Chapter 5 Spacetime Particle Modelonlyspacetime.com/Chapter_5.pdf · This is the structure of the spacetime ... Even though 10113 J/m3 is an incredibly large ... electrons and quarks

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Chapter5

SpacetimeParticleModel

“Thinkofaparticleasbuiltoutofthegeometryofspace;thinkofaparticleasageometrodynamicexcitation.”JohnArchibaldWheeler

Early Wave-Particle Model: In1926,ErwinSchrodingeroriginallyproposedthepossibilitythatparticlescouldbemadeentirelyoutofwaves.However,inanexchangeofletters,HenrikLorentzcriticizedtheidea.Lorentzwrote,

“Awavepacketcanneverstaytogetherandremainconfinedtoasmallvolumeinthelongrun.Evenwithoutdispersion,anywavepacketwouldspreadmoreandmoreinthetransversedirection,whiledispersionpullsitapartinthedirectionofpropagation.Becauseofthisunavoidableblurring,awavepacketdoesnotseemtometobeverysuitableforrepresentingthingstowhichwewanttoascribearatherpermanentindividualexistence.”

Schrodinger’sideaofawave‐particlewasagroupofdifferentfrequencywavesthat,whenaddedtogether, formed a Gaussian shaped oscillating wave confined to a small volume Fouriertransformation .SchrodingereventuallyagreedwithLorentzthatthewavesthatformedsucha“particle”woulddisperse.However,thisinitialfailureshouldnotbeinterpretedascondemningallpossiblewaveexplanationsforparticles.Forexample,opticalsolitonsarecompactpulsesoflaserlight waves thatpropagateinnonlinearopticalmaterialswithoutspreading.Theyexhibitparticle‐likepropertiesandwillbediscussedlater.In this chapter a model of a fundamental particle will be proposed made entirely out of aquantizeddipolewave in the spacetime field. Even though thismodel givesa structureandphysicalsizetoanisolatedfundamentalparticle,thereaderisaskedtoreservejudgmentaboutthismodeluntilitcanbefullyexplained.Thespacetimebasedmodelofafundamentalparticlehaswaveswithphysicalsize,butthismodelwillbeshowntobeconsistentwithexperimentsthat indicate no detectable size in collision experiments. Also the spacetime based modelexplainshowanelectroncanformacloud‐likedistributionundertheboundaryconditionsofaboundelectroninanatom.

Brief Summary of the Cosmological Model: Wewill startwith a brief description of thecosmologicalmodelproposedtobecompatiblewiththestartingassumption.Thecosmologicalmodeliscoveredindetailinchapters13and14.Iftheuniverseisonlyspacetimetoday,itmusthavealwaysbeenonlyspacetime.Notonlyareallparticles,fieldsandforcesderivedfromthe


propertiesof4dimensionalspacetime,butallthecosmologicalpropertiessuchastheexpansionoftheuniversearealsoderivedfromthechangingpropertiesof4dimensionalspacetime.Thiswillbediscussedlater.ThehighestenergydensitythatspacetimecansupportisPlanckenergydensity ~10113J/m3 .Onepointofpossibleconfusionisthat~10113J/m3isboththeenergydensityatthestartoftheBigBangandthecurrentenergydensityofthespacetimefield.Whatisthedifference?Todaytheenergydensityoftheuniverseobtainedfromgeneralrelativityandcosmological observations is about 10‐9 J/m3. However, this is proposed to only be the“observable”energydensityof theuniversepossessedbyall the fermionsandbosons in theuniverse.Wecanonlydirectlyinteractwithfermionsandbosonswhicharewavesthatpossessquantizedangularmomentum.However,thevastlylargerenergydensity ~10113J/m3 isthe“unobservable”vacuumenergyofthespacetimefield.ThisisthePlanckamplitudewavesinthespacetimefieldwhichlackangularmomentum.Thisisthestructureofthespacetimefielditself.Thisstructuregivesthespacetimefieldsconstantssuchasc,ħ,εo,G,Zs,etc.

