counting energy packets in the electromagnetic wave

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1、Countingenergypacketsintheelectromagneticwave12StefanPopescuandBernhardRothenstein1)SiemensAG,Erlangen,Germanystefan.popescu@siemens.com2)PolitehnicaUniversityofTimisoara,PhysicsDepartment,Timisoara,Romaniabrothenstein@gmail.comAbstract.Wediscusstheconcept

2、ofenergypacketsinrespecttotheenergytransportedbyelectromagneticwavesandwedemonstratethatthisphysicalquantitycanbeusedinphysicalproblemsinvolvingrelativisticeffects.Thisrefinedconceptprovidesresultscompatibletothoseobtainedbysimplerdefinitionofenergydensity

3、whenrelativisticeffectsapplytothefreeelectromagneticwaves.Wefoundthisconceptfurthercompatibletoquantumtheoryperceptionsandweshowhowitcouldbeusedtoconciliatebetweendifferentphysicalapproachesincludingtheclassicalelectromagneticwavetheory,thespecialrelativit

4、yandthequantumtheories.1.IntroductiontoelectromagneticwavetheoryTheplaneelectromagneticwavetravelsinvacuumasfleetingorthogonalelectricandmagneticfields.Thefieldintensitiesoscillatespatiallyalongthedirectionofpropagationandtemporarynormaltothedirectionofpro

5、pagationasdepictedbyfigure1.YE(x,t)-BEmaxmaxcSmaxXSmaxPropagationdirectionZB(x,t)Bmax-Emaxλ=c⋅TFigure1.Time-spacepropagationoftheplaneelectromagneticwaveinvacuumdepictstheorthogonalelectricandmagneticcomponentsthatoscillatebothtemporaryatanypointwithperiod

6、Tandlongitudinallyatanytimeinstantwithperiodλ.AstationaryobserverlocatedatsomearbitrarypointxalongthepropagationdirectionmeasuresthelocalamplitudeoftheelectricandmagneticfieldandrecordssynchronouselectricandmagneticoscillationshavingthesameperiodTandthesam

7、ephase.Agroupofobserversequippedwithsynchronizedwatchesanddistributedalongthepropagationdirectionmeasurethelocalamplitudeoftheelectricandmagneticfield.Whencomparingtheirmeasurementsmadeatanyarbitrarytimettheseobserversidentifyalongitudinallyoscillatingelec

8、tricandmagneticfieldhavingthe1sameperiodλ=c⋅Tandthesamephase.Invacuumthesefleetingoscillationsaremathematicallydescribedbythefamiliarwaveequations:⎛x⎞⎛x⎞E(x,t)=Emaxsinω⎜t−⎟B(x,t)=Bmaxsinω⎜t−⎟(1)⎝c⎠⎝c⎠1andweha