Editing Faster-than-light (section)

===Quantum mechanics===
Certain phenomena in [[quantum mechanics]], such as [[quantum entanglement]], might give the superficial impression of allowing communication of 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 behavior does not violate local causality or allow FTL communication, it follows that neither does the additional effect of wavefunction collapse, whether real ''or'' apparent.

The [[uncertainty principle]] implies that individual photons may travel for short distances at speeds somewhat faster (or slower) than ''c'', even in vacuum; this possibility must be taken into account when enumerating [[Feynman diagram]]s for a particle interaction.<ref>
{{cite book
|last1=Grozin |first1=A.
|year=2007
|title=Lectures on QED and QCD
|url=https://archive.org/details/lecturesonqedqcd00groz |url-access=limited |page=[https://archive.org/details/lecturesonqedqcd00groz/page/n101 89]
|publisher=[[World Scientific]]
|isbn=978-981-256-914-1
}}</ref> However, it was shown in 2011 that a single photon may not travel faster than ''c''.<ref>
{{cite journal
|last1=Zhang |first1=S.
|last2=Chen |first2=J. F.
|last3=Liu |first3=C.
|last4=Loy |first4=M. M. T.
|last5=Wong |first5=G. K. L.
|last6=Du |first6=S.
|year=2011
|title=Optical Precursor of a Single Photon
|journal=[[Physical Review Letters]]
|volume=106 |issue=24 |pages=243602
|bibcode=2011PhRvL.106x3602Z
|doi=10.1103/PhysRevLett.106.243602
|pmid=21770570
|url=http://repository.ust.hk/ir/bitstream/1783.1-7246/1/PhysRevLett.106.243602.pdf |archive-url=https://web.archive.org/web/20191205034808/http://repository.ust.hk/ir/bitstream/1783.1-7246/1/PhysRevLett.106.243602.pdf |archive-date=2019-12-05 |url-status=live
}}</ref> 

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.<ref>
{{cite book
|last1=Kåhre |first1=J.
|year=2012
|title=The Mathematical Theory of Information
|url=https://books.google.com/books?id=1ozlBwAAQBAJ&pg=PA425
|page=425 |edition=Illustrated
|publisher=[[Springer Science & Business Media]]
|isbn=978-1-4615-0975-2
}}</ref><ref>
{{cite thesis
|last1=Steinberg |first1=A. M.
|year=1994
|title=When Can Light Go Faster Than Light?
|url=https://books.google.com/books?id=E25MAQAAMAAJ
|page=100
|publisher=[[University of California, Berkeley]]
|bibcode=1994PhDT.......314S
}}</ref> However, as stated above, a superluminal phase velocity cannot be used for faster-than-light transmission of information<ref>
{{cite book
|last1=Chubb |first1=J.
|last2=Eskandarian |first2=A.
|last3=Harizanov |first3=V.
|year=2016
|title=Logic and Algebraic Structures in Quantum Computing
|url=https://books.google.com/books?id=mWVbCwAAQBAJ&pg=PA61
|page=61 |edition=Illustrated
|publisher=[[Cambridge University Press]]
|isbn=978-1-107-03339-9
}}</ref><ref>
{{cite book
|last1=Ehlers |first1=J.
|last2=Lämmerzahl |first2=C.
|year=2006
|title=Special Relativity: Will it Survive the Next 101 Years?
|url=https://books.google.com/books?id=avy6BQAAQBAJ&pg=PA506
|page=506 |edition=Illustrated
|publisher=Springer
|isbn=978-3-540-34523-7
}}</ref> 

====Hartman effect====
{{Main|Hartman effect}}

The Hartman effect is the tunneling effect through a barrier where the tunneling time tends to a constant for large barriers.<ref>
{{cite journal
|last1=Martinez |first1=J. C.
|last2=Polatdemir |first2=E.
|year=2006
|title=Origin of the Hartman effect
|journal=[[Physics Letters A]]
|volume=351 |issue=1–2 |pages=31–36
|bibcode=2006PhLA..351...31M
|doi=10.1016/j.physleta.2005.10.076
}}</ref><ref>
{{cite journal
|last1=Hartman |first1=T. E.
|year=1962
|title=Tunneling of a Wave Packet
|journal=[[Journal of Applied Physics]]
|volume=33 |issue=12 |pages=3427–3433
|bibcode=1962JAP....33.3427H
|doi=10.1063/1.1702424
}}</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 non-zero probability that the photon will tunnel across the gap rather than follow the refracted path. 

