Speed of light.docx
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Speed of light.docx
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Speedoflight
Speedoflight
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Forotheruses,seeSpeedoflight(disambiguation).
"Lightspeed"redirectshere.Forotheruses,seeLightspeed(disambiguation).
Speedoflight
Sunlighttakesabout8minutesand19secondstoreachtheEarth(basedontheaveragedistance).
Exactvalues
Metrespersecond
299,792,458
Planckunits
1
Approximatevalues
kilometrespersecond
300,000
kilometresperhour
1,080million
milespersecond
186,000
milesperhour
671million
astronomicalunitsperday
173
Approximatelightsignaltraveltimes
Distance
Time
onefoot
1.0ns
onemetre
3.3ns
fromgeostationaryorbittoEarth
119ms
thelengthofEarth'sequator
134ms
fromMoontoEarth
1.3s
fromSuntoEarth(1AU)
8.3min
fromneareststartoSun(1.3pc)
4.24years
fromthenearestgalaxy(theCanisMajorDwarfGalaxy)toEarth
25,000years
acrosstheMilkyWay
100,000years
fromtheAndromedaGalaxytoEarth
2.5millionyears
Thespeedoflightinvacuum,usuallydenotedbyc,isaphysicalconstantimportantinmanyareasofphysics.Itsvalueis299,792,458metrespersecond,afigurethatisexactsincethelengthofthemetreisdefinedfromthisconstantandtheinternationalstandardfortime.[1]Inimperialunitsthisspeedisapproximately186,282milespersecond.
Accordingtospecialrelativity,cisthemaximumspeedatwhichallenergy,matter,andinformationintheuniversecantravel.Itisthespeedofallmasslessparticlesandassociatedfields—includingelectromagneticradiationsuchaslight—invacuum,anditispredictedbythecurrenttheorytobethespeedofgravity(thatis,gravitationalwaves).Suchparticlesandwavestravelatcregardlessofthemotionofthesourceortheinertialframeofreferenceoftheobserver.Inthetheoryofrelativity,cinterrelatesspaceandtime,andappearsinthefamousequationofmass–energyequivalenceE = mc2.[2]
Thespeedatwhichlightpropagatesthroughtransparentmaterials,suchasglassorair,islessthanc.Theratiobetweencandthespeedvatwhichlighttravelsinamaterialiscalledtherefractiveindexnofthematerial(n = c / v).Forexample,forvisiblelighttherefractiveindexofglassistypicallyaround1.5,meaningthatlightinglasstravelsatc/1.5≈200,000 km/s;therefractiveindexofairforvisiblelightisabout1.0003,sothespeedoflightinairisabout90 km/sslowerthanc.
Inmostpracticalcases,lightcanbethoughtofasmovinginstantaneously,butforlongdistancesandverysensitivemeasurementsthefinitespeedoflighthasnoticeableeffects.Incommunicatingwithdistantspaceprobes,itcantakeminutestohoursforamessagetogetfromEarthtothespacecraftorviceversa.Thelightweseefromstarsleftthemmanyyearsago,allowingustostudythehistoryoftheuniversebylookingatdistantobjects.Thefinitespeedoflightalsolimitsthetheoreticalmaximumspeedofcomputers,sinceinformationmustbesentwithinthecomputerfromchiptochip.Finally,thespeedoflightcanbeusedwithtimeofflightmeasurementstomeasurelargedistancestohighprecision.
OleRømerfirstdemonstratedin1676thatlighttravelledatafinitespeed(asopposedtoinstantaneously)bystudyingtheapparentmotionofJupiter'smoonIo.In1865,JamesClerkMaxwellproposedthatlightwasanelectromagneticwave,andthereforetraveledatthespeedcappearinginhistheoryofelectromagnetism.In1905,AlbertEinsteinpostulatedthatthespeedoflightwithrespecttoanyinertialframeisindependentofthemotionofthelightsource,[3]andexploredtheconsequencesofthatpostulatebyderivingthespecialtheoryofrelativityandshowingthattheparameterchadrelevanceoutsideofthecontextoflightandelectromagnetism.Aftercenturiesofincreasinglyprecisemeasurements,in1975thespeedoflightwasknowntobe299,792,458 m/swithameasurementuncertaintyof4partsperbillion.In1983,themetrewasredefinedintheInternationalSystemofUnits(SI)asthedistancetravelledbylightinvacuumin1⁄299,792,458ofasecond.Asaresult,thenumericalvalueofcinmetrespersecondisnowfixedexactlybythedefinitionofthemetre.[4]
[edit]Numericalvalue,notation,andunits
Thespeedoflightinvacuumisusuallydenotedbyc,for"constant"ortheLatinceleritas(meaning"swiftness").Originally,thesymbolVwasused,introducedbyJamesClerkMaxwellin1865.In1856,WilhelmEduardWeberandRudolfKohlrauschusedcforaconstantlatershowntoequal√2timesthespeedoflightinvacuum.In1894,PaulDruderedefinedcwithitsmodernmeaning.EinsteinusedVinhisoriginalGerman-languagepapersonspecialrelativityin1905,butin1907heswitchedtoc,whichbythenhadbecomethestandardsymbol.[5][6]
Sometimescisusedforthespeedofwavesinanymaterialmedium,andc0forthespeedoflightinvacuum.[7]Thissubscriptednotation,whichisendorsedinofficialSIliterature,[4]hasthesameformasotherrelatedconstants:
namely,μ0forthevacuumpermeabilityormagneticconstant,ε0forthevacuumpermittivityorelectricconstant,andZ0fortheimpedanceoffreespace.Thisarticleusescexclusivelyforthespeedoflightinvacuum.
