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Quantum tunnelling
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== Faster than light == {{See also|Faster-than-light}} Some physicists have claimed that it is possible for spin-zero particles to travel faster than the [[speed of light]] when tunnelling.<ref name="Razavy" /> This appears to violate the principle of [[causality (physics)|causality]], since a [[frame of reference]] then exists in which the particle arrives before it has left. In 1998, [[Francis E. Low]] reviewed briefly the phenomenon of zero-time tunnelling.<ref>{{cite journal |first=F. E. |last=Low |title=Comments on apparent superluminal propagation |journal=[[Annalen der Physik]] |volume=7 |issue=7β8 |pages=660β661 |year=1998 |doi=10.1002/(SICI)1521-3889(199812)7:7/8<660::AID-ANDP660>3.0.CO;2-0 |bibcode = 1998AnP...510..660L |s2cid=122717505 }}</ref> More recently, experimental tunnelling time data of [[phonons]], [[photons]], and [[electrons]] was published by [[GΓΌnter Nimtz]].<ref>{{cite journal |first=G. |last=Nimtz |title=Tunneling Confronts Special Relativity |journal=[[Foundations of Physics|Found. Phys.]] |volume=41 |issue=7 |pages=1193β1199 |year=2011 |doi=10.1007/s10701-011-9539-2 |arxiv = 1003.3944 |bibcode = 2011FoPh...41.1193N |s2cid=119249900 }}</ref> Another experiment overseen by [[Aephraim M. Steinberg|A. M. Steinberg]], seems to indicate that particles could tunnel at apparent speeds faster than light.<ref>{{cite web |date=22 July 2020 |title=Quantum-tunnelling time is measured using ultracold atoms β Physics World |url=https://physicsworld.com/a/quantum-tunnelling-time-is-measured-using-ultracold-atoms/ |accessdate= |format=}}</ref><ref name="urlQuanta Magazine">{{cite web |date=20 October 2020 |title=Quanta Magazine |url=https://www.quantamagazine.org/quantum-tunnel-shows-particles-can-break-the-speed-of-light-20201020/ |accessdate= |format=}}</ref> Other physicists, such as [[Herbert Winful]],<ref>{{cite journal |first=H. G. |last=Winful |title=Tunneling time, the Hartman effect, and superluminality: A proposed resolution of an old paradox |journal=[[Physics Reports|Phys. Rep.]] |volume=436 |issue=1β2 |pages=1β69 |year=2006 |doi=10.1016/j.physrep.2006.09.002|bibcode=2006PhR...436....1W }}</ref> disputed these claims. Winful argued that the wave packet of a tunnelling particle propagates locally, so a particle can't tunnel through the barrier non-locally. Winful also argued that the experiments that are purported to show non-local propagation have been misinterpreted. In particular, the group velocity of a wave packet does not measure its speed, but is related to the amount of time the wave packet is stored in the barrier. Moreover, if quantum tunneling is modeled with the relativistic [[Dirac equation]], well established mathematical theorems imply that the process is completely subluminal.<ref>{{Cite book |url=https://link.springer.com/book/10.1007/978-3-662-02753-0 |title=The Dirac Equation |date=1992 |language=en |doi=10.1007/978-3-662-02753-0 |last1=Thaller |first1=Bernd |isbn=978-3-642-08134-7 }}</ref><ref>{{Cite journal |last1=Gavassino |first1=L. |last2=Disconzi |first2=M. M. |date=2023-03-13 |title=Subluminality of relativistic quantum tunneling |url=https://link.aps.org/doi/10.1103/PhysRevA.107.032209 |journal=Physical Review A |volume=107 |issue=3 |pages=032209 |doi=10.1103/PhysRevA.107.032209|arxiv=2208.09742 |bibcode=2023PhRvA.107c2209G }}</ref>
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