chapter 9 electromagnetic fields & spacetime unitsonlyspacetime.com/chapter_9.pdfthe universe is...

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Chapter9

ElectromagneticFields&SpacetimeUnits

Introduction: In the last chapterwe analyzed gravitational attraction and established thenecessityofvacuumenergy/pressureingeneratingthegravitationalforce.Thischapterisanintroductiontotheelectromagnetic EM radiationandelectricalcharge.Wewillstartwithapreliminaryexaminationofspacetimecharacteristicsresponsiblefortheelectricfieldofchargedparticles. After some insights aredevelopedwith chargedparticleswewill then switchandexaminethepropertiesofspacetimethatareaffectedwhenelectromagneticradiationispresent.Anexperimentwillbeproposed.Wewillthenswitchbackandusesomeoftheinsightsgainedfromelectromagneticradiationtodevelopfurtherthemodelofachargedparticle’selectricfield.Finally,wewilldevelopasystemoffundamentalunitsbasedonlyonthepropertiesofspacetime.Theseunitsdesignatechargeutilizingonlythepropertiesofspacetime.WetendtothinkoftheelectricandmagneticfieldsassociatedwithEMradiationasbeingverysimilartotheelectricandmagneticfieldsassociatedwithchargedparticles.However,thereareobviousdifferences. The fieldsassociatedwithEMradiationarealwaysoscillatingand theypropagateatthespeedoflight.Thefieldsassociatedwithchargedparticlesarenotoscillatingandtheyarenot freelypropagating. Withthesedifferences, itshouldbeexpectedthat thereshouldalsobeconsiderabledifferencesintheexplanationsoftheelectricfieldassociatedwithphotonscomparedtotheelectricfieldassociatedwithelectrons.Developingamodelofelectricandmagnetic fields has been themost difficult task of this entire book. While considerableprogresshasbeenmade,themodelisnotcomplete.Furthermore,themodeloftheelectricfieldassociatedwithchargedparticlesislesscompletethanthemodelofEMradiation.Thischapterbeginsby examining themagnitude and typeof distortionof spacetime required toproduceelementarychargee. Spacetime Interpretation of Charge: Iftheuniverseisonlyspacetime,thereshouldbeaninterpretationofelectricalcharge,permeability,electricfield,etc.thatconvertstheseelectricalcharacteristics into properties of spacetime. Like gravity, we might be looking for both anoscillatingcomponentandanon‐oscillatingstraininthespacetimefieldcausedbytheoscillatingcomponent wavesinspacetime .Itwillberecognizedthattherearetwotypesofelectricfield:1 Theelectricfieldassociatedwithachargedparticlewhichappearstobeonlystaticbutmustalso have an oscillating component and 2 the oscillating electric field of electromagneticradiation.Thisdistinctionismadebecauseitwillbeshownthattheelectricfieldassociatedwithachargedparticleismorecomplex.


To obtain an insight into the electrical properties of nature,wewill start by expressing theelectricalpotential thevoltagerelativetoneutrality forasingleparticlewhichhasPlanckcharge 4p oq c atdistanceris:

4

4 4p o

Eo o

q c

r r

.

The symbol E willbeused tosignify thatweareassumingPlanckchargeqp.NextwewillexpresselectricalpotentialofPlanckchargeindimensionlessPlanckunits.Thisisdonebecausedimensionless Planck units are fundamentally basedon the properties of spacetime.We areattemptingtogainaninsightintothedistortionofspacetimecausedbyelectriccharge.IfweexpressthiselectricalpotentialindimensionlessPlanckunits E noteunderlined ,thenweareconvertingtodimensionlessPlanckunitswhichinthiscasemakesaratiorelativetothelargest

possibleelectricalpotential,Planckvoltage 1/24 274 1.043 10p oc G Volts

E E p 4

4 4

4o o

o

c G

r c

3

1 pLG

r rc

Before commenting,wewill next calculate the electric field indimensionlessPlanckunits atdistancerfromPlanckchargeqp.Thesymbolusedwillbe: E E p where 24E p oq r and

Planckelectricfieldis 7 24p oc G

22

2 7 3 2 2

4 4

4po o

E E po

Lc G G

r c c r r

Whatisthephysicalinterpretationof E pL r and 2 2

E pL r ?Expressingelectricalpotential

and electric field in dimensionless Planck units is expressing these in the natural units ofspacetime.Therefore,wewillminethistoextracthintsabouttheeffectthatPlanckchargehasonspacetime.

1 Sincethereisnotimetermineitherequation,theimplicationisthatanelectricalchargeonlyaffectsthespatialpropertiesofspacetime.Thisisalsoreasonablesinceagradientintherateoftimealwaysimpliesgravitationalacceleration.Ifelectricalchargeproducedarateoftimegradient,thenneutralobjectssuchasaneutronwouldbeacceleratedbyanelectric field. Therefore, it is reasonable that an electric field affects only the spatialdimension theLpterm

2 ThepresenceofPlancklengthterm Lp inthevoltageandelectricfieldequationsimpliesthat Planck length is somehow associatedwith the electric field produced by Planckcharge.

3 Thedimensionless ratio Lp/r implies a slope. Thiswill have to be a spatial strain ofspacetimethatcanbeexpressedasaslope.

4 Onlytheradialspatialdimension r seemstobeaffected.


Charge Conversion Constant η:Toquantifythemagnitudeoftheeffectonspacetimeproducedbyacharge,wewillattempttofindanewconstantofnaturewhichconvertsunitsofelectricalcharge Coulomb intoapropertyofspacetime.Consideringtheprevious4points,wewouldexpectthatchargemightproduceapolarizedstrainofspace radiallengthdimension withoutaffecting the rate of time. The validity of this approachwill be established only if it passesnumeroustests.There aremanyways to derive this charge conversion term.Wewill use one of the aboveequations:VE/Vp Lp/rwhereVEistheelectricalpotentialgeneratedbyaPlanckchargeqpatdistancer.IfwesolveforPlanckchargeqp,whileretainingPlancklengthLp,wewillbeabletodeduce a charge conversion constant that converts charge into a spatial distortion of thespacetimefield.

4

p p pE

o

q L

r r

The proposed conversion between charge and a spatial distortion of spacetime will bedesignatedasthe“chargeconversionconstant”anddesignatedaseta .

≡ 8.61 10 m/Cchargeconversionconstant

Eta hasunitsofmetersperCoulomb.Thisunitisreasonablebecauseweareexpectingtoconvertchargeintoapropertyofspacetimeandthetimedimensionhasbeeneliminated.The“meters”referencedinmeters/coulombaretheradialdirectionifwearereferringtotheeffectachargedparticlehasonthesurroundingspacetimeorifwearereferringtoanelectricfield,thenthe“meters”are inthedirectionof theelectric field.Weknowthatthisconstant iscompatiblewiththedimensionlessvoltageequationforPlanckcharge E Lp/r sincethatequationwasusedtodefinetheconstant.However,totestthisfurther,wewilluseeta toeliminateCoulombfromotherconstantsandequations.Wewillstartwithtwoconstants:1 theCoulombforceconstant1 4 o withunitsofm3kg/s2C2and2 themagneticpermeabilityconstantµo/4πwithunits of kgm/C2. Bothof thesehave1/C2. To eliminate1/C2 requiresmultiplyingbothoftheseby1/η2.

Fp 1.21 1044N

Coulombforceconstant convertstoPlanckforce withunitsofNewton.

1.35 1027kg/m


Therefore,vacuumpermeabilityμ4 convertsto withunitsofkg/m.

ItisquitereasonablethattheCoulombforceconstant1 4 o getsconvertedtoFpPlanckforce.Ifelectricchargeandanelectricfieldaredistortionsofthespacetimefield,thenitisreasonablethattheCoulombforceconstantconvertstothelargestforcethatthespacetimefieldcanexertwhichisPlanckforceFp c4/G.Infact,thisconversionstronglysupportsthevalidityofeta . If the universe is only spacetime, then it is reasonable that all forces, including theelectromagneticforce,shouldreferencePlanckforce.Thevacuumpermeabilityalsoconvertstoanimportantpropertyofspacetimewhichisc2/Gwithunitsofkg/m.Thisistheconstantthatconvertsmassintolength theradiusofablackhole .Thenexttestistoseeifc2 1/εoµoisstillcorrectwhenwesubstituteεo G/4πc4andµo 4πc2/G.Weobtain: 4 ⁄ 4⁄ .NextwewillalsoconvertelementarychargeeandPlanckchargeqptoadistortionofspacetimebymultiplyingbyη.

eη √ Lpconversionofelementarychargeewhere:ħ

qpη LpconversionofPlanckchargeqpWecannowdoamorerevealingtest.Wewillcalculatetheforcebetweentwoelectrons chargee twodifferentways.FirstwewillusetheconventionalCoulomblawequationtocalculatethisforce,thenwewillcalculatetheforceusingtheaboveconversions.

ħCoulomblawforcebetweentwoelectrons:chargee 1.6 10‐19C

ħ ħ

ForceequationwhichconvertseandεotospacetimestrainThisisasuccessfultest.Itisinterestingtoseehow1/4πεoconvertstoPlanckforceandstillgivesthe same answer as the Coulomb law equation which utilizes electrical charge and thepermittivityoffreespace.Itisinterestingtomakeothertestsofη.Italwaysworkscorrectly.

ImpedanceCalculationBeforeproceedingwith the following test calculation, Iwant to tell a story. There are twocalculationsinthisbookthatgavemethebiggestthrill. OneofthemwaswhenIwasabletoderive Newton’s gravitational equation from my starting assumptions. The second is thefollowingcalculationthatconvertstheimpedanceoffreespaceZointoadistortionofspacetime.Thisdoesnotseemlikeaparticularlyimportantrelationship,whichisperhapsthereasonthatitwassosurprising.


Impedance of Free Space and Planck Impedance:TheimpedanceoffreespaceZowithunitsofohmsisaphysicalconstantthatrelatesthemagnitudesoftheelectricfield andthemagneticfieldstrength ofelectromagneticradiationpropagatinginavacuum.

Zo≡ / μoc 376.7Ωimpedanceoffreespace

PlanckimpedanceZpis:

Zp 4 29.98ΩPlanckimpedance

The units of the impedance of free space Zo and Planck impedance Zp are both L2M/Q2T.Thereforetoeliminate1/Q2wemustmultiplyZpandZsby1/η2.