Fromourcurrentperspective,spaceappearstobeanemptyvoid.However,asJohnArchibaldWheeler1said,“Emptyspaceisnotempty…Thedensityoffieldfluctuationenergyinthevacuumarguesthatelementaryparticlesrepresentpercentage‐wisealmostcompletelynegligiblechangeinthelocallyviolentconditionsthatcharacterizethevacuum.”Itisthisenergeticvacuumthatwearecallingthe“spacetimefield”.Vacuumenergycanbesaidtohaveatemperatureofabsolutezerobecauseitlacksanyquantizedunitsandtemperatureisdefinedasenergyperquantizedunit.ThesameenergydensityatthestartoftheBigBangwasintheformof100%quantizedspin units. The energy per quantized unit was equal to Planck energy and therefore thetemperature at the start of the Big Bang was approximately equal to Planck temperature∿1032°K .

Even though10113 J/m3 isan incredibly largenumber, it isnota singularitywhichwouldbeinfiniteenergydensity.ForthespacetimefieldtoreachPlanckenergydensity Up spacetimemust have dipolewaves at the highest possible frequency ωp Planck frequency and thelargestpossibleamplitude A 1 .

U A2ω2Z/cset:A 1,ω ωp /ħ 1.9 1042s‐1Z Zs c3/G

U ħ

4.6 10113J/m3 Planckenergydensity

Unlike virtual particle pairs which have a very short lifetime, Planck amplitude waves inspacetime can last indefinitely because they are undetectable even if there is continuousobservationtime.APlancklengthdisplacementofspaceoraPlancktimedisplacementoftimeadvance or retard clocks is fundamentally undetectable. Only if a Planck amplitudewavepossessesquantizedangularmomentumofħor½ħdoesitbecomedetectable observable by

1 Misner, C. W., Thorne, K. S. and Wheeler, J A.: Gravitation. (W. H. Freeman and Company, New York 1973) P. 975.


us. Therefore today’s spacetime has vacuum energy density of 10113 J/m3 but none of thisvacuumenergypossessesquantizedangularmomentum.ThespacetimeatthebeginningoftheBig Bang also had energy density of 10113 J/m3 but then 100% of that energy density wasobservable. Photons propagating in spacetime today are undergoing a redshift because ofuniversal expansion. The photon’s lost energy possesses no angular momentum. All of thephoton’s angular momentum remains in the form of approximately the same number ofredshiftedphotons.In chapters 13 and 14 the casewill bemade thatwhatwe perceive as an expansion of theuniverse is actually a more complex transformation of spacetime. Even fermions such aselectrons and quarks are also losing energy on a proposed absolute scale. Ultimately, thistransformation of spacetime is responsible for converting spacetime from being 100%observable at a temperature of about 1032 °K Planck temperature times a constant at thebeginningoftheBigBang 100%quantizedangularmomentum totodaywherealmostalltheenergyof thespacetime field is in the formofwaves that lackangularmomentum. ItwillbeshownthatthisexplanationgivesthecorrectdifferenceintemperaturebetweenthestartoftheBigBangandtoday’sCMBtemperatureof2.725°K.

Ifwejumpforwardintime,todayonlyabout1partin10122ofthetotalenergyintheuniverseincludingvacuumenergy possessesquantizedangularmomentumofħor½ħ.Furthermore,thisfractioniscontinuouslydecreasingbecauseofthecosmicredshiftandanothercharacteristicdescribedlater.Allthefundamentalparticlesandforcesthatwecandetectarethe1partin10122thatpossessesquantizedangularmomentum.Thevastlylargerenergyintheuniverseistheseaofvacuumfluctuations dipolewavesinspacetime thatdoesnotpossessangularmomentum.TheonlyhintwehavethatthisvastenergydensityexistsisthequantummechanicaleffectssuchastheLambshift,Casimireffect,vacuumpolarization,theuncertaintyprinciple,etc.However,itwillbeshownthatthisseaofvacuumfluctuationsisessentialfortheexistenceoffundamentalparticlesandforces.Vacuum Energy Has Superfluid Properties: Ifwe are going to be developing amodel offundamental particles incorporating waves in spacetime, it is important to understand theproperties of the medium supporting the wave. In the last chapter we enumerated manypropertiesofthespacetimefield.Thepointwasmadethatthepropertiesofvacuumfluctuationsareanintegralpartofthepropertiesofthespacetimefield.However,onepropertyofvacuumenergy was intentionally saved for this chapter because it is particularly important in theexplanationoffundamentalparticlesformedoutofwavesinspacetime.It is proposed that vacuum energy has the property that it does not possess angular momentum. Any angular momentum present in the midst of the sea of vacuum energy is isolated into units that possess quantized angular momentum. These quantized angular momentum units have different properties than vacuum energy.


ThisconceptiseasiesttoexplainbymakingananalogytