archive.org/web/20040405031103/http://physicsweb.org/article/world/17/3/7 |archivedate=2004-04-05 |title=PhysicsWeb - Breaking Lorentz symmetry |publisher=Web.archive.org |date=2004-04-05 |accessdate=2011-09-26 }}</ref> 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 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.
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| In current models of Lorentz symmetry violation, the phenomenological parameters are expected to be energy-dependent. Therefore, as widely recognized,<ref name="CERNCourrier">Mavromatos, Nick E.; ''Testing models for quantum gravity'', ''CERN Courier'', http://cerncourier.com/cws/article/cern/28696 (August 2002)</ref><ref name="NYT">Overbye, Dennis; [http://www.nytimes.com/2002/12/31/science/interpreting-the-cosmic-rays.html?n=Top/News/Science/Topics/Space ''Interpreting the Cosmic Rays''], The New York Times, 31 December 2002</ref> 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 the [[Standard-Model Extension]].<ref name="autogenerated1" />
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| Lorentz symmetry violation is expected to become stronger as one gets closer to the fundamental scale.
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| Another recent theory (see [[EPR paradox]] above) resulting from the analysis of an EPR communication set up, has the simple device based on removing the effective retarded time terms in the Lorentz transform to yield a preferred absolute reference frame. This frame cannot be used to do physics (i.e., compute the influence of light-speed limited signals) but it provides an objective, absolute frame all could agree upon, if [[superluminal communication]] is possible. If this sounds indulgent, it allows simultaneity, absolute space and time and a deterministic universe (along with [[decoherence]] theory) whilst the status-quo permits time travel/causality paradoxes, subjectivity in the measurement process and multiple universes.
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| ===Superfluid theories of physical vacuum===
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| {{main|Superfluid vacuum}}
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| In this approach the physical [[vacuum]] is viewed as the quantum [[superfluid]] which is essentially non-relativistic whereas the [[Lorentz symmetry]] is not an exact symmetry of nature but rather the approximate description valid only for the small fluctuations of the superfluid background.<ref name="volovik03">{{cite journal |last1=Volovik |first1=G. E. |year=2003 |title=The Universe in a helium droplet |journal=International Series of Monographs on Physics |volume=117 |pages=1–507 }}</ref> Within the framework of the approach a theory was proposed in which the physical vacuum is conjectured to be the [[Bose-Einstein condensate|quantum Bose liquid]] whose ground-state [[Wave function|wavefunction]] is described by the [[logarithmic Schrödinger equation]]. It was shown that the [[General relativity|relativistic gravitational interaction]] arises as the small-amplitude [[collective excitation]] mode<ref>{{cite journal |title=Spontaneous symmetry breaking and mass generation as built-in phenomena in logarithmic nonlinear quantum theory |last1=Zloshchastiev |first1=Konstantin G. |year=2009 |doi=10.5506/APhysPolB.42.261 |journal=Acta Physica Polonica B |volume=42 |issue=2 |pages=261–292 |arxiv=0912.4139 }}</ref> whereas relativistic [[elementary particles]] can be described by the [[Quasi-particle|particle-like modes]] in the limit of low momenta.<ref>{{cite journal |arxiv=1108.0847 |bibcode=2011JPhB...44s5303A |doi=10.1088/0953-4075/44/19/195303 |title=Quantum Bose liquids with logarithmic nonlinearity: Self-sustainability and emergence of spatial extent |year=2011 |last1=Avdeenkov |first1=Alexander V. |last2=Zloshchastiev |first2=Konstantin G. |journal=Journal of Physics B: Atomic, Molecular and Optical Physics |volume=44 |issue=19 |page=195303 }}</ref> The important fact is that at very high velocities the behavior of the particle-like modes becomes distinct from the [[Theory of relativity|relativistic]] one - they can reach the [[Speed of light#Upper limit on speeds|speed of light limit]] at finite energy; also the faster-than-light propagation is possible without requiring moving objects to have [[imaginary mass]].<ref>{{cite journal |arxiv=0906.4282 |bibcode=2010AIPC.1206..112Z |doi=10.1063/1.3292518 |title=Logarithmic nonlinearity in theories of quantum gravity: Origin of time and observational consequences |series=AIP Conference Proceedings |year=2010 |last1=Zloshchastiev |first1=Konstantin G. |last2=Chakrabarti |first2=Sandip K. |last3=Zhuk |first3=Alexander I. |last4=Bisnovatyi-Kogan |first4=Gennady S. |page=112 }}</ref><ref>{{cite journal |arxiv=1003.0657 |bibcode=2011PhLA..375.2305Z |doi=10.1016/j.physleta.2011.05.012 |title=Vacuum Cherenkov effect in logarithmic nonlinear quantum theory |year=2011 |last1=Zloshchastiev |first1=Konstantin G. |journal=Physics Letters A |volume=375 |issue=24 |page=2305 }}</ref>
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| ==Time of flight of neutrinos==
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| ===MINOS experiment===
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| {{main|MINOS}}
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| In 2007 [[MINOS]] collaboration reported results measuring the flight-time of 3 [[electronvolt|GeV]] [[neutrinos]] yielding a speed exceeding that of light by 1.8-sigma significance.<ref>{{cite journal |arxiv=0706.0437 |bibcode=2007PhRvD..76g2005A |doi=10.1103/PhysRevD.76.072005 |title=Measurement of neutrino velocity with the MINOS detectors and NuMI neutrino beam |year=2007 |last1=Adamson |first1=P. |last2=Andreopoulos |first2=C. |last3=Arms |first3=K. |last4=Armstrong |first4=R. |last5=Auty |first5=D. |last6=Avvakumov |first6=S. |last7=Ayres |first7=D. |last8=Baller |first8=B. |last9=Barish |first9=B. |journal=Physical Review D |volume=76 |issue=7 }}</ref>
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| However, those measurements were considered to be statistically consistent with neutrinos traveling at the speed of light.<ref>
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| {{cite news |author=Overbye, Dennis |date=22 September 2011 |title=Tiny neutrinos may have broken cosmic speed limit |url=http://www.nytimes.com/2011/09/23/science/23speed.html |newspaper=[[New York Times]] |quote=That group found, although with less precision, that the neutrino speeds were consistent with the speed of light. }}</ref>
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| 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.<ref>{{cite web|title=MINOS reports new measurement of neutrino velocity |publisher=Fermilab today|url=http://www.fnal.gov/pub/today/archive_2012/today12-06-08.html|date=June 8, 2012|accessdate= June 8, 2012}}</ref>
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| ===OPERA neutrino anomaly===
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| {{main|Faster-than-light neutrino anomaly}}
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| On September 22, 2011, a paper<ref>{{cite arXiv |eprint=1109.4897 |author1=Adam |author2=Agafonova |author3=Aleksandrov |author4=Altinok |author5=Alvarez Sanchez |author6=Aoki |author7=Ariga |author8=Ariga |author9=Autiero |title=Measurement of the neutrino velocity with the OPERA detector in the CNGS beam |class=hep-ex |year=2011 }}</ref> from the [[OPERA experiment|OPERA Collaboration]] indicated detection of 17 and 28 GeV muon neutrinos, sent 730 kilometers (454 miles) from [[CERN]] near [[Geneva, Switzerland]] to the [[Laboratori Nazionali del Gran Sasso|Gran Sasso National Laboratory]] in [[Italy]], traveling faster than light by a factor of 2.48×10<sup>−5</sup> (approximately 1 in 40,000), a statistic with 6.0-sigma significance.<ref>Cho, Adrian; [http://news.sciencemag.org/sciencenow/2011/09/neutrinos-travel-faster-than-lig.html ''Neutrinos Travel Faster Than Light, According to One Experiment''], Science NOW, 22 September 2011</ref> On 18 November 2011, a second follow-up experiment by OPERA scientists confirmed their initial results.<ref name="Opera-20111118">{{cite news |last=Overbye |first=Dennis |title=Scientists Report Second Sighting of Faster-Than-Light Neutrinos |url=http://www.nytimes.com/2011/11/19/science/space/neutrino-finding-is-confirmed-in-second-experiment-opera-scientists-say.html |date=18 November 2011 |publisher=New York Times |accessdate=2011-11-18 }}</ref><ref name="Opera-arxiv">{{cite arXiv |author=Adam, T.; et al.; ([[OPERA experiment|OPERA Collaboration]]) |date=17 November 2011 |title=Measurement of the neutrino velocity with the OPERA detector in the CNGS beam |eprint=1109.4897v2 |class=hep-ex |year=2011}}</ref> However, scientists were skeptical about the results of these experiments, the significance of which was disputed.<ref>[http://www.reuters.com/article/2011/11/20/us-science-neutrinos-idUSTRE7AJ0ZX20111120 Reuters: Study rejects "faster than light" particle finding]</ref> In March 2012, the [[ICARUS (experiment)|ICARUS collaboration]] failed 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.<ref>{{Citation| last = ICARUS collaboration| title = Measurement of the neutrino velocity with the ICARUS detector at the CNGS beam| date = March 15, 2012| accessdate = March 17, 2012| arxiv = 1203.3433|ref = {{harvid|ICARUS|2012}} |bibcode = 2012arXiv1203.3433A }}</ref> Later the OPERA team reported two flaws in their equipment set-up that had caused errors far outside of their original [[confidence interval]]: a [[fiber optic cable]] attached improperly, which caused the apparently faster-than-light measurements, and a clock oscillator ticking too fast.<ref>Strassler, M. (2012) [http://profmattstrassler.com/articles-and-posts/particle-physics-basics/neutrinos/neutrinos-faster-than-light/opera-what-went-wrong/ "OPERA: What Went Wrong"] ''profmattstrassler.com''</ref>
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| ==Tachyons==
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| {{Main|Tachyon}}
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| In special relativity, it is impossible to accelerate an object ''to'' the [[speed of light]], or for a massive object to move ''at'' the speed of light. However, it might be possible for an object to exist which ''always'' moves faster than light. The hypothetical [[elementary particle]]s with this property are called [[tachyon|tachyonic particles]]. Attempts to [[Tachyonic field|quantize]] them failed to produce faster-than-light particles, and instead illustrated that their presence leads to an instability.<ref name="Randall">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 for science fiction fans, tachyons are not real physical particles that appear in nature."</ref><ref>{{cite journal |first=S. James |last=Gates |authorlink=S. James Gates |title=Superstring Theory: The DNA of Reality }}</ref>
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| Various theorists have suggested that the [[neutrino]] might have a [[tachyon]]ic nature,<ref>Chodos, A.; Hauser, A. I.; and Kostelecký, V. Alan; ''The Neutrino As A Tachyon'', Physics Letters B 150, 431 (1985)</ref><ref>{{cite journal |author1=Chodos, Alan |author2=Kostelecký, V. Alan |author3=IUHET 280 |title=Nuclear Null Tests for Spacelike Neutrinos |doi=10.1016/0370-2693(94)90535-5 |year=1994 |journal=Physics Letters B |volume=336 |issue=3–4 |pages=295–302 |arxiv=hep-ph/9409404 |bibcode=1994PhLB..336..295C }}</ref><ref>Chodos, Alan; Kostelecký, V. Alan; Potting, R.; and Gates, E.; ''Null experiments for neutrino masses'', Modern Physics Letters A7, 467 (1992)</ref><ref>[http://inspirebeta.net/search?ln=en&p=refersto%3Arecid%3A15887 List of articles on the tachyonic neutrino idea (may be incomplete)]. InSPIRE database. http://arxiv.org/abs/hep-ph/0208239</ref><ref>Chang, Taso; ''Parity Violation and Neutrino Mass'', Nuclear Science and Techniques, Vol. 13, No. 3 (2002) 129</ref> while others have disputed the possibility.<ref>Hughes, R. J.; and Stephenson, G. J., Jr.; ''Against tachyonic neutrinos'', Physics Letters B 244, 95-100 (1990)</ref>
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| ==General relativity==
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| [[General relativity]] was developed after [[special relativity]] to include concepts like [[gravity]]. It maintains the principle that no object can accelerate to the speed of light in the reference frame of any coincident observer.{{citation needed|date=October 2009}}{{clarify|date=October 2009}} However, it permits distortions in [[spacetime]] that allow an object to move faster than light from the point of view of a distant observer.{{citation needed|date=March 2012}}{{clarify|date=March 2012}} One such [[distortion]] is the [[Alcubierre drive]], which can be thought of as producing a [[wiktionary:ripple|ripple]] in [[spacetime]] that carries an object along with it. Another possible system is the [[wormhole]], 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 hypothetical [[exotic matter]] or negative energy.
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| [[General relativity]] also recognizes that any means of faster-than-light [[travel]] could also be used for [[time travel]]. This raises problems with [[causality]]. Many physicists believe that the above phenomena are impossible and that future theories of [[gravity]] will 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|date=March 2013}} In [[string theory]], Eric G. Gimon and [[Petr Hořava (theorist)|Petr Hořava]] have argued<ref>{{cite arXiv |eprint=hep-th/0405019 |title=Over-rotating black holes, Gödel holography and the hypertube |first=Eric G. |last=Gimon |coauthors=Hořava, Petr |year=2004 |class=hep-th }}</ref> that in a [[supersymmetric]] five-dimensional [[Gödel metric|Gödel 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.