Zp Zs

Zo 4π 4πZs

Zp ZsandZo 4πZs

PlanckimpedanceZpcorrespondstotheimpedanceofspacetimeZsandtheimpedanceoffreespaceZocorrespondsto4πZs–Fantastic!Impedance of free Space Converts to the Impedance of Spacetime: Whenweconverttheimpedance of free space Zo ≡ / using the charge conversion constant, Zo becomes theimpedanceof spacetimeZs timesa constant 4π . We can ignore the4πand in factPlanckimpedancedoeseliminatethisnumericalfactor.Thisisafantasticoutcomebecauseitimpliesthatelectromagneticradiationissomeformofwaveinthespacetimefield.Hereisthereasoning.From gravitational wave equations we know that waves propagating in the medium of thespacetimefieldexperienceimpedanceofZs c3/G 4 1035kg/s.Nowwediscoverthatnotonlydoeselectromagneticradiationpropagateatthesamespeedasgravitationalwaves,andhastransversewaveslikegravitationalwaves,butelectromagneticradiationalsoexperiencesthesameimpedanceasgravitationalwaves theimpedanceofspacetime .Theconclusionis:Electromagnetic radiation must be a wave propagating in the medium of the spacetime field.TheequationZs c3/Gisonlyapplicablewhenwavesusethespacetimefieldasthepropagationmedium.Thisisunderstandableandfullyexpectedforgravitationalwaves,butnowwefindthatelectromagnetic radiationmust also use the spacetime field as a propagationmedium. The


impedanceoffreespaceZo fundamentaltoeverythingelectromagnetic is:Zo/η2 4πZswhenexpressed using a conversion constant η that converts charge to a strain of spacetimewithdimensionsoflength ignore4π .ThissaysthatphotonsarenotpacketsofenergythattravelTHROUGH theemptyvoidofspacetime.PhotonsarewavesIN themediumofthespacetimefield.Theyappeartoalsohaveparticlepropertiesbecausephotonspossessquantizedangularmomentum. The superfluid spacetime field quarantines angularmomentum into quantizedunitsofħforbosonsor½ħforfermions.Itisnotpossibletobreakapartaunitofquantizedangularmomentum.Thetransferofquantizedangularmomentumisallornothing 100%or0% . The photon’s energy also becomes quantized because the energy of a photon isfundamentally associatedwith the quantized angularmomentum. The proposed property ofunity makes the energy in the distributed waves collapse transfer their quantized angularmomentum at faster than the speed of light. This apparently localized interaction givesparticle‐likepropertiestophotons.TheequationZo/η2 4πZs alsoimpliesthatphotonsarefirstcousinstogravitationalwaves.Photonsandgravitationalwavesdisturbthespacetimefield’sseaofsuperfluiddipolewavesindifferentways, but they both are transverse disturbances in the spacetime field that do notmodulatetherateoftimeandpropagateatthespeedof light. Recallfromchapter4thatthespacetimefieldisanelasticmediumwithimpedanceandtheabilitytostoreenergyandreturnenergytoawavepropagatinginthismedium.Theimplicationisthatgravitationalwavesarealsoquantizedandcarryquantizedangularmomentum.Lightwavesarenotdipolewavesinspacetimesincewecandetectlightwavesasdiscretewaves.Recall that it is impossible to detect dipole waves in spacetime. Dipole waves in spacetimemodulate the rate of time and proper volume. Their amplitude must be limited to Planckamplitude Lp and Tp . A larger amplitude would produce effects that violate theconservationofmomentumandenergy.Also,alightwavecannotcauseanoscillationintherateoftimebecauseagradientintherateoftimeproducesgravitation‐likeeffects.Forexample,astrong light wave would cause a neutron to undergo a detectable transverse oscillatorydisplacement similar to the effect on an electron. Therefore, lightwaves are a spacialwavedistortionofthehomogeneousspacetimefield.Eachindividualphotonhasquantizedangularmomentumandotherspecialpropertieswhichwillbediscussedlater.ConstantSpeedofLight: Is itreasonablethatlightwavesarepropagatinginthemediumofspacetime?Forexample,ifthepropagationmediumisthespacetimefield,wouldweexpectthatitshouldbeimpossibletodetectmotionrelativetothismedium?First,weknowthatεoandµoarepropertiesofthespacetimefield.Wealsoknowthatεoandµoremainconstantinallframes

ofreference.Sincec 1 μ⁄ itfollowsthatawavepropagationspeedthatscaleswithεoandµoshouldalsobeindependentoftheframeofreference.


Second,gravitationalwavesaredefinitelypropagatinginthemediumofthespacetimefieldandtheyalwayspropagateatthespeedoflightinallframesofreference.IfitwaspossibletodoaMichelson‐Morleyexperimentusinggravitationalwaves,thisexperimentwouldobtainthesameresultastheexperimentusinglight.Inbothcasestherewouldbeanullresult–nomotionwouldbedetectedrelativetothepropagationmedium.Thespacetimefield isaseaofdipolewavespropagatingatthespeedoflightbutalsostronglyinteracting.Nomotionisabletobedetectedrelativetothismedium.Alsoallobservableobjects allparticles,fieldsandforces areobtainedfromthesinglebuildingblockof4dimensional spacetime.Therefore,allparticles, fieldsandforcescompensatewithaLorentztransformationwhichmakesthelocallymeasuredspeedoflight constant. Therefore, thespacetime fieldpossesses theproperties required tomake thespeedoflightconstantinallaccessibleframesofreference. Attheendofchapter14wewillexplorethelimitsofextremeframesofreferencewherethisbreaksdown. CosmicSpeedLimit:Thefollowingquestionhaspuzzledphysicists:Whyisthereacosmicspeedlimit? Now we can answer this question. A photon is not a quantized packet of energypropagatingthroughtheemptyvoidofthevacuum.Atrulyemptyvacuumwouldnotdictateanyspeedlimittoa“packetofenergy”thatismerelypropagatingthroughit.However,ifaphotonisawave propagating in the spacetime fieldmedium, then the impedance and energy densitycharacteristicsofthismediumdictateaspecificspeedofwavepropagation.Themediumnamedthe“spacetimefield”consistsofstronglyinteractingdipolewavesinspacetimepropagatingatthespeedof lightatall frequenciesup toPlanckangular frequency ωp 1043s‐1 . Photonsdisturbthehomogeneityofthismediumandthisdisturbancealsopropagatesatthespeedoflight.Photonsappeartobeparticlesbecausephotonspossessangularmomentumandangularmomentumisquarantinedintoħor½ħunitsbythesuperfluidspacetimefield.Sinceangularmomentumisonlytransferredinquantizedunits,thisgivesparticle‐likepropertiestoquantizedwaves. Thephrase“wave–particleduality”cannotbeconceptuallyunderstoodsince“wave”impliesaperiodicvariationoveravolumeand“particle”impliesapointdiscontinuity.Theyaremutuallyexclusiveterms.Iproposethatbosonsandfermionsarefundamentallywaveswhichactlikeparticlesbecausetheypossessangularmomentumwhichisquantizedbythesuperfluidspacetimefield.Allparticles,fieldsandforcesarealsodistortionsofthespacetimefield.ThereisasinglespeedlimitforallframesofreferencebecauseallparticlesfieldsandforcescompensatetheirsizeandothercharacteristicsinawaythatachievesaLorentztransformationwhichkeepsthelawsofphysics constant. Even the forces between particles compensate to maintain the distancebetweenparticlesthatpreservesthelocallymeasuredconstantspeedoflight.Accuracy Check: ThereisanothermoresubtleimplicationfromtheequationZo/η2 4πZs.andthesuccessofthechargeconversionconstant.Theseequationsimplytomethatthemanysteps that startedwith gravitationalwave equations and endedwith these relationships arecorrect.Theimpedanceofspacetimec3/Gwasdeducedfromgravitationalwaveequations.The


impedanceoffreespaceZowasderivedfromMaxwell’sequationsofelectromagnetism.Startingfrom the assumption that the universe is only spacetime,wewent looking for a constant toconvertchargeintoadistortionofspacetime: ≡ 4⁄ / .ThisresultedinZo/4πη2 Zs.Theseapparentlydissimilarimpedancesarethesamewhenweassumethattheuniverseisonlyspacetime.Thisunificationofimpedancessupportsthestartingassumption.

SpacetimeModelofanElectricFieldElectric Field Conversion:Nextwewillattempttogainadditionalinsightsintoelectricfields.We had some success describing the voltage and electrical field produced by Planck charge

E pL r and 2 2E pL r . However the underlyingmechanismbywhich a charged particle

producesanelectricfieldissomewhatmorecomplexthananelectricfieldproducedbyaphoton.Thereforewewillswitchtoelectromagneticradiationtoexamineelectricandmagneticfieldsthencomebacktochargedparticleslater.In chapter 4 itwas stated that thewave‐amplitude equation for intensity kA2ω2Z is auniversalclassicalequationthatisapplicabletowavesofanykindprovidedthattheamplitudeand impedance is stated in units that are compatible with this equation. Electromagneticradiationcommonlyuseselectricfield toquantifywaveamplitudeofEMradiation.Also,theimpedanceoffreespace Zo 377ohms isusedtoquantifytheimpedanceencounteredbyEMradiation.Thiswayofstatingamplitudeandimpedanceisnotcompatiblewiththeotherunitsoftheabovewave‐amplitudeequation.Therefore,thiscreatestheimpressionthatthiswave‐amplitudeequationislessthanuniversal.However,itispossibletoconvertelectricfieldofEMradiationintoanamplitudetermthatiscompatiblewiththe5wave‐amplitudeequations.Forexample, amplitude of EM radiation can be expressed using strain amplitude A, angularfrequencyωand the impedanceof spacetimeZs. It is informative to analyze the connectionbetweenelectricfield ormagneticfield andthestraininspacetime.Thiscanbeeasilydoneusingthetwodifferentwaysofexpressingintensity: kA2ω2Zsand ½ 2/Zo.Wewillequatetheseandsolvefor and .SincetheseassumeEMradiationandnotnecessarilytheelectricfield of a charged particle,wewill designate the electric field of EM radiation as γ and themagneticfieldofEMradiationas γ.γ2/Zo kA2ω2Zsintensityequationsignoringnumericalfactorsnear1

γ kAω γ ElectricfieldofEMradiationexpressedutilizingA,ω,ZsandZo

γ kAω γ magneticfieldofEMradiationobtainedfrom γ k γ/Zo


Thisisinteresting,butitstillusesZowhichimpliescharge.NextwewillconverttheelectricfieldandmagneticfieldofEMradiationintoadistortionofspacetimeusingη.ThisresultsinZobeingconvertedtoZs.Applyingthisto γ kAω and γ kAω ⁄ weobtain:γ/η kAωZs γ electricfieldstrengthofEMradiationγη kAω γ magneticfieldstrengthofEMradiation

Theseequationsexpress and intermsofA,ωandZs.However,theremainingtaskistobeabletodefinetheelectromagneticwaveamplitudeasastraininspacetime defineamplitudeA .

Also,thereshouldbeafactorof√4 intheseequations,butthereareotherunknownnumericalfactorsnear1whichhavebeenignored,sotheseequationsarestatedusingktorepresenttheunknownnumericalfactornear1.What Is an Electric Field?Ifindthecurrentlyacceptedexplanationofanelectricfieldastotallyinadequate. The electromagnetic force that exists between charged particles is supposedlycarriedbyexchangingvirtualphotons.However,anelectricfieldhasenergydensity,thereforeithasatangiblequality.Theenergydensityimpliesthatanelectricfieldmustalsohaveinertiaandgenerateitsowngravitationalfield.Thisimpliesthatanelectricfieldhasmoreofaphysicalpresencethanimpliedbytheconceptofvirtualphotons.Oneofthecharacteristicsofavirtualphotonisthatitisundetectable;thereforeitisnot“falsifiable”.Sometimesanelectricfieldisdescribedasacloudofvirtualphotons.Moreoften,physicistsprefertodescribetheeffectsofanelectric field and avoid addressing the question ofwhat an electric field is. Still, the closestanswerusuallyinvolvesavaguereferencetovirtualphotons.If we require virtual photons to describe an electric field, this leaves many unansweredquestions. Forexample,dorealphotonsgenerateanelectric fieldbysendingout transversevirtualphotons?Whydovirtualphotonstransferforcebutnotangularmomentum?Whydoesanelectricfieldhaveenergydensityiftheenergyofvirtualphotonsmustaverageouttoequalzero?Howexactlydovirtualphotonsachieveattraction?Whatpreventstheimpliedpressureassociatedwith theenergydensityofa staticelectric field fromdissipating? Ifanelectron issmallerthantheclassicalelectronradius ∿10‐15m ,thenwhatpreventstheenergyinitselectricfieldfromexceedingthetotalenergyoftheelectron?Somephysicists freelyadmit thatvirtualphotonsaremerelyamathematical tool. Thepath‐integralformulationofquantummechanicsassumesthatvirtualphotonstakeallpossiblepathsbetweentwochargedparticles.Inthecalculation,pathsareallowedwherethevirtualphotonisgoingfasterthanthespeedof lightorviolatingenergyconservation. Thesecalculationsgivecorrectanswers,butthephysicalmodelislacking.

