Editing Speed of light (section)

=== Upper limit on speeds ===
An object with [[rest mass]] ''m'' and speed ''v'' relative to a laboratory has [[kinetic energy]] {{nowrap|''(γ-1)mc''{{i sup|2}}}} with respect to that lab, where ''γ'' is the Lorentz factor defined above. The ''γ'' factor approaches infinity as ''v'' approaches&nbsp;''c'', and it would take an infinite amount of energy to accelerate an object with mass to the speed of light.<ref>{{Cite book |last1=Kleppner |first1=Daniel |title=An introduction to mechanics |last2=Kolenkow |first2=Robert J. |date=2014 |publisher=Cambridge university press |isbn=978-0-521-19811-0 |edition=2nd |location=Cambridge}}</ref>{{rp|loc=13.3}} The speed of light is the upper limit for the speeds of objects with positive rest mass. Analysis of individual photons confirm that information cannot travel faster than the speed of light.<ref>{{Cite web |last=Voss |first=David |date=2011-06-16 |title=Single photons obey the speed limits |url=https://physics.aps.org/articles/v4/s88 |access-date=2025-04-17 |website=Physics |pages=s88 |language=en |doi=10.1103/PhysRevLett.106.243602}}</ref><ref>
{{Cite journal |title=Optical Precursor of a Single Photon |author1=Shanchao Zhang |author2=J. F. Chen |author3=Chang Liu |author4=M. M. T. Loy |author5=G. K. L. Wong |author6=Shengwang Du |journal=[[Physical Review Letters]] |volume=106 |issue=243602 |pages=243602 |date=16 June 2011 |doi=10.1103/physrevlett.106.243602|pmid=21770570 |bibcode=2011PhRvL.106x3602Z |url=http://repository.ust.hk/ir/bitstream/1783.1-7246/1/PhysRevLett.106.243602.pdf }}
</ref> This is experimentally established in many [[tests of relativistic energy and momentum]].<ref>
{{Cite web
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 |date=March 2008
 |title=Notes on Special Relativity
 |url=http://galileo.phys.virginia.edu/classes/252/SpecRelNotes.pdf
 |page=56
 |publisher=University of Virginia
 |access-date=7 May 2010
}}</ref>

[[File:Relativity of Simultaneity.svg|thumb|Event&nbsp;A precedes&nbsp;B in the red frame, is simultaneous with&nbsp;B in the green frame, and follows&nbsp;B in the blue frame.|alt=Three pairs of coordinate axes are depicted with the same origin&nbsp;A; in the green frame, the x axis is horizontal and the ct axis is vertical; in the red frame, the x′ axis is slightly skewed upwards, and the ct′ axis slightly skewed rightwards, relative to the green axes; in the blue frame, the x′′ axis is somewhat skewed downwards, and the ct′′ axis somewhat skewed leftwards, relative to the green axes. A point&nbsp;B on the green x axis, to the left of&nbsp;A, has zero ct, positive ct′, and negative ct′′.]]
More generally, it is impossible for signals or energy to travel faster than&nbsp;''c''. One argument for this is known as [[causality (physics)|causality]].  If the spatial distance between two events&nbsp;A and&nbsp;B is greater than the time interval between them multiplied by&nbsp;''c'' then there are frames of reference in which&nbsp;A precedes&nbsp;B, others in which&nbsp;B precedes&nbsp;A, and others in which they are simultaneous. As a result, if something were travelling faster than&nbsp;''c'' relative to an inertial frame of reference, it would be travelling backwards in time relative to another frame, and causality would be violated.<ref>{{Cite book |last=Fayngold |first=Moses |url=https://www.worldcat.org/title/180478876 |title=Special relativity and how it works |date=2008 |publisher=Wiley-VCH |isbn=978-3-527-40607-4 |series=Physics textbook |location=Weinheim |oclc=180478876}}</ref>{{rp|497}}<ref>
{{Cite journal
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{{Cite book
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}}</ref> In such a frame of reference, an "effect" could be observed before its "cause". Such a violation of causality has never been recorded,<ref name=Zhang/> and would lead to [[paradox]]es such as the [[tachyonic antitelephone]].<ref>
{{Cite book
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 |year=2009 |orig-year=1917
 |chapter=Velocities greater than that of light
 |title=The Theory of the Relativity of Motion
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}}</ref>

In some theoretical treatments, the [[Scharnhorst effect]] allows signals to travel faster than&nbsp;''c'', by one part in 10<sup>36</sup>.<ref>De Clark, S. G. (2016). The scharnhorst effect: Superluminality and causality in effective field theories. The University of Arizona.</ref> However other approaches to the same physical set up show no such effect.<ref>See, for example:
* {{Cite journal|last=Ben-Menahem|first=Shahar|date=November 1990|title=Causality between conducting plates|url=https://linkinghub.elsevier.com/retrieve/pii/037026939091167A|journal=Physics Letters B|language=en|volume=250|issue=1–2|pages=133–138|doi=10.1016/0370-2693(90)91167-A|bibcode=1990PhLB..250..133B|osti=1449261}}
* {{Cite journal |last=Fearn |first=H. |date=10 November 2006 |title=Dispersion relations and causality: does relativistic causality require that n (ω) → 1 as ω → ∞ ? |url=http://www.tandfonline.com/doi/abs/10.1080/09500340600952085 |journal=Journal of Modern Optics |language=en |volume=53 |issue=16–17 |pages=2569–2581 |doi=10.1080/09500340600952085 |bibcode=2006JMOp...53.2569F |s2cid=119892992 |issn=0950-0340|url-access=subscription }}
* {{Cite journal |last=Fearn |first=H. |date=May 2007 |title=Can light signals travel faster than c in nontrivial vacua in flat space-time? Relativistic causality II |url=http://link.springer.com/10.1134/S1054660X07050155 |journal=Laser Physics |language=en |volume=17 |issue=5 |pages=695–699 |doi=10.1134/S1054660X07050155 |arxiv=0706.0553 |bibcode=2007LaPhy..17..695F |s2cid=61962 |issn=1054-660X}}</ref> and it appears the special conditions in which this effect might occur would prevent one from using it to violate causality.