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| ==Variable speed of light==
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| {{Main|Variable speed of light}}
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| In conventional [[physics]], the speed of light in a [[vacuum]] is assumed to be a constant. However, [[theories]] exist which postulate that the [[speed of light]] is not a constant. The interpretation of this statement is as follows.
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| The speed of light is a dimensional quantity and so, as has been emphasized in this context by [[João Magueijo]], it cannot be measured.<ref>{{cite journal |authorlink=João Magueijo |first=João |last=Magueijo |coauthor=Albrecht, Andreas |title=A time varying speed of light as a solution to cosmological puzzles |year=1999 |issue=4 |volume=59 |doi=10.1103/PhysRevD.59.043516 |journal=Physical Review D |arxiv=astro-ph/9811018 |bibcode=1999PhRvD..59d3516A }}</ref> Measurable quantities in physics are, without exception, dimensionless, although they are often constructed as ratios of dimensional quantities. For example, when the height of a mountain is measured, what is really measured is the ratio of its height to the length of a meter stick. The conventional [[International System of Units|SI]] system of units is based on seven basic dimensional quantities, namely [[distance]], [[mass]], [[time]], [[electric current]], [[thermodynamic temperature]], [[amount of substance]], and [[luminous intensity]].<ref>{{cite web |url=http://physics.nist.gov/cuu/Units/units.html |title=SI base units }}</ref> These [[units of measurement|units]] are defined to be [[Independent variable|independent]] and so cannot be described in terms of each other. As an alternative to using a particular system of units, one can reduce all measurements to dimensionless quantities expressed in terms of ratios between the quantities being measured and various fundamental constants such as [[Newton's constant]], the [[speed of light]] and [[Planck's constant]]; physicists can define at least 26 dimensionless constants which can be expressed in terms of these sorts of ratios and which are currently thought to be independent of one another.<ref>{{cite web |url=http://math.ucr.edu/home/baez/constants.html |title=constants }}</ref> By manipulating the basic dimensional constants one can also construct the [[Planck time]], [[Planck length]] and [[Planck energy]] which make a good system of units for expressing dimensional measurements, known as [[Planck units]].
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| Magueijo's proposal used a different set of [[units of measurement|units]], a choice which he justifies with the claim that some equations will be simpler in these new units. In the new units he fixes the [[fine structure constant]], a quantity which some people, using units in which the speed of light is fixed, have claimed is time-dependent. Thus in the system of units in which the fine structure constant is fixed, the observational claim is that the speed of light is time-dependent.
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| While it may be [[mathematical]]ly possible to construct such a system, it is not clear what additional explanatory power or physical insight such a system would provide, assuming that it does indeed accord with existing empirical data.
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| ==See also==
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| {{main
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| |:Category:Faster-than-light travel |l1 = Category:Faster-than-light travel
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| |:Category:Faster-than-light communication |l2 = Category:Faster-than-light communication
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| }}
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| {{col-begin}}
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| {{col-3}}
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| * [[Intergalactic travel]]
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| * [[Krasnikov tube]]
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| * [[Alcubierre drive]]
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| {{col-3}}
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| * [[Wheeler–Feynman absorber theory]]
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| * [[Faster-than-light neutrino anomaly]]
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| * [[Tachyonic field]]
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| {{col-3}}
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| * [[Tachyon]]
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| {{col-end}}
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| ;[[Science Fiction]]
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| {{col-begin}}
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| {{col-3}}
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| * [[Animorphs]] (Zero Space)
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| * [[Battlestar (reimagining)]]
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| * [[Jump drive]]
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| * [[Jumpgate]]
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| * [[TARDIS]] ([[Doctor Who]])
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| * [[Warp drive (Star Trek)]]
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| * [[Hyperdrive]]
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| * [[Starburst (Farscape)]]
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| {{col-3}}
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| * [[Slipstream (science fiction)]]
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| * [[Skip drive]]
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| * [[Infinite Improbability Drive]]
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| * [[Inertialess drive]]
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| * [[Stargate (device)]]
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| * [[Ansible]]
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| {{col-3}}
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| * [[Mass Effect]] Relay
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| * [[Macross#Space Fold|Macross Space Fold]]
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| * [[FTL:2448]] by [[Tri Tac Games]]
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| * [[Taelon#Interdimensional travel|Interdimensional Drive (Earth Final Conflict)]]
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| * [[BattleTech technology#Space travel|Kearny-Fuchida jump drive (BattleTech)]]
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| * [[Ultrawave]]
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| {{col-3}}
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| * [[Battlestar Galactica (2004 TV series)|FTL drive (Battlestar Galactica)]]
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| * [[Eureka (U.S. TV series)|FTL engine (Eureka)]]
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| {{col-end}}
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| {{Portal bar|Space|Science fiction}}
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| ==Notes==
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| {{Reflist|30em}}
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| ==References==
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| * {{cite journal
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| |last=Falla |first=D. F.
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| |last2=Floyd |first2=M. J.
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| |year=2002
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| |title=Superluminal motion in astronomy
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| |journal=[[European Journal of Physics]]
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| |volume=23 |issue= |pages=69–81
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| |arxiv=
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| |bibcode= 2002EJPh...23...69F
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| |doi= 10.1088/0143-0807/23/1/310
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| }}
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| * {{cite book
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| |last=Kaku |first=Michio
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| |author-link=Michio Kaku
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| |year=2008
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| |chapter=Faster than Light
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| |title=[[Physics of the Impossible]]
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| |pages=197–215
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| |publisher=[[Allen Lane]]
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| |isbn=978-0-7139-9992-1
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| }}
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| * {{cite book
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| |last=Nimtz |first=Günter
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| |year=2008
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| |author-link=Günter Nimtz
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| |title=Zero Time Space
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| |publisher=[[Wiley-VCH]]
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| |isbn=978-3-527-40735-4
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| |display-authors=1
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| }}
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| * {{cite book
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| |last=Cramer |first=J. G.
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| |year=2009
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| |chapter=Faster-than-Light Implications of Quantum Entanglement and Nonlocality
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| |editor=Millis, M. G.; et al.
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| |title=Frontiers of Propulsion Science
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| |pages=509–529
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| |publisher=[[American Institute of Aeronautics and Astronautics]]
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| |isbn=1-56347-956-7
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| }}
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| ==External links==
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| ===Scientific links===
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| * [http://iysn.org/2011/10/19/measurement-of-the-neutrino-velocity-with-the-opera-detector-in-the-cngs-beam/ Measurement of the neutrino velocity with the OPERA detector in the CNGS beam]
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| * [http://www.rp-photonics.com/superluminal_transmission.html Encyclopedia of laser physics and technology on "superluminal transmission"], with more details on phase and group velocity, and on causality
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| * [http://dustbunny.physics.indiana.edu/~dzierba/HonorsF97/Week1/NYTJuly22.html July 22, 1997, The New York Times Company: Signal Travels Farther and Faster Than Light]
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| * [http://www.aei-potsdam.mpg.de/~mpoessel/Physik/FTL/tunnelingftl.html Markus Pössel: Faster-than-light (FTL) speeds in tunneling experiments: an annotated bibliography]
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| * Alcubierre, Miguel; [http://www.yellowknife.com/warp/ ''The Warp Drive: Hyper-Fast Travel Within General Relativity'', Classical and Quantum Gravity 11 (1994), L73–L77]
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| * [http://www.eleceng.adelaide.edu.au/personal/dabbott/publications/PIE_withayachumnankul2010.pdf A systemized view of superluminal wave propagation]
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| * [http://www.physicsguy.com/ftl/index.html Relativity and FTL Travel FAQ]
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| * [http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html Usenet Physics FAQ: is FTL travel or communication Possible?]
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| * [http://scienceworld.wolfram.com/physics/Superluminal.html Superluminal]
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| * [http://www.theculture.org/rich/sharpblue/archives/000089.html Relativity, FTL and causality]
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| * [http://adsabs.harvard.edu/abs/2006PrGeo..21...38Y Superluminal velocity] fusing with Einstein special relativity
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| * [http://prl.aps.org/abstract/PRL/v108/i17/e173902 Stimulated Generation of Superluminal Light Pulses via Four-Wave Mixing]
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| ===Proposed FTL Methods links===
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| * [http://www.petar-bosnic-petrus.com/science-articles/conical-and-paraboloidal-superluminal-particle-accelerators/ Conical and paraboloidal superluminal particle accelerators]
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| * [http://www.physicsguy.com/ftl/ Relativity and FTL (=Superluminal motion) Travel Homepage]
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| {{DEFAULTSORT:Faster-Than-Light}}
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| [[Category:Faster-than-light travel]]
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| [[Category:Interstellar travel]]
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| [[Category:Physics in fiction]]
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| [[Category:Theory of relativity]]
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| [[Category:Science fiction themes]]
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| [[Category:Tachyons]]
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| [[Category:Warp drive theory]]
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