Icouldgoonwithmoreexamples,butthetruthisthattherearesomanyconceptualmysteriesinthequantummechanicsthatphysicistslearntoembracethelackofconceptualunderstanding.


Thedesireforconceptualunderstandingisoftencriticizedasaruminantofclassicalphysicsthatcannotbefulfilledbyquantummechanics.Theequationsofquantummechanicsobviouslyarecorrectbuttheconceptualmodelsarelacking. Theobjectiveofthisbookistopresentanewmodel that is conceptually understandable yet is compatible with the equations andexperimental verifications of quantummechanics and general relativity. We start with theelectricfieldassociatedwithEMradiation.Maximum Confinement of a Photon: Wewill first look at the simplified case of a photonconfinedinareflectingchamber.Ifwehad100%reflectingwalls,whatisthesmallestvolumethatwouldconfineasinglephoton?Combiningthetransmissioncharacteristicsofwaveguideswiththeresonancecharacteristicsoflasers,itispossibletoanswerthisquestion.Inwaveguides,asharpcutoffoccurswhenthewidthofthewaveguideinthepolarizationdirectionisequaltoor less than ½ wavelength. However, the width needs to only be slightly larger than ½wavelengthtoachievegoodtransmission.Forcircularlypolarizedelectromagneticradiation,acylindricalwaveguideslightlymorethan½wavelengthindiameteristhesmallestwaveguidewhichhasgoodtransmission.Makingawaveguideintoaresonatorrequiresaddingtwoflatandparallel reflectors separated by½wavelength and oriented perpendicular to the axis of thecylinder. Thiscylindricalwaveguideresonatoristheminimumevacuatedvolume maximumconfinement that we can achieve for coherent circularly polarized light of a particularwavelength.Thisconfigurationwillbecalledthe“maximumconfinementresonator”andwillbeutilizedinbothcalculationsandaproposedexperimentlater.When electromagnetic radiation is freely propagating, the electric and magnetic fields areperpendiculartoeachotherandinphase.However,whenelectromagneticradiationisconfinedinaresonatorsuchasthemaximumconfinementwaveguideresonatordescribedhere orevenina laser resonator theradiation formsstandingwaves thathave theelectricandmagneticfields90°outofphase.Thisiseasiesttoseebyimaginingelectromagneticradiationreflectingoffametalmirror.Theelectricfieldisaminimumatthesurfaceofeachmirrorbutthemagneticfieldisatamaximumatthemirrorsurfaces.Theelectronsinthemetalmirrorareundergoingamotion thatminimizes the electric field but this creates an oscillatingmagnetic field. If thereflectorsareseparatedby½wavelength,thestandingwavecreatedbetweenthetwomirrorshasmaximumelectricfieldoscillationsinthecentralplaneofthe½wavecavity antinode andtheminimumelectricfieldatthemirrorsurfaces nodes .Conversely,themagneticfieldisataminimum node inthecentralplaneandatamaximumatthemirrorsurfaces antinodes .Displacement of Spacetime Produced by a Single Photon: Next we will calculate thedisplacementofthespacetimefieldproducedbyasinglephotoninthismaximumconfinementresonator. Byspecifying the “maximumconfinementcondition”,wecanavoidspecifying thecharacteristicsofafreelypropagatingphotonthatwillbediscussedinchapter11.Sinceweareignoringnumericalfactorsnear1,wewillmodelthedisplacementrequiredtoproduceauniformoscillating electric field over the central volume of λ3 and assume zero electric field in the


remainder of themaximumconfinement cavity. Alsowe are not specifyingwhetherwe aredesignatingthepeakelectricfieldstrengthortheRMSelectricfieldstrength.Therefore,ignoringthesefactors assumingavolumeofλ3 ,theenergydensityofasinglephotonwithenergyħωanduniformenergydensityinavolumeofλ3wehave:U ħω/λ3 ħc/λ4 ħω4/c3 Lp/λ 4Up.Tofindthedisplacementamplitudeofspacetimerequiredtoproducethisenergydensity,wewillequateU ħω4/c3withU A2ω2Zs/candsolveforΔLinA ΔL/λ.

U ħ

solveforΔL

ΔL ħ Lpdisplacementamplitudeofasinglephotonin“maximumconfinement”

A Lp/λthestrainamplitudeAofasinglephotonin“maximumconfinement”TheequationΔL Lpisforasinglephotoninvolumeλ3.ThereforethiscalculationpresumesthatΔLisoveratotalpathlengthofλ ignoringnumericalfactorsnear1 .Atotalpathlengthofπλ the diameter of the maximum confinement waveguide is within the allowed range,especiallysincetheelectricfieldismaximizedoverthecentralλ.Sincephotonsarebosonsandmanyphotonscanoccupythesamevolume,wewillnextcalculatethedisplacementofspacetimerequiredifmanycoherentphotons samefrequencyandphase areintroducedintothevolumeλ3.Inthiscalculationwewilluse“n ”asthenumberofphotonsoccupyingthevolume.ThereforeU n ħω/λ3 n ħω4/c3.

U ħ

SolveforΔL

ΔL Lpdisplacementamplitudeofn photonsin“maximumconfinement”TheequationΔL Lp istheoscillatingdisplacementofspacetimefor“n ”photonsinthemaximumconfinementpreviouslydiscussed.ThisvalueofΔLisoverdistanceλ,thereforethestraininspacetimeproducedbyn coherentphotonsinmaximumconfinementis:

A strainproducedbynγcoherentphotonsinmaximumconfinementTheequationΔL Lpisveryrevealing.First,itincorporatesPlancklengthLp.Previously

wefoundthatPlancklengthwasalsoassociatedwithPlanckcharge E pL r and 2 2E pL r


Therefore,thefactthataphotonexhibitsthisamplitudeinmaximumconfinementsupportsthemodel.Also,itisnotpossibletoactuallymeasuretheelectricfieldormagneticfieldproducedbyasinglephoton.NowwecanunderstandthisbecausemeasuringtheelectricfieldproducedbyasinglephotonwouldbeattemptingtomeasureadisplacementofPlancklength.Referencesinchapter4showedthatitisfundamentallyimpossible deviceindependent todetectadisplacementofspacetimeequaltoorlessthanPlancklength.Itistheoreticallypossibletodetectandmeasurethe oscillating electric field produced by many photons n 1 photons because manycoherentphotonsproducesΔL Lp.Nowwecanconceptuallyunderstandthiseffect.Similarity to Gravitational Wave: WepreviouslylearnedthatPlanckimpedanceZpisthesameas the impedance of spacetime Zs when we use the charge conversion constant η. Thisconversionconstantandawave‐amplitudeequationalsogivethatn photonsinthemaximumconfinementconditiongivestheoscillatingstrainamplitude inthespacetimefieldAequal toA ⁄ .Thisimpliesthatelectromagneticwavesareverysimilartogravitationalwaves.

Whilegravitationalwavesappear tobecompletelydissimilar toelectromagneticwaves, theymustbefirstcousins.Botharetransversewavesthatpropagateatthespeedoflightthroughthemedium of the spacetime field. They both experience the same impedance thereforeelectromagneticwavesmustalsobewavesinspacetime.Thequantummechanicaldescriptionof the spacetime field is vacuum fluctuations with Planck length/time displacements at allfrequenciesuptoPlanckfrequency. Thisdescriptionofthespacetimefieldhasahighenergydensity.Thespacetimefieldhaselasticityandverylargeimpedance. Wavesinthespacetimefieldpropagateatthespeedof lightbutthedisplacementofthespacetimefield isverysmallbecausethespacetimefieldalsohasanincrediblylargeimpedanceandbulkmodulus.Asinglephotoninmaximumconfinement volumeλ3 onlyaffectsthespacetimefieldbyaPlancklengthdisplacementoveradistanceofλ.One of the biggest differences is that positive and negative electrically chargedparticles areavailabletogenerateelectromagneticradiation.Gravitationalwavescanonlybegeneratedbyparticlesthathaveasinglepolarity onlypositivemass thereforeonlyquadrupolegravitationalwavesarepossible.However,ifweareattemptingtounderstandthephysicsofelectromagneticradiationpropagatinginthespacetimefieldthedifferencesingenerationarenottooimportant.Agravitationalwaveisatransversewavethatcausesasphericalvolumetobecomeatransverseoscillatingellipsoid.Ifwefreezethisellipsoidforamomentthereisanaxisthatincreasesthedistancebetweenpointsandanorthogonalaxisthatdecreasesthedistancebetweenpoints.Thepoints themselves are not accelerated and physicallymoved by the gravitationalwave. Thespatialpropertiesofthespacetimefieldareaffectedinawaythatincreasesordecreasesproperdistance as might be measured by a tape measure. With gravitational waves there is nopolarization vector that distinguishes between opposite directions along either of these two


axes.Theeffectonthespacetimefieldbygravitationalwavesissymmetrical reciprocal .Thiseffectcanbethoughtofasadifferencebetweenthecoordinatespeedof lightandtheproperspeed of light along the two axes. We interpret this difference as a change in the distancebetweenpointsbecauseweassumethattheproperspeedoflightisconstant.Also,allphysicalobjects metersticks,protonradius,etc. scaletheirsizewithproperlengthwhichinturnscaleswiththeproperspeedoflight.Thisisunderstandablefromtheproposedspacetimebasedmodeloftheuniversebecauseallmatterandforcesareultimatelywavesinthespacetimefieldwhichscalewiththeproperspeedoflight.Proposed Model of an Electric Field: Electromagnetic radiation has transverse oscillatingelectricandmagnetic fields. Ifwe imagine freezing thewave, theelectric fieldhasaspecificvectordirectionwhichbyconventionwesaypointsawayfrompositiveandtowardsnegative.ThemagneticfieldbyconventionpointsfromNorthtoSouth.Thereforeonedifferencebetweenanelectromagneticwaveandagravitationalwaveisthattheelectromagneticwaveproducestransverse vectorswhich are not reciprocal electric andmagnetic fields vectors while thegravitationalwaveisareciprocaltransversewave.Reversingdirectionalongeitherthelongorshort axis distortion produced by a gravitationalwave produces the samedistance betweenpoints. Wewill designate the unsymmetrical non‐reciprocal effect on the spacetime fieldproducedbyEMradiationas“polarizedspacetime”.BothEMradiationandgravitationalwavesdonotmodulateeithertherateoftimeorpropervolume.Ifwearegoing toexplainelectromagnetic fieldsusingonly thepropertiesof spacetime, it isnecessarytoincorporateintotheexplanationanonreciprocal polarized effectthatdoesnotproduceanoscillationofeitherpropervolumeortherateoftime.Explaininganelectricfieldandlateramagneticfield usingonlythepropertiesofspacetimehasbeenthemostdifficulttask invention ofanycreativenewideadescribedinthisbook.Inparticular,itwasdifficultto1 initiallyrecognizethatthesolutionmustinvolvepolarizedspacetime,2 tofindamodelthatwould generate the correct force 3 not modulate proper volume and 4 result in thenon‐reciprocal polarized characteristicsrequiredforanelectricfield.Forexample,theremustbeaphysicaldifferencebetweenthepositiveelectric fielddirectionandthenegativeelectricfielddirection theoppositedirection .A gravitationalwave does not produce a net change in proper volume. An increase in onedimension is offset by a decrease in the orthogonal transverse dimension to keep the totalvolumeconstant.Iftherewasadetectablechangeinvolume,therewouldalsobeadetectablechangeintherateoftimeandthiswouldcreateconditionswheretherecanbeaviolationoftheconservationofmomentum seedipolewavediscussioninchapter4 .Anoscillatingelectricfieldmustmodulatedistancebetweenpointswithoutmodulatingpropervolume.Thewaythisis accomplished is even simpler than the mechanism used by a gravitational wave. In anoscillatingelectricfieldthedimensionalincreaseanddecreasehappensinonlyonedimension.Onepropagationdirectionexperiencestheincreasewhiletheoppositepropagationdimension


experiencesthedecrease.Theroundtrippropagationtime roundtripdistance isunchangedthereforethereisnochangeinpropervolume.Thisisthesimplestpossiblewaythatproducesanetpolarizationofthespacetimefieldwithoutalsoproducinganetchangeinvolumeoranetchangeintherateoftime.Thisproposedmodelofanelectricfieldwillbefurthersupportedinchapter10byacalculationwhichshowsthatthismodelproducesthecorrectelectrostaticforcebetweenrotarswithelementarychargee.Thecalculationcannotbepresentedherebecauseitrequirestheintroductionofadditionalconcepts.It is proposed that an electric field is an asymmetric distortion of the spatial dimension of the spacetime field parallel to the electric field direction. This results in a slight asymmetric distance between points propagating in the positive electric field direction compared to propagating in the negative electric field direction. There is neither a net volume change nor a rate of time change because the round trip time between the points is unchanged (except for the slight gravitational effect). The proposed model of an electric field implies that n photons in maximum confinementproduceaneffectonspacethatresultsinadistortionofΔL Lpoverdistanceλ.Thevectordistortion implies that if therotatingelectric is imaginedasbeingmomentarily frozen, therewould be a difference in the distance of ΔL Lp progressing from to – compared to

progressing in theoppositedirection – to . It is not knownwhichpolarizationdirectionproducesthelongerdistance,buthypotheticallythisisexperimentallymeasurable.Thisnon‐reciprocalpropertyseemsstrange,butanotherexampleofanon‐reciprocaleffectisaFaraday rotator. When a magnetic field is imposed on any transparent material, circularlypolarizedlightexperiencesadifferentpathlengthdependingonwhetheritispropagatingintheNorth magnetic direction compared to propagating in the South magnetic direction. ThisdifferenceinpathlengthbetweenthetwooppositedirectionscanbeexpressedasΔL/L.Italsocauses linearly polarized light to exhibit a different rotation direction when propagating inoppositedirections. Thiseffectiscommonlyusedtoformanopticalisolatorthatonlyallowslaserbeamstopropagateonedirection.ChargedParticles:SinceEMradiationhasanoscillationatfrequencyω,itiseasytoimaginethatthattheoscillatingelectricfield oscillatingdistortionofthespacetimefield producedbyEMradiationhasenergydensity.However,theelectricfieldproducedbyachargedparticleappearstobestaticandyetitalsopossessesenergydensity.Ofweinsertω 0intotheenergydensityequationU kA2ω2Z,weobtainthatthereshouldbenoenergydensityifthereisnooscillation.Yetweknowthattheelectricfieldproducedbychargedparticlesalsohasenergydensity.Itwillbe proposed in chapter 10 that all particles charged and neutral produce an oscillatingdisturbance in the surrounding volume of spacetime. This will be shown to be oscillatingstandingwavesat theparticle’sCompton frequency.Thesestandingwavesproducenotonly


particle’sdeBrogliewavesbutalso theyare required for theproductionof anon‐oscillatingportionoftheelectricfieldandalsogravitationaleffects.Electric Field Produced by Charged Particles:Earlierinthischapterwederivedtheelectricalpotential for Planck charge in dimensionless Planck units as: E pL r . When we assume

elementarychargee designatedwithsubscript“e” theequationbecomes:

ee

p

√

ThereforethevoltageexpressedindimensionlessPlanckunitsisadimensionlessnumberthatisdescribingtheslopeofthepolarizedstrainofspacetime.Aspreviouslyexplained,anelectricfield produces polarized spacetime where there is a difference in distance progressing inoppositedirections.ThedifferenceindistanceisdesignatedΔLsotheratioΔL/ΔrcanbethoughtofasatypeofslopedesignatingthedifferenceindistancebetweenoppositedirectionsΔLoverradiallinesegmentΔr.Forexample,wewillstartwithasingleradialvectorpointingawayfromachargedparticle.Wewilldesignatedistancesr1andr2alongthisradialvectorandspecifythatr2 r1.Thedistancebetweenr1andr2isslightlydifferentifatimeofflightdistancemeasurementis made progressing from r1 to r2 compared to progressing in the opposite direction. ThisdifferenceΔLproducedbyaparticlewithelementarychargee,isequalto:ΔL √ Lpln r2/r1 distortionproducedbytheelectron’schargebetweenr2andr1Forexample,ifr2 1meterandr1 10‐12meter,thenΔL √ Lp 27.6 3.26 10‐36m.Whilethisseemslikeaverysmallnetdistance,itmustberememberedthatthestrainisaffectingtheenormouslylargeenergydensity,impedanceandbulkmodulusofthespacetimefield.Lateritwillbeshownthatthistypeofpolarizedstrainofspacetimecanproducethemagnitudeoftheforceweexpectofanelectricfieldactingonanelectron rotar .Iftherearemultiplecharges,the strain produced by each elementary charge is a vectorwhich adds to the vector strainsproducedbyall theothercharges. Forexample, if therearea largenumberofelectrons neelectrons onachargedsphere,thenthevalueofΔLbecomes:ΔL √ Lpln r2/r1 .Thus farwe have dealt with the distortion produced by a spherical electric field such as isproduced by a single electron of a charged sphere. However, what about the distortion ofspacetimeproducedbyaparallelplatecapacitor?WewillassumeavacuumcapacitormadewithparallelplatesofdimensionsDxDandseparatedbydistanceD. This is an idealizedvacuumcapacitor which forms a cube. We will ignore the effects of fringing electric fields in thisexploratory discussion. The same way that expressing voltage electrical potential indimensionlessPlanckunits forasinglechargedparticlegavestrainΔL/r,soalsoexpressingthe voltage on a vacuum capacitorwith separation distance D gives the strain of spacetimeproducedbytheelectricfieldgeneratedbyavacuumcapacitor.


p

L

D

L D

Forexample,atimeofflightdistancemeasurementalongtheelectricfieldofavacuumcapacitormightbemadeifasmallholeisprovidedinthecenterofbothplates.Thepredictionisthatthetimeofflightdistanceproceedingfrompositivetonegativeshoulddifferby L D compared

toproceedingtheoppositedirection.However,thiswouldbehardtomeasure.Forexample,ifD 1mandvoltagewas1,000,000volts,thensince 2710p volts, ≈ 10-22 and ΔL ≈ 10-22 m.

This is much smaller than current interferometer technology can measure. However, there is also another problem which will be discussed later relating to whether light can ever be used to measure the ΔL effect. Comparison of Electric Fields: TheequationΔL Dforacubicvacuumcapacitorspecifiesthelengthdifferenceintermsof andD.Sinceanelectricfield /LandinthecaseofavacuumcapacitorL D,wecanalsoexpressΔLoverdistanceLinauniformelectricfieldas:

ΔL 2

p

L

Withphotonswewereable tospecifyΔL in termsof thenumberofphotonsnγ inmaximumconfinement ΔL Lp .NextwewillcalculateΔLinacubicvacuumcapacitorintermsofthenumberofelectronsneonthevacuumcapacitorwithdimensionsDxDxD.Thiscalculationwillmakeuseofthefollowingsubstitutions:

q/C, q = nee, C = kεoD2/D = kεoD, knee/εoD, p c /4πε G, Lp ħ ⁄ , ,

e α4 ħ , ne = numberofelectrons

L D = 4

4 4 44e o e o o

e pp o p o

n D c n cD Gn L

D c

L √ neLp Theaboveequationwillbeexpressedinwords.Thenon‐reciprocaldistortionofspacetimeΔLproducedacrossthewidthofacubicvacuumcapacitor D isequalto1.38 10‐36metersperelectron.Thisholdsforallsizecubicvacuumcapacitors allvaluesofD . Convertingelementarychargeetocoulomb,thestrainofspacetimeproducedbyacoulombofchargeonacubicvacuumcapacitoris:


ΔL/q = √ /e = 8.62×10-18 meters/coulomb η thechargeconversionconstant

Thereforeoneofthephysicalinterpretationsofthechargeconversionconstantηisthatthisisthe distortion of spacetime produced over the width D of a cubic vacuum capacitor by acoulombofcharge.

Previously itwascalculated ΔL Lp forn photons in themaximumconfinementcavity

approximatelyofvolumeλ3.NowwehaveΔL √ neLp foravacuumcapacitorwithdimensionsDxDxD ignoringnumerical factorsnear1 .Theelectric fielddistortionproducedbyphotonsandelectricchargebecomeverysimilarifwehavesimilarsize(λ ≈ D). Thecalculationisnotshownhere,butanelectricfieldgeneratedbyphotonsproducesthesamepolarizeddistortionofspacetime ΔL asanequalelectricfieldstrengthproducedbychargedparticlesonavacuumcapacitor. Inotherwords, 2

pL L holds for electric fields generated by either photons or

electrons. Thephotonfieldisoscillatingandhasanassociatedmagneticfield,sotherearealsodifferencesinthevalueofkwhichisbeingignored.However,thepointisthateventhoughthephotonequationscaleswiththesquarerootofthenumberofphotons andthecapacitor

equationscaleswiththenumberofelectronsne nosquareroot ,stillwhentheeffectisreducedtoelectricfieldofequalstrengthinequalvolumes,thevaluesofΔLarethesame ignoringk . ExperimentsUsingLight: Inearlierversionsofthisbookandinanearliertechnicalpaper,Idiscussed possible experiments using light in an attempt to measure the predicted non‐reciprocal path length difference between opposite propagating directions. However, now Idoubt that light canmeasure this effect. The doubt has nothing to dowith the fact that allpracticalexperimentsproduceavalueofnon‐reciprocallengthchangeΔLintherangeof10‐20to10‐18m.Thebestinterferometerscurrentlycanseeamodulatedlengthchangeontheorderof10‐18m.Therefore,iftheeffectsweremeasurablebyinterferometers,theywouldbenearthedetectable limit. However, the real problem is that it now appears as if the light from aninterferometerwillnotbeabletoseeanyvalueofΔLproducedbyanelectricfieldnomatterthemagnitude.Theproblemhastodowiththewaythatlightpropagatesthroughspacetime.BeforeIexplaintheproblem,Iwanttogivesomehistoryabouttheunderstandingoflight.In the late1600’soneof thebiggestmysteriesof sciencewasdouble refraction. When lightpassesthroughacrystalknownasIcelandspar acrystalofCaCO3 ,thelightisbrokenintotwobeamsanddoubleimagesappear.IsaacNewtonproposedacorpusculartheoryoflightbuthiscorpusculartheorycouldnotexplaindoublerefraction.In1690,ChristianHuygensproposedawave‐basedtheoryoflight.Huygensalsoderivedapartialexplanationofdoublerefraction.TheHuygensPrincipleconsiderseachpointonawavefronttobethesourceofanewwave.Huygensrealizedthatifthevelocityoflightvariedwiththedirectioninthecrustal,thenthesphereswoulddeformintoellipsoidsandbeabletopartiallyexplaindoublerefractionofIcelandspar.Eventhoughhisexplanationcouldbereducedtoanequationwhichcorrespondedtoexperiment,the