IntheInternationalSystemofUnits(SI),themetreisdefinedasthedistancelighttravelsinvacuumin1⁄299,792,458ofasecond.Thisdefinitionfixesthespeedoflightinvacuumatexactly299,792,458 m/s.[8][9][10]Asadimensionalphysicalconstant,thenumericalvalueofcisdifferentfordifferentunitsystems.[Note1]Inbranchesofphysicsinwhichcappearsoften,suchasinrelativity,itiscommontousesystemsofnaturalunitsofmeasurementinwhichc=1.[12][13]Usingtheseunits,cdoesnotappearexplicitlybecausemultiplicationordivisionby1doesnotaffecttheresult.
[edit]Fundamentalroleinphysics
Seealso:
Introductiontospecialrelativity,Specialrelativity, andOne-wayspeedoflight
Thespeedatwhichlightwavespropagateinvacuumisindependentbothofthemotionofthewavesourceandoftheinertialframeofreferenceoftheobserver.[Note2]ThisinvarianceofthespeedoflightwaspostulatedbyEinsteinin1905,[3]afterbeingmotivatedbyMaxwell'stheoryofelectromagnetismandthelackofevidencefortheluminiferousaether;[14]ithassincebeenconsistentlyconfirmedbymanyexperiments.Itisonlypossibletoverifyexperimentallythatthetwo-wayspeedoflight(forexample,fromasourcetoamirrorandbackagain)isframe-independent,becauseitisimpossibletomeasuretheone-wayspeedoflight(forexample,fromasourcetoadistantdetector)withoutsomeconventionastohowclocksatthesourceandatthedetectorshouldbesynchronized.However,byadoptingEinsteinsynchronizationfortheclocks,theone-wayspeedoflightbecomesequaltothetwo-wayspeedoflightbydefinition.[13][15]Thespecialtheoryofrelativityexplorestheconsequencesofthisinvarianceofcwiththeassumptionthatthelawsofphysicsarethesameinallinertialframesofreference.[16][17]Oneconsequenceisthatcisthespeedatwhichallmasslessparticlesandwaves,includinglight,musttravelinvacuum.
TheLorentzfactorγasafunctionofvelocity.Itstartsat1andapproachesinfinityasvapproaches c.
Specialrelativityhasmanycounterintuitiveandexperimentallyverifiedimplications.[18]Theseincludetheequivalenceofmassandenergy(E=mc2),lengthcontraction(movingobjectsshorten),[Note3]andtimedilation(movingclocksrunslower).Thefactor γbywhichlengthscontractandtimesdilate,isknownastheLorentzfactorandisgivenbyγ=(1−v2/c2)−1/2,wherevisthespeedoftheobject.Thedifferenceofγfrom1isnegligibleforspeedsmuchslowerthan c,suchasmosteverydayspeeds—inwhichcasespecialrelativityiscloselyapproximatedbyGalileanrelativity—butitincreasesatrelativisticspeedsanddivergestoinfinityasvapproachesc.
Theresultsofspecialrelativitycanbesummarizedbytreatingspaceandtimeasaunifiedstructureknownasspacetime(with crelatingtheunitsofspaceandtime),andrequiringthatphysicaltheoriessatisfyaspecialsymmetrycalledLorentzinvariance,whosemathematicalformulationcontainstheparameter c.[21]Lorentzinvarianceisanalmostuniversalassumptionformodernphysicaltheories,suchasquantumelectrodynamics,quantumchromodynamics,theStandardModelofparticlephysics,andgeneralrelativity.Assuch,theparameter cisubiquitousinmodernphysics,appearinginmanycontextsthatareunrelatedtolight.Forexample,generalrelativitypredictsthat cisalsothespeedofgravityandofgravitationalwaves.[22][23]Innon-inertialframesofreference(gravitationallycurvedspaceoracceleratedreferenceframes),thelocalspeedoflightisconstantandequalto c,butthespeedoflightalongatrajectoryoffinitelengthcandifferfrom c,dependingonhowdistancesandtimesaredefined.[24]
Itisgenerallyassumedthatfundamentalconstantssuchas chavethesamevaluethroughoutspacetime,meaningthattheydonotdependonlocationanddonotvarywithtime.However,ithasbeensuggestedinvarioustheoriesthatthespeedoflightmayhavechangedovertime.[25][26]Noconclusiveevidenceforsuchchangeshasbeenfound,buttheyremainthesubjectofongoingresearch.[27][28]
Italsoisgenerallyassumedthatthespeedoflightisisotropic,meaningthatithasthesamevalueregardlessofthedirectioninwhichitismeasured.Observationsoftheemissionsfromnuclearenergylevelsasafunctionoftheorientationoftheemittingnucleiinamagneticfield(seeHughes–Dreverexperiment),andofrotatingopticalresonators(seeResonat
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