Classical Electrodynamics and the Quantum Nature o

arXiv:hep-th/9610028v15Oct1996ClassicalElectrodynamicsandtheQuantumNatureofLightManoelitoMdeSouzaUniversidadeFederaldoEsp´ıritoSanto-DepartamentodeF´ısica29065.900-Vit´oria-ES-Brasil(February1,2008)AreviewofoldinconsistenciesofClassicalElectrodynamics(CED)andofsomenewideasthatsolvethemispresented.Problemswithcausalityviolatingsolutionsofthewaveequationandoftheelectronequationofmotion,andproblemswiththenon-integrablesingularityofitsself-fieldenergytensorarewellknown.Thecorrectinterpretationofthetwo(advancedandretarded)Lienard-Wiechertsolutionsareintermsofcreationandannihilationofparticlesinclassicalphysics.Theyarebothretardedsolutions.PreviousworkontheshortdistancelimitofCEDofaspinlesspointelectronarebasedonafaultyassumptionwhichcausesthewellknowninconsistenciesofthetheory:adivergingself-energy(thenon-integrablesingularityofitsself-fieldenergytensor)andacausality-violatingthirdorderequationofmotion(theLorentz-Diracequation).ThecorrectassumptionfixestheseproblemswithoutanychangeintheMaxwell’sequationsandletexposed,inthezero-distancelimit,thediscretenatureoflight:thefluxofenergyfromapointchargeisdiscreteintime.CEDcannothaveatrueequationofmotionbutonlyaneffectiveone,asaconsequenceoftheintrinsicmeaningoftheFaraday-Maxwellconceptoffieldthatdoesnotcorrespondtotheclassicaldescriptionofphotonexchange,butonlytothesmearingofitseffectsinthespacearoundthecharge.This,invarieddegrees,istransferredtoQEDandtootherfieldtheoriesthatarebasedonthesameconceptoffieldsasspace-smearedinteractions.PACSnumbers:03.50.De11.30.CpI.INTRODUCTIONClassicalandquantumphysicsareconsideredtoinvolvesharplydistinctconceptsandkindsoftheories.Classicalphysicsrepresentsanapproximationofthemorerefinedandclosertoatruedescriptionoftheworldwhichissupposedlydonebyquantumphysics.Theshort-distancelimitofbothhasalwaysbeenplaguedbyunsurmountableproblems,whichinCEDareattributedtotheassumedpointlikenatureoftheelectron.Assumingafinitenonzerodimensionfortheelectronbrings,however,moreproblemsthansolutions.Theblameisnotonthepointlikeelectronbutonanincorrectapproachontakingthetheoryzerodistancelimit.Amorecarefulapproachwillfreethetheoryofthesesproblemsandwillrevealsomequantumaspects,uptonowunsuspected,inaclassicaltheory.CEDofapointelectronisbasedontheLienard-Wiechertsolution(LWS);itsmanyoldandunsolvedproblems[1–3]makeofitanon-consistenttheory.TheLienard-Wiechertadvancedsolutionrepresentsitselfacausalityproblemthathasrequiredsome,atleastverbal,effortstobecircumvented.Onemustalsomentionthefieldsingularityortheself-energyproblem;thenon-integrablesingularitiesofitsenergytensor;thecausality-violatingbehaviourofsolutionsoftheLorentz-Diracequation[4–8];etc.Itwillbeshownherethatthesolutiontotheseproblemsisconnectedtoamorestrictimplementationofcausality(extendedcausality),alreadypresent,althoughnotyetrecognized,intheLienard-Wiechertsolution.InsectionIIthenotationisdefinedinabriefreviewofthestandardinterpretationofthetwo(advancedandretarded)LWS.Causalitycanbeseenasarestrictiontoaccesstoregionsofthespacetimemanifold,asdiscussedinsectionIII,wherethenotionofextendedcausalityisintroduced;itallowsanewinterpretationofthetwoLWSintermsofcreationandannihilationofclassicalparticles.Thenotionofaclassicalphotonisintroduced.InsectionIVthesingularitiesandnon-integrabilityoftheelectronself-fieldenergytensorastheyaredescribedintheliteraturearereviewedanddiscussed.Itisthenpointedthattheyareallconsequencesofusinganimplicitassumptionaboutthezerodistancelimitthatwillbeprovedfaultyinthefollowingsection.SectionVshowshowtocorrectlytakethezerodistancelimitinCEDandtogivetoitaconsistentphysicalinterpretation.Theanticipatedrecognitionintheclassicaltheoryoftheactualquantumnatureoftheelectromagneticradiationisnecessaryforhavingaclearphysicalpicturebehindthesenewmathematicalresults.Somealgorithms,thatwillbeusedintherestofthepaperfortakingthezerodistancelimit,arepresentedinsectionVI.InsectionVII,whilesearchingforanelectron“equationofmotion”,itisconfirmedbyanexplicitdirectcalculationthattheoldproblemofsingularityandnon-integrabilityoftheelectronself-fieldenergytensorhasvanishedjustwithcorrectlytakingthezero-distancelimit.Notamperingwiththemaxwell’sequationsandwiththeenergytensoriseverdoneinthispaper.Allthatisallowedisapossiblereinterpretationoftheirphysicalmeaning.Themostremarkablenewfeatureisthattheenergyfluxfromapointchargeisdiscreteintime,whichrequiresaninterpretationoflightintermsofdiscreteemissionofpointlikeobjects(classicalphotons)andarevisionofthephysicalmeaningoftheGauss’slawandoftheFaraday-Maxwellconceptof1field.Thiswillbedoneinthelastsection.Theelectron“equationofmotion”,derivedinsectionVIII,doesnothavetheproblematicSchotttermbutitisjustaneffectiveequation.Thisisaconsequenceofthebi-localcharacteroftheLWS,asitdependsontwopossiblyfarapartpoints:thepointwherethesignalisdefined,andthepoint,inthesourceworldline,whereitwascreated.ItisarguedthenthatCEDcannotproduceatrueequationofmotionforitssourcesasfarasitsformulationisbasedontheFaraday-Maxwellconceptoffields.SectionIXisincludedlikeanappendixofsectionVIIIforshowinganalterna