explanationdidnotgiveconceptualunderstandingofthefundamentaldifferencebetweenthetwo beams. He, and everyone else for the next 100 years, assumed that light waves werelongitudinalwaveslikesoundwavesinair.Theproblemwasthatlongitudinalwavescouldnotexplaindoublerefraction.Thepuzzleofdoublerefractionwassoiconic,thatin1807theFrenchInstituteofferedacashprize to anyone who could explain this phenomena. The prize was initially awarded to aFrenchman,EtienneMalus,in1810andasecondcashprizewasawardedtoaFrenchwoman,Sophie Germain, in 1816. However, these were only partial solutions. Themost importantinsightwasmadebyThomasYoungseveralyearslaterwhenheshowedthatlightisatransversewave. Thetransversewavesofunpolarized lightwerebeingsplit intotwoorthogonal linearpolarizationsbythecrystal. Thisgaveanexplanationofdoublerefractionoflightwhichwasbothconceptuallyunderstandableandmathematically rigorous.However,ThomasYoung,anEnglishman,wasnotawardedathirdcashprizebytheFrenchInstitute.Thisstoryaboutdoublerefractionandpolarizedlightistoldtopreparethereaderforamorecomplexmodelofthedistortionofspacetimeproducedbyaphoton.InearlierdraftsofthisbookIproposedthatthedistortionofspacetimecouldbemeasuredbyaninterferometerwherethetwo beams propagate in opposite directions across the rotating electric field produced bymicrowaveradiation inamaximumconfinementcavity. One laserbeamwouldexperienceadecreaseinpathlengthwhiletheoppositepropagationbeamwouldexperienceanincreaseinpathlength.Ahalfcyclelatertherotatingmicrowaveelectricfieldwouldhavereversedpolarity.IftheintensityoftherotatingEMradiation probablymicrowaves couldbemadehighenough,themodulatedpathlengthmightbedetectableasanintensitymodulationwhenthetwolaserbeamsarecomparedinaninterferometer.The problemwith this experiment is that it does not properly address the transversewavestructure of light. As previously stated, a photon is not a packet of energy that propagateslinearly through the empty voidof spacetime. Instead, aphoton is a transversewave that isinteractingwith thepropertiesof spacetime transverse to thedirectionofpropagation. Thespeedoflightforlinearlypolarizedlightissetbythespeedofwavepropagationintheplaneofpolarization.Therefore,lightcannotbeusedtoaccuratelymeasuredistanceinthedirectionofpropagationifthemediumbeingprobedisnothomogeneous.Thistransversewavepropertycreatesaproblemforanyexperiment thatattempts touse light tomeasure thedistortionofspacetimeproducedbyanelectricfield.When light propagates through homogeneous glass, it has a speed of light less than 1. Therelative permittivity ε of the glass and the index of refraction are both homogeneous in alldirections.However,supposethattheglassisstressedbyauniformcompressionalongwhatwewillconsidertobetheZaxisoftheglass.ThepermittivityεintheZdirectionbecomesdifferentthanthepermittivitymeasuredintheXandYaxis.Linearlypolarizedlightwithitselectricfield


vectoralongtheZaxispropagatesthroughtheglassatadifferentspeedthanlightofthesamewavelengthbutpolarizedalonganyorthogonaldirection.Whenlightispropagatingthroughauniformmedium,thenwecanignorethetransversewavenatureoflight.However,whenthemediumisnotuniforminalldirections,wehavetobecarefulabouttheactualmechanicsofwavepropagationthroughthemediumwhenattemptingtomakeadistancemeasurement.Normally,thevacuumisconsideredtobeperfectlyhomogeneous.However,theproposalisthatboth gravitationalwaves and electric fields distort the vacuum spacetime so that it is nothomogeneousinalldirections.Theinhomogeneityisextremelysmall,butweareattemptingtodeviseexperimentstomeasurethiseffect.Therefore,theexperimentisspecificallydesignedtoenhance the inhomogeneity to ameasurable level. However, there is aproblem thatwill beillustratedwithanexample.Supposethatavacuumcapacitorcontainstwosmallholesinthemiddleofeachflatplateofthecapacitor.Sendingalaserbeamthroughtheholeswouldhavethelaserbeampropagatingonewayalongtheelectricfieldofthecapacitor.Thepredictionisthatthe distance along the electric field should be different for a “time of flight measurement”proceeding in the two opposite directions positive to negative compared to negative topositive .However, the speed of propagation of the laser beam is determined by the properties ofspacetimeperpendiculartothepropagationdirection.Evenwithanextremelystrongelectricfield,itshouldbeimpossibleforabeamofEMradiationtomeasureanyeffect.Evenifthebeamdirectionischangedsothatitpropagatesperpendiculartotheelectricfieldwiththepolarizationdirectionparalleltotheprobedelectricfield,therestillshouldbealmostnodetectableeffect.Recall that the round tripdistance in anelectric field shouldbeunchanged compared to theroundtripdistancewithnoelectricfield.TheEMradiationhasanoscillating reversing electricfieldsoitisprobingtheroundtrippropertiesofspacetime.Onecompletecycleoftheoscillatingelectric fieldshouldproducenofirstordereffect. Therewouldbeaverysmallsecondordernonlineareffectassociatedwith thegravityproducedby theelectric field,but thatwouldbevastlysmallerthanthefirstordereffect.Itwouldalsobesymmetrical.ThereisanotherhypotheticalwaytoprobethedistortionofspacetimeproducedbyanelectricfieldthatgetsaroundtoproblemsofEMradiationbuthasitsownpracticalproblems.Supposethataneutralparticlesuchasaneutronorneutrinocouldbesentalongtheelectricfield.Ifthespeedwasaccuratelyknown,thendistancecouldtheoreticallybemeasuredbyatimeofflightmeasurement. This is not subject to the transverse wave problems of light and it shouldhypothetically give the oneway distance. The obvious problem is that neutron or neutrinobeamsarecompletelyimpracticaltoexperimentallymeasuredistanceaccurately.Implied Maximum Energy Density for Photons: Even though experimental verificationappears impractical, there are other ways of checking the validity of the predictions. Thefollowingcalculationstestthemodelatthehighestenergydensity.WhenIfirstdevelopedthe


equations for the distortion of the spacetime field produced by electromagnetic radiation, Iquickly realized that therewas an implied limit. The finite properties of the spacetime fieldimpliedthatthereshouldbeamaximumintensitylimitforEMradiation.ThislimitissetbecauseEMradiationproducesadistortionofthespacetimefieldwhichhasfiniteproperties.Itshouldbeimpossibletoexceed100%distortionofanyportionofthespacetimefield if themodel iscorrect.Initially,thispredictionwascounterintuitiveandappearedtoberevealingaflawinthemodel.Thisimpliedlimitwillbeexplainedusingthemaximumconfinementcavitybutitapplieseventoalaserbeamfocusedinavacuum.Forexample,theequationΔL appliestoacavity

ofvolumeλ3.ThisequationimpliesthatthereisamaximumpossiblevalueofΔLthatcanbeachieve.WhenΔL λ,thenthedistortionΔLequalsthesize λ ofthemaximumconfinementcavity ignoringnumericalfactorsnear1 .Thereforeifthemodelofthedistortionofspacetimeproduced by the electric field generated by photonswas correct, it should be impossible toexceed the condition where ΔL λ in a volume of λ3 because this would require 100%modulationofthepropertiesofthespacetimefieldwithinthisvolume.As you probably have guessed, experimentally testing this prediction would require a peakpower that is totally beyond human capability. For example, suppose that we attempted toexceedthe100%modulationofspacetimelimitusingapulsedlaserwithawavelengthof10‐6m1micron . Ifweassumeapulselength1wavelengthlong 3 10‐15spulsehasalengthof1micron andthebeamfocusedtoaspot1wavelengthindiameter,thenthevolumeofthefocusedpulsewould be about 1micron in diameter. To exceed the ability of the spacetime field totransmit thisradiation, thepeakpower inthepulsewouldhavetobeabout1053watts. Theenergy in the 3 10‐15 s pulsewould have to be about 1038 Joules to reach this theoreticaltransmission limit for a 1 micron diameter volume. To put this energy requirement inperspective,thisrequiredenergyisequivalenttotheannihilationenergyofabout1021kgwhichisaboutthemassofalltheoceansonearth.Anexperimentisobviouslynotpossible,butitisquiteeasytocheckthispredictiontheoretically.We will return to the maximum confinement resonator previously described which had adiameterof½wavelengthandalengthof½wavelength.Sincetheenergydensityinsideisnotuniform and maximum near the center, we loosely defined this volume as λ3 by ignoringnumerical factors near 1. For this condition, we previously determined the displacementamplitudeΔLas:ΔL Lp.wherenγequalsthenumberofphotonsintheresonator.Wewillnowdesignate nc as the critical number of photons at frequencyω required to theoreticallyachieve100%modulationatwavelengthλ.ThisconditionoccursatΔL λ.Thiscriticalnumberofphotons involumeλ3hasacriticalamountofenergyofEc. Thereforewewillanalyze thecriticalenergyEcinvolumeλ3toseeifthereisanyobviousreasonpreventingelectromagneticradiation from exceeding the implied limit that would achieve 100% modulation achieveΔL λ.


nc ħ

ħsetΔL2 ncLp2

ΔL2 ncLp2 ħ

ħsetΔL λ

λ RswhereRs≡Gm/c2theSchwarzschildradiusforenergyof

Thisisafantasticresult!Itisnotnecessarytodoanexperimenttoprovethatthispredictioniscorrect. The intensity energy density that would achieve 100%modulation of spacetimewouldalsomakeablackhole!Themaximumconfinementresonatorcanbeconsideredtohavearadiusequaltoλ.Forthecriticalcondition,λ Rs,whereRs≡Gm/c2 isthepreviouslydefinedSchwarzschildradiusofablackhole.Therefore,itisindeedimpossibletoexceedtheimpliedlimitthatwouldachieve100%modulationofspacetimebecausethisistheconditionthatcreatesablackhole.Ifmoreenergythanthetransmissionlimitwasprovided,theenergydensitywouldformablackholewhichwouldblocktransmissionthroughthevolume.Whilethecalculationassumedamaximumconfinementcavity,thissamelimitwouldapplyifthelaserbeamachievedthissizeandenergydensitybymerelybeingfocusedinavacuum.Thissuccessfultesthasseveralprofoundimplications.

1 Theproposedquantummechanicalmodelofspacetime dipolewavesinthespacetimefield isstronglysupported.

2 The concept that EM radiation is awave propagating in themedium of spacetime issupported.

3 Thedisplacementamplitudeofn photonsin“maximumconfinement”is:ΔL Lp4 Theconditionthatcreatesablackholecannowbeunderstoodmorecompletelythan

merelydiscussingvaguetermssuchas“curvedspacetime”.Nowtheinternalworkingsofspacetimethatcreatescurvedspacetimecanbequantified.

We cannot exceed the intensity that would demand more than 100% modulation of thespacetimefield.ThisfieldhasallfrequenciesuptoPlanckfrequencyandatotalenergydensityofabout10113J/m3.However,itisnotnecessarytoexceed10113J/m3toachieveablackhole.ThatistheintensityrequiredtoachieveablackholewithwavelengthequaltoPlancklength.Toachieveablackholeusing1micronlight,itisonlynecessarytoachieve100%modulationoftheportionofthespacetimefieldwithfrequencyofabout3 1014Hzinavolumeabout1micronindiameter thisexampleignoresnumericalfactorsnear1 .MaximumVoltageonaVacuumCapacitor:Thereisanotherpredictionthatwilltesttheproposedmodelofthedistortionofspacetimeproducedbyanelectricfield.Inthecaseofthecubicvacuumcapacitorcalculatedearlier,wegeneratedtheequationΔL D foravacuumcapacitorwithdimensionsDxDxD. In otherwords, the distance between the parallel plates of the vacuumcapacitorisD.ThereforethemaximumdistortionofthespacetimefieldoccurwhenΔL D.Thiswould also be 100% distortion of the properties of the spacetime field within the vacuum


capacitorvolume DxDxD .Thisconditionisreachedwhen 1.Sincethedefinitionof is:p ,itshouldbeimpossibletoexceedtheconditionwherethevoltageonthecubicvacuum

capacitorequalsPlanckvoltage p becauseatthisvoltage 1.Thislimitseemsstrange

becausethisfixedmaximumvoltageappliestoanysizecubicvacuumcapacitor.Therefore,thereisnotamaximumelectricfieldbutamaximumvoltage.WewillcalculatetheenergycontainedinacubicvacuumcapacitorwhenitischargedtoPlanckvoltage.Substitutionstobeused: p c /4πε G, E = kC 2,C = kεoD2/D = kεoD where:C capacitance

E = kC p2 kεoD)

D Rs

ThereforetheequationD Rssaysthattheconditionwhichachieves100%modulationofthepropertiesofspacetimewithinthevacuumcapacitoralsoformsablackholewithradiusRs.ItisimpossibletoexceedPlanckvoltageonacubicvacuumcapacitorbecausethisrequiresenergywhichwouldformablackhole. Thisstatementignoresnumericalfactorsnear1andignoresfringingoftheelectricfieldaroundtheedgesoftheplates. Again,thisanalysisofthemaximumvoltage on any size vacuum capacitor is revealing something about the mechanics of theformationofablackholebeyondthestandardgravitationalexplanations.GravitationalWaveDetection:Wearegoingtopausefromthediscussionofelectricfieldsandbriefly examine the implications for the detection of gravitational waves. For review, agravitationalwaveisatransversewavethatpropagatesthroughthespacetimefieldatthespeedof light. It causes a spherical volume of spacetime to become an oscillating ellipsoid. If thegravitationalwavepropagatesintheZaxisdirection,theellipticalelongationandcontractionwill occurperpendicular to theZ axis. We candefine theXandYaxis to correspond to thetransversedirectionsofmaximumoscillation.ThereisnoeffectontherateoftimeandnochangeinpropervolumebecauseanexpansionoftheXaxisisoffsetbyacontractionoftheYaxisandviceversa.TheLIGOexperimentwillbeusedasanexampleofexperimentsaroundtheworldcurrentlyattempting to detect gravitational waves. This experiment is a power recycled Michelsoninterferometer. Massive mirrors suspended by wires are located at each of the corners ofL‐shapedevacuatedtubeswhichare4kmlong.Supposethatalargegravitationalwavepasseswithpropertieswouldproduce themaximumdifference inpath lengthbetween themirrors.What isphysicallyhappening? Is therea forceexertedon themirrorscausing themirrors tophysicallymove accelerateanddecelerate ?Alternatively,doesthechangeintheseparationdistanceresultfromachangeinthepropertiesofthespacetimefieldwithnoforceexertedonthemirrors noaccelerationanddecelerationofthemirrors ?


Thissecondalternativeisproposedtobecorrect.Thepropertiesofspacetimechangeinwaythataffectsthesizeofrotars,atoms,etc.Thiswouldmakephysicalobjectssuchasmetersticksandtapemeasuredchangetheirsize.Thedistancebetweenthemirrorswouldchangeaccordingtophysicalmeasurements,buttherewouldbenophysicalmotionofthemirrors.Therewouldbenoforce,andnoaccelerationofthemirrors.Herearetworeasonsforbelievingthis.

1 Supposethatoneofthetwomirrorshadvastmass,equivalenttothemassdensityofaneutronstar.Theforcethatmustbeexertedtoachievetherequiredphysicalmotionofthismirrorwouldalsohavetobevast.Yetthereisnooffsettingmassacceleratingintheoppositedirectionrequiredtoachievetheconservationofmomentum.Assumingthatthemirrorsphysicallymoveisaviolationoftheconservationofmomentum.

2 Agravitationalwavedoesnotaffecttherateoftime.Ifagravitationalwaveachievestheaccelerationofmatterusinggravity,thegravitationalwavewouldhavetoaffecttherateoftimeandpossessarateoftimegradient.Asdiscussedinchapter2,allgravitationalaccelerationimpliesarateoftimegradient.Sinceagravitationalwavedoesnotexertagravitationalforce,isthereanyotherforcewhichmightacceleratethemirrors?

Therefore, a gravitational wave affects the spatial properties of two of the three spatialdimensions.Thereisnoeffectonpropervolumebutthethreeorthogonaldirections X,YandZaxis ofthespacetimefieldhavereceiveddifferentdistortions.Nowthequestionis:whateffectdoesthisspatialchangehaveonEMradiation?Ifyouthinkofaphotonasbeingabullet‐likepacket of energy, then only one dimension the propagation direction is being probed anddistanceasmeasuredbytimeofflightofphotonsinthatonedimensionshouldagreewiththemeterstickmeasurement.However,ifthemodelofphotonsisatransversewavepropagatingin themedium of the spacetime field, then it is not obviouswhat effect the two transversedimensionsmightexertonthedistancemeasurement.Toexplorethisquestion,wewilltemporarilyshiftfromagravitationalwaveaffectingspacetimetoagravitationalwaveaffectingatransparentcubemadeofahomogeneousmaterialsuchasglass.ThefacesofthecubearealignedwiththeX,YandXaxispreviouslydefined.Agravitationalwave passing through this transparent cube will cause the cube to become an oscillatingrectangle which exhibits both modulated birefringence and a modulation of the relativepermeabilityε.Themodulatedbirefringenceandmodulatedpermittivityinglasswouldcauseasinglebeamofcircularlypolarizedlightpropagatinginanydirectionintheglasscubetobecomeanoscillatingellipticalpolarizedbeamoflight.ThebiggesteffectonpolarizationofcircularlypolarizedlightwouldbeforthebeampropagatingalongtheZaxis.Thisisthedirectionthatdoesnotexperienceanychangeinthetimeofflightpathlength.However,sincelightisatransversewave,changesinεoorthespeedoflightforlightpolarizedintheXandYdirectionsconvertcircularlypolarizedlightpropagatingintheZdirectionintooscillatingellipticallypolarizedlight.IfweconsiderthespacetimefieldtobeamediuminwhichEMradiationpropagates,thenitshouldreacttothe


passageofagravitationalwavesimilartothewaythatatransparenthomogeneousmaterialsuchasglasswouldreact.Inparticular,thepropagationspeed inverseindexofrefraction dependsonthepolarizationdirection,notthedirectionofpropagation.Thereissomeuncertaintyinthis,butifgravitationalwavesturnthespacetimefieldintoanoscillatingbirefringentmaterial,thentherewouldbesimplerandmoresensitivewaysofdetectinggravitationalwaves.Presently,thebiggestsourceofnoiseusinginterferometersistheseismicnoise.Interferometersare attempting to detect very small difference in optical path length between the two arms.Anything that produces even a very small vibration is a source of noise. Even the photonpressureofthelightmakingthemeasurementisasourceofnoise.Ifthespacetimefieldbecomesabirefringentmedium,thenitwouldbepossibletodetectgravitationalwaveswithoutusinganinterferometer. Forexample,circularlypolarized lightpropagating in theZdirection,shouldencounterabirefringence differenceinε intheXandYdirections.Thiswouldcauseevenasingle beamof circularly polarized light to become an oscillating ellipsoid of polarized light.Otherexperimentscanalsobedevisedbutthepointisthatitismucheasiertodetectchangesinasinglepolarizedbeamthanchangesinthepathlengthoftwobeamspropagatingintwowidelyseparatedarmsofaninterferometer.Also,thisproposedbirefringencecanalsocreateproblemsforinterferometers.Ifthetwobeamsofaninterferometerhavethesamepolarizationdirection,thenthiswouldcausethesamepathlengthchangetooccurinbotharmsoftheinterferometer.Eveniftherewasalargesignal,botharms would experience the same path length change. The interferometer would detect nodifferenceinpathlengthandtherewouldbenosignal.

MagneticFieldAnalysisComparison between Electric and Magnetic Fields:Whatistheeffectonspacetimeproducedbyamagneticfield?Weknowthatanelectricfieldandamagneticfieldareintimatelyconnectedbythespeedoflight c .Amagneticfieldinoneframeofreferencecanappeartobeanelectricfieldandmagneticfieldinanotherframeofreference.Therearetwocommonwaysofproducingamagneticfield1 anelectriccurrentinawireand2 themagnetic field associatedwith the spin of subatomic particles. There is a very goodexplanationofamagneticfieldgeneratedbycurrentinawire.ThisexplanationbyEdLowry1isbasedonthespecialrelativitytransformationofanelectricfield.Whencurrentflowsinawire,the negatively charged electrons in the wire are moving relative to the positively charged

1 http://users.rcn.com/eslowry/elmag.htm


protonsinthewire.Therefore,thepositiveandnegativechargesinthewireareintwodifferentaverageframesofreference.Whenanexternalelectronmovesparalleltothewire,italsoisinadifferentframeofreference. Themovingelectronexperiencesatransverseelectric fieldthatexertsa transverse forceon theelectron. This forcewillbe towards thewire if theexternalelectronismovinginthesamedirectionastheelectronsinthewire.Theforcewillbeawayfromthewireifthemovementsareinoppositedirections.Whilethisexplanationgivesimportantinsights,itdoesnotexplainthedistortionofspacetimeproducedbyamagneticfield.Theforceontheexternalelectronincreaseswithrelativespeed.Whentheelectronistravelingnear the speedof light, theenergydensity of themagnetic fieldhasbeenalmost completelytransformed into a transverse electric field. A photon is propagating at the speed of light,thereforeifitispropagatinginatransversemagneticfieldthephotonexperiencesatransverseelectricfield.Thedirectionoftheelectricfieldis90°relativetothetransversemagneticfield.Whateffectwouldthishaveonaphoton?Unfortunately,atransverseelectricfieldproducesasubtle effect. A transverse electric field is polarized spacetime exhibiting the asymmetrypreviouslydiscussed. Thetransversedirectionoftheasymmetrywouldproducenoeffectondistanceandnoeffectonthepolarizationof the light. Instead, Iproposethat theonlyeffectwouldbethatthedirectionofpropagationofthelightwouldnotbepreciselyperpendiculartothewavefront.Aconvergingbeamoflaserlightwouldcometoafocusatonespotwhenthereisno transversemagnetic fieldand focusataslightlydifferentspotwhen there isa transversemagneticfield.Inatypicalexperimentthesespotswouldoverlaptoadegreethatitwouldnotbepossibletomeasurethedifference.Thesignaltonoiseratiowouldbetoolow.An Electron’s Magnetic Field:Thespinofanelectronproducesamagneticfieldthatisalignedwiththespinaxis. Therefore,perhapsitispossibletoobtainaninsightintothedistortionofspacetimeproducedbyastaticmagneticfieldbylookingattherotarmodelofanelectron.Sinceamagneticfieldiscloselyrelatedtoanelectricfield,amagneticfieldmustalsobeassociatedwithastrainofthelengthdimensionswithnodistortionoftherateoftimeandnochangeintotalvolume.Anelectronismostwell‐knownforitselectricfield,butthespinoftheelectronalsoproducesamagnetic field. Theenergydensityofanelectron’smagnetic fielddecreasesmore quickly with distance than the electron’s electric field. Therefore the electric fielddominateswhendistancerismuchgreaterthananelectron’srotarradius .However,whenr ,theelectron’smagneticfieldshouldhaveacomparableenergydensitytotheelectron’selectricfield.We will begin the quest to deduce the spacetimemodel of a magnetic field by doing someplausibilitycalculationstoseeiftherotarmodelofanelectroncangiveplausibleagreementwiththemagneticpropertiesofanelectron.Iftheuniverseisonlyspacetime,thenamagneticfieldmust be a distortion of the spacetime field. We are going to attempt tomake a connectionbetweenanelectricalcurrentflowingaroundaloopofwireandtherotarmodelofafundamentalparticle.Weknowthatacurrentflowingaroundaloopofwireproducesamagneticfield.Ifthe


properconnectionismade,thenweshouldbeabletoseehowtherotatingdipolewaveoftherotarmodelproducesanelectron’smagneticfield.Therotarmodelofafundamentalparticlehasadipolewaveinthespacetimefieldchaoticallypropagatingatthespeedoflightaroundavolumeofspace.Thisvolumecanbemathematicallyapproximated by the rotar model with a circumference equal to the particle’s Comptonwavelength.Thereforetheradiusofthisvolumeisequalto .Eventhoughthepropagationischaotic,thereisadefinableexpectationrotationdirectionandrotationaxis.Supposethatwetestthepostulatethatthemagneticfieldproducedbyanelectronisequivalenttoapointparticlewithchargeepropagatingatthespeedoflightaroundaloopwithradiusequaltotherotar’srotarradius . Thisradiushasacircumferenceequaltotherotar’sComptonwavelengthλc.Sincethepropagationspeedequalsthespeedoflight,therotationfrequencyaroundtheloopwouldbeequaltotheparticle’sComptonfrequencyνc ωc/2π.Wewillassumeafixedaxisofrotationratherthanthechaoticaxisofthedipolewave.Withtheseassumptions,itispossibletodeterminetheelectron’scirculatingcurrent designatedIe thatwouldbeflowingaroundthishypotheticalloop.Wewillassumetheconstantsassociatedwithanelectron.Therefore 3.86 10‐13mandanelectron’sComptonfrequencyisequalto:νc c/λc 1.23 1020Hz.Theelectron’sequivalentcirculatingcurrent symbolIe issimplyelementary charge e 1.602 10‐19 Coulomb times the electron’s Compton frequencyνc 1.236 1020Hz.e eνc 19.796amps e electron’sequivalentcirculatingcurrent~19.8ampsWecanchecktoseeifthiscurrentproducesthecorrectmagneticeffectsifweimaginealoopofwirewithradiusequaltoanelectron’srotarradius .Specifically,wewillseeifthiscurrentinthissize loopofwirewouldproducethesamemagneticmomentasanelectron beforeQEDinteractions . Themagneticmomentμmofaloopofwirewitharea πr2andcurrent is:μm .Tosimulateanelectron,wewilluse: π and c eνc.μm π c π 3.8616 10‐13m 2 19.796amp 9.274 10‐24J/TeslaThis is a successful test because 9.274 10‐24 J/Tesla equals an electron’s Bohr magneton

μB eħ/2me 9.274 10‐24 J/Tesla. A more rigorous calculation not shown here

incorporating ,e,νcetc.showsthattherotarmodelofanelectrongivesμB eħ/2me.Theterm“Bohr magneton” is used to express a simplified version of an electron’s magnetic dipolemoment.Theexperimentallymeasuredvalueofanelectron’sdipolemomentdiffersfromthisBohrmagnetronnumberbyabout0.1%.ThissmallcorrectionfactorobtainedfromQED theanomalousmagneticmoment will not bediscussed further because the objective here is todevelop a spacetime basedmodel of amagnetic field. To achieve this goal,wewill test thepostulatethattherotarmodelofanelectron onaxis producesthesamemagneticfieldasif


therewasapointparticlewithchargeepropagatingatthespeedof lightaroundaloopwithradiusequaltotheelectron’srotarradius .Fromthispostulate,theelectron’smagneticfieldcalculatedfrom cand willbedesignated e.Theequationforthemagneticfieldatthecenterofasinglecircularloopofwirewithradiusrandcurrentis:

μo /2rset candr foranelectron 3.86 10‐13m e 3.22 107Tesla e electron’sequivalentmagneticfield

Thislargemagneticfieldwouldhaveenergydensityof3.22 1022J/m3.Totestthepostulate,wemustaskthequestion:Isthisreasonable?Howdoestheimpliedenergyinthemagneticfieldcompare to the energy in the electron’s electric field external to the electron’s rotar volumeexternalto ?Thecalculationisnotshownhere,buttheenergyintheelectricfieldexternaltoanelectron’sradius is ½ αEi 3 10‐16J.Wewanttotestwhetherthelargemagneticfieldof3.22 107Teslaisreasonablebymakingacomparisontotheenergyintheelectron’sexternalelectricfield.Wewillmaketheassumptionthatthemagneticfieldfillsavolumeequaltotheelectron’srotarvolume Vr 4π/3 2.41 10‐37m3 .Italsoproducesanexternalmagneticfield,sothisestimateshouldbelow.Istheenergyintheelectron’sexternalelectricfield ~3 10‐16J comparableto,butmorethan,theenergyina3.22 107Teslamagneticfieldfillingtheelectron’srotarvolume?E UVr B2/2μo 4π/3 10‐16JenergyinthecalculatedmagneticfieldinvolumeVrThereforethissimplecalculationshowsthatamagneticfieldof3.22 107Teslaisreasonable.Wecanalsoperformamoreexacttest.Recallthatforanyfundamentalrotarsuchasanelectron,theslopeofthestraincurveatarbitrarydistancewasalwaysimpliedaspatialdisplacementatthecenterofanelectronof√ Lpwhichis1.38 10‐36m.Outofcuriosity,wewilllookattheimpliedΔL fora3.22 107Teslamagnetic fieldoveradistanceequal to theelectron’srotarradius 3.86 10‐13m.EventhoughwehavenotyetproposedthephysicalinterpretationofΔLproducedbyamagneticfield,itisstillpossibletocalculatethemagnitudeofΔLforthismagneticfieldof3.22 107Teslaoveradistanceequalto .ForauniformelectricfieldoverdistanceL,wepreviouslyhadΔL 2

pL which converts to 2L L (note underlines implying

dimensionless Planck units). NowwewillreplaceLwith ,whichistheradiusoftherotarmodelofafundamentalparticle.Wewillnotproveithere,butaLorentztransformationofanelectricfield expressed in dimensionlessPlanckunits / p canbe considered equivalent to amagnetic field expressed in dimensionless Planck units / p . In this equation p isPlanckmagnetic fieldwhich is p Zs/qp 2.15 1053 Tesla. Thismeans that, ignoringnumericalfactorsnear1,itisreasonabletoconvert 2L L to 2

cL whenwearedealingwithafundamentalparticlewithradius .

2cL dimensionless Planck units

ΔL = / pLpconvertedfromdimensionlessPlanckunitstoSIunitsSet 3.22 107Tesla, p 2.15 1053Tesla,Lp 1.6 10‐35m, 3.86 10‐13m


ΔL ≈ 1.38 × 10-36 m ≈ √ LpAmoregeneralcalculation notusingnumbers canbemadeanditgivesthesameanswerthatΔL = √ Lp.Therefore,thisisasuccessfulplausibilitycalculationontwofronts.First,itsaysthatthecalculatedmagneticfieldproducesthesamemagnitudeofΔLoverthesamedistance astheelectricfieldfortherotarmodelofanelectron.However,thephysicalinterpretationofΔLisdifferentforamagneticfieldthanforanelectricfield.Secondly,itgivesaddedassurancethatwecanlooktotherotarmodelofanelectrontounderstandthedistortionofthespacetimefieldthatproducesamagneticfield.Aspreviouslyexplained,therotationofanelectron’sextremelysmalldistortionofthespacetimefield ischaoticbecause it isat the limitofcausality. However foranalysis,wecan imagineastabilizedelectronrotationwithafixedaxisofrotation.Proceedingalongthisaxisofrotation,wewouldexperiencethedistortionofthespacetimefieldthatisproducingamagneticfieldofabout3 107Tesla. This is a very strongmagnetic field compared to anything that canbegeneratedbyman.However,itisalsoveryweakcomparedtoPlanckmagneticfieldofabout1053 Tesla. What is different about this rotar volume compared to a typical volume of thespacetimefieldthatisnotinsideanelectronanddoesnothaveamagneticfield?The“typical”volumeofthespacetimefieldcontainschaoticdipolewaveswithPlanckenergydensity about10113J/m3 ,butthedipolewavedistortionaveragesouttobeingashomogeneousasquantummechanicsallows Theobviousdifferenceisthattheelectron’saxialvolumealsocontainsanorganized spatial and temporal distortion of the spacetime field that has a small rotatingcomponentwithstrainamplitudeequaltoAβ 4.2 10‐23.Forreview,seefigures5‐1and5‐2from chapter 5. This would produce a rotational path length difference that is difficult toarticulate.Recallthatanelectricfieldisproposedtobea distortion of one spatial dimension of the spacetime field (parallel to the electric field direction) that results in a slight asymmetric distance proceeding in opposite propagation directions. The round trip distance is unchanged. A magnetic field is similar except that the plane transverse to the magnetic field has a rotational distance asymmetry. The time required for a particle with known speed to proceed around the circumference of a circle proceeding clockwise in this plane would be slightly different than the time required to proceed counterclockwise. Since light is a transverse wave, it is not accurate to imply that a pulse of light propagating around a circle would be able to measure this subtle effect. Therefore terms like “speed of light” would be misleading. However, since light is a transverse wave, the implication is that a total vacuum should exhibit a Faraday effect for light propagating parallel to the magnetic field direction. Ifaphotonwasabullet‐likeenergypacket,thenwewouldnotexpectanyeffectifitpropagatesthroughavolumeof space that is experiencing a rotational asymmetry of the spacetime field. However, atransverse wave propagating through a rotationally strained volume of spacetime would


experience a polarization effect. Linearly polarized light propagating along amagnetic fieldshouldexperienceaslightrotationoftheplaneofpolarization.Circularlypolarizedlightwouldexperienceapathlengthchange.ThevalueΔLcanbethoughtofasthedifferenceinpathlengthexhibitedbyoppositecircularpolarizationspropagatinginamediumwithamagneticfield.ThisisessentiallyapredictionthatacompletevacuumcontainingamagneticfieldshouldexhibitaFaradayeffect. Themagnitudeoftheeffectisdifficulttopredictsinceitisnotclearhowtotreatthetransversesizeofaphotonpropagatingalongthemagneticfield.Ifitispossibletomakeananalogytoanelectricfield,thenhereisoneattemptatacalculation. ThemagnitudeofΔLcanperhapsbecalculated from 2

cL which converts to 2 2 2p pL L L L when we set L . Also

p 2.15 1053TeslaandLp 1.6 10‐35m.

2

2p p p

L L

L L

2

53 352 10 1.6 10

LL

tesla meter

= 3x10-19 L2meter

Thereisaspecialwaythatthelengthtermmustbecalculatedexplainedintheanalogouselectricfield experiment calculation. Without going into the details, the experiment is marginallydetectable ΔL 10‐18or10‐19m forsomehypotheticalvalues.Therearesomepossibleeffectswhichmight hide the proposed vacuumeffect. For example, any residual gas in the vacuumwouldexhibitacompetingFaradayeffect.However,themagnitudeoftheeffectduetoresidualgascouldbeapproximatelyoffsetbychangingthegaspressureandattemptingtosubtractoutthiseffect.Comparison of Models: As a parting gesture, I justwant to stand back and compare theproposedspacetimebasedmodelofastaticelectricormagneticfieldtothecurrentlyacceptedstandardmodel. In the standardmodel all force is conveyedby “messengerparticles”. Theelectromagneticforceisconveyedbyvirtualphotonswhicharenottobeconfusedwithvirtualphotonpairs seechapter7 .Astaticelectricfieldandastaticmagneticfieldbothhaveenergydensity.Thisisarealeffectthat implies some tangible difference between a volume of spacetime that has anelectric/magnetic field and a volume of spacetime that has no electric/magnetic field. The“Reissner‐Nordstrom"solutiontoEinstein'sfieldequationgivesthegravitationaleffectofthisenergy density, but there is no theoreticalmodel of an electric ormagnetic field itself. Theelectromagnetic force issupposedlytransferredbymessengerparticles. This impliesthatanelectricormagneticfieldmustgeneratevirtualphotonswithoutanycontactwiththematterthatisgeneratingthefield.Twoexampleswillillustratethis.First,supposethatafreeneutronisstationaryinamagneticfield.Whenitdecaysitgeneratesarapidlymovingelectron,aproton


andelectronantineutrino.Therapidlymovingelectronandtheslowerprotonimmediatelyfeela Lorentz force exerted by the magnetic field. The force happens before speed of lightcommunicationexerts anopposing forceon the sourceof themagnetic field. Therefore, theLorentzforceonthemovingelectronisbeinggeneratedbyvirtualphotonswhichmustoriginatefromwithinthemagneticfielditself.Istherealimittotheamountofforcethatcanbegeneratedbyaweakmagneticfieldwithoutcommunicationbacktothesource?Thesecondexamplewillexaminethisquestion.Supposethatthemagneticfieldofastarequalstheearth’smagneticfieldstrength ~5 10‐5Tesla atadistanceof3 109mfromthestar.Therefore,atthisdistanceanyforceexertedbythemagneticfieldtakesabout10secondstobecommunicatedbacktothestar.Nowatthisdistance,supposethatthereisasquareloopofwirethatisonemeteroneachside.Furthermore,supposethattwoofthe4sidesareparalleltothemagneticfieldandtwoofthe4sidesareperpendiculartothemagneticfield.Ifacurrentflowsinthiswire,aLorentzforcewillbeexertedonthetwoperpendicularsectionsofwire onemetereach andanettorquewillbeexertedontheloopofwire.Theoretically,anycurrentcanbemadetoflowintheloopofwireuptoPlanckcurrentwhichisabout3.5 1025amps.Forexample,acurrentof2millionampswouldexerta100Newtonforceoneachofthetwowiresectionsthatareperpendiculartothemagneticfield.Ifthecurrentflowisstartedquickly,thenallthetorqueexertedonthewireloopcomesfromaninteractionwithalimitedvolumeofthemagneticfield.Theenergydensityofa5 10‐5Teslamagneticfieldisonlyabout10‐3 J/m3and it takes10 seconds to transfer this torque to the star. Therefore, if thecurrentstartedover3 10‐8seconds,themaximumvolumethatcouldbeaccessedatspeedoflightcommunicationwouldbeabout1,000m3.Thislimitedvolumehasonlyabout1Jouleofenergyinitsmagneticfield.Whilenoenergyisbeingextractedfromthestar’smagneticfield,itwouldtake3 1010wattsofrealphotonstogeneratea100Nforceifthisforcewasgeneratedbyphotonpressure.A100Newtonforcelasting10‐8swouldrequireabout300Joulesifitwasgeneratedbydeflectingrealphotons.Howdovirtualphotonswithnorealenergyaccomplishthis?Thisexampledoesnotimplyaviolationoftheconservationofmomentum.Apowerfulmagneticfieldisbeingestablishedandthestar’sweakmagneticfieldisdistortingtheformationofthenewmagnetic field. However, thequestion remains:Howexactlydoes thevirtualphotonmodelexplain the forcemagnitude 100N and forcevectorsexertedon thesewires?Carrying thisthoughtexperimenttoanextreme;Planckcurrentwouldgenerateaforceofabout1021Noneachofthetwowiresectionswithoutcommunicatinganytorquebacktothestar.Thereisnocommonlyacceptedexplanationinthestandardmodelforanelectric/magneticfieldintermsofsomethingmorefundamental.Ontheotherhand,thespacetimebasedmodeloftheuniversecaneasilyexplainanelectric/magneticfieldintermsofadistortionofthespacetimefield.Eventheinstantaneousgenerationofa1021Newtonforcecanbeexplained.Themagnetic


fieldisadistortionofthespacetimefieldwithitsseaofdipolewaves.ThemaximumforcethatthespacetimefieldcanexertisequaltoPlanckforcewhichisabout1044N.Thespacetimemodeloftheuniversehastheabilitytoexplainmanyofthemysteriesofquantummechanics.

SpacetimeUnitsIn chapter 10 we will try to combine the insights gained from charged particles and fromelectromagneticradiationtogiveaconceptuallyunderstandablemodeloftheexternalvolumeofchargedrotars.Thelaststepinthischapteristobuildontheinsightsthatweregainedintheexercisethateliminatedchargeasaunit.Eliminatingchargeandreplacingthiswithastraininspacetimeisasteptowardsdevelopingunitsbasedonthepropertiesofspacetime.However,thisstepdoesnottaketherealplunge.Itisnecessarytoeliminatemassasthefundamentalunitanddevelopunitsbasedonlyonthepropertiesofspacetime.Eventhoughlengthandtimearerelatedtospacetime,themeterandsecondarehumanconstructs.Planckunitshavealwaysbeenconsideredthemostfundamentalofunitssincetheyarenothumanconstructs.Ithasbeensaidthatifaliensattemptedtocommunicatewithus,theywouldusePlanckunitsbecausetheseunitsarederivedfromtheconstantsofnature.Whatcouldbemorefundamentalthanasystemofunitsbasedonħ,Gandc?Iftheuniverseisonlyspacetime,itshouldbepossibletoexpressconstantsandunitssuchaskilogram, Newton and Coulomb using only the fundamental properties of spacetime. Thisspacetimeconversion isnotparticularlyconvenient touse,and it iscloselyrelatedtoPlanckunits.However,itisveryinformativetoseehowcommonunitscanbeconstructedoutoftheproperties of spacetime. In particular, it is important to grasp the idea that mass is not afundamental unit when we look at the universe from the standpoint of spacetime beingfundamental.Massisameasurementofinertiaandinertiaisacharacteristicofenergytravelingatthespeedoflightinaconfinedvolume.Deflectingenergytravelingatthespeedoflightcausesmomentumtransfer.Thisisthesourceofall forcesincludingthepseudo‐forceof inertia.Thegoalistoexpresseverything,includingmass,intermsofthepropertiesofspacetime.Wewillstartthesearchforspacetimeunitsbylookingatoneofthe5wave‐amplitudeequationspreviouslydescribed.U A2ω2Z/cequationgivingtheenergydensityinawaveWhenweapply thiswave‐amplitudeequation tospacetime, it shouldbeeasy toexpress thisequationifweusethefundamentalpropertiesofspacetime.Thefirstobviouscandidateforafundamental property of spacetime is “Z” the impedance of spacetime Zs c3/G . Anothercandidateis“c”,thespeedoflight,butthisisnotascertainasZs.


OthercandidatesforbeingfundamentalunitsofspacetimemustbecontainedintheamplitudetermA.Weknowthatageneralexpressionofthemaximumpermitteddipolewaveinspacetimeis:Amax Lp/λ Tpω.Thisisthemaximumstrainamplitudewhichinturnisdictatedbythemaximumdisplacementamplitudeofspacetime:dynamicPlancklengthLpanddynamicPlancktimeTp. It is proposed thatdynamicPlanck lengthLp anddynamicPlanck timeTp arebothfundamental properties of spacetime. They are added to our list making a total of fourcandidates.Therefore,thefourcandidatesareZs,Lp,Tpandc.Wereallyonlyneedthreetermstoexpresseverythingintheuniverse,thereforetherearethreepossiblecombinationsofthreetermsthatcouldserveasthebasicunitsofspacetime.Theseare:1 Tp,Lp,Zs;2 c,Lp,Zs;and3 c,Tp,ZsAllofthesecombinationshaveadvantagesanddisadvantages.Iwillusethecombinationof:c,Tp,Zs, as the units of spacetime. After working with the different combinations I find thiscombinationthemostintuitive.Forexample,thespeedoflightandtheimpedanceofspacetimeseem to belong together. The unit of Planck time becomes the quantized heartbeat of theuniverse.Whileworkingtodevelopthemodelofelectricfieldandcharge,thiscombinationissomehoweasiertovisualize.RecallthattheimpedanceofspacetimeisPlanckmassdividedbyPlanck time. Zs Mp/Tp . Thereforeall conventionalunits canbeexpressedusing these3propertiesof spacetime. However, theuseof c,Tp, andZs gives answers that correspond toPlanckunitswhicharenotconvenientforeverydayuse.Toillustratehowthesespacetimeunitswork,theunitofforcehasdimensionalanalysisunitsofML/T2andconventionalunitsofkgm/s2.ThespacetimeunitsofforcearecZs.However,theseunitsspecifyPlanckforce ~1.2 1044N whichisthelargestforcespacetimecanexert.Foranotherexample,tospecifythegravitationalconstantGusingconventionalunitsitisnecessarytoincludeaconstant 6.673 10‐11 andtheunitsofm3/kgs2.Withspacetimeunitsthegravitationalconstantisequalto1andtheunitsofthegravitationalconstantarec3/Zs.Thespacetimeunitsonthenextpagetreatchargeasastrainofspacetimewithunitsoflength.Recallthatthechargeconversionconstantηis:Wehave longago found theoptimumwaysof expressingconversionconstants that simplifycalculations.Instead,thisexerciseisintendedtoillustratehowthepropertiesofspacetimecanbemanipulatedtoproducefamiliarconstantsandunitsofphysics. Itmaybedifficultforthereader to imagine physicswithoutmass or energy being a fundamental unit. However, themaximum force that spacetimecansupport is cTpand themaximumquantizedmass isTpZs.Massandenergyareaquantificationofpropertiesofspacetime.Thischangeinperspectivehasagreatdealofappealonceitisinternalized.Onthefollowingtable:

η≡ √

8.617 10‐18meter/Coulomb


Spacetime Units NameSpacetimeConversionelementarychargee 1/η √ cTpimpedanceoffreespaceZo η24π Zsspeedoflightc cPlanck’sconstantħ c2Tp2ZsgravitationalconstantG c3/Zs

Coulombforceconstant 1/4πεo η2cZspermeabilityoffreespace μo/4π η2Zs/cTransformationofPlanckUnitsintoSpacetimeUnitsPlanckUnitsStandardConversionSpacetimeConversion

PlancklengthLp ħ ⁄ Lp cTp

Planckmassmp ħ / mp TpZs

Planckfrequencyωp /ħ ωp 1/Tp

PlanckenergyEp ħc /GEp c2TpZsPlanckforceFp c4/GFp cZsPlanckpowerPp c5/GPp c2ZsPlanckenergydensityUp c7/ħG2Up Zs/cTp2PlanckimpedanceZp 1/4πεocZp η2ZsPlanckchargeqp 4πε ħcqp 1/η cTp

Planckelectricfield p c4/G 4πε ħ p ηZs/Tp

Planckmagneticfield p c3/G 4πε ħc p ηZs/cTp

Planckvoltage p c /4πε G p ηcZsWhileitispossibletoexpressalltheunitsofphysicsusingonlythepropertiesofspacetime c,TpandZs ,itwillbeshowninchapter14thatitisnecessarytoaddoneadditionaldimensionlessdesignation Гu to quantify the changing properties of spacetime. Aswill be explained inchapter14,thespacetimefieldisundergoingatransformationthatischangingalltheunitsofphysicsrelativetoanabsolutestandardthatisunchangedsincetheBigBang.


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chapter 9 electromagnetic fields & spacetime unitsonlyspacetime.com/chapter_9.pdfthe universe is...

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