However, it has been claimed that the Hartman effect cannot actually be used to violate relativity by transmitting signals faster than ''c'', also because the tunnelling time "should not be linked to a velocity since evanescent waves do not propagate".<ref>
{{cite journal
|last1=Winful |first1=H. G.
|year=2006
|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
|bibcode=2006PhR...436....1W
|doi=10.1016/j.physrep.2006.09.002
}}</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.

====Casimir effect====
{{Main|Casimir effect}}

In physics, the [[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.

====EPR paradox====
{{Main|EPR paradox}}

The EPR paradox refers to a famous [[thought experiment]] of [[Albert Einstein]], [[Boris Podolsky]] and [[Nathan Rosen]] that was realized experimentally for the first time by [[Alain Aspect]] in 1981 and 1982 in the [[Aspect experiment]]. In this experiment, the two measurements of an [[quantum entanglement|entangled]] state are correlated even when the measurements are distant from the source and each other. However, no information can be transmitted this way; the answer to whether or not the measurement actually affects the other quantum system comes down to which [[interpretations of quantum mechanics|interpretation of quantum mechanics]] one subscribes to.

An experiment performed in 1997 by [[Nicolas Gisin]] has demonstrated quantum correlations between particles separated by over 10 kilometers.<ref>
{{cite web
|last=Suarez |first=A.
|date=26 February 2015
|title=History
|url=http://www.quantumphil.org/history.htm
|publisher=Center for Quantum Philosophy
|access-date=2017-06-07
}}</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. The situation is akin to sharing a synchronized coin flip, where the second person to flip their coin will always see the opposite of what the first person sees, but neither has any way of knowing whether they were the first or second flipper, without communicating classically. See [[No-communication theorem]] for further information. A 2008 quantum physics experiment also performed by Nicolas Gisin and his colleagues has determined that in any hypothetical [[hidden-variable theory#Non-local hidden-variable theory|non-local hidden-variable 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
|last1=Salart |first1=D.
|last2=Baas |first2=A.
|last3=Branciard |first3=C.
|last4=Gisin |first4=N.
|last5=Zbinden |first5=H.
|year=2008
|title=Testing spooky action at a distance
|journal=[[Nature (journal)|Nature]]
|volume=454 |issue=7206 |pages=861–864
|arxiv=0808.3316
|bibcode=2008Natur.454..861S
|doi=10.1038/nature07121
|pmid=18704081
|s2cid=4401216
}}</ref>

====Delayed choice quantum eraser====
{{Main|Delayed-choice quantum eraser}}

The [[delayed-choice quantum eraser]] 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 journal
|last1=Kim |first1=Yoon-Ho
|last2=Yu |first2=Rong
|last3=Kulik |first3=Sergei P.
|last4=Shih |first4=Yanhua
|last5=Scully |first5=Marlan O.
|year=2000
|title=Delayed "Choice" Quantum Eraser
|journal=[[Physical Review Letters]]
|volume=84 |issue=1 |pages=1–5
|arxiv=quant-ph/9903047
|bibcode=2000PhRvL..84....1K
|doi=10.1103/PhysRevLett.84.1
|pmid=11015820
|s2cid=5099293
}}</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 cannot be observed until both photons have been measured, ensuring that an experimenter watching only the photons going through the slit does not obtain information about the other photons in an faster-than-light or backwards-in-time manner.<ref>
{{cite web
|last1=Hillmer |first1=R.
|last2=Kwiat |first2=P.|author2-link=Paul Kwiat
|date=16 April 2017
|title=Delayed-Choice Experiments
|url=https://www.scientificamerican.com/article/quantum-eraser-delayed-choice-experiments/
|website=[[Scientific American]]
}}</ref><ref>
{{cite web
|last=Motl |first=L.
|date=November 2010
|title=Delayed choice quantum eraser
|url=https://motls.blogspot.com/2010/11/delayed-choice-quantum-eraser.html
|website=[[The Reference Frame]]
}}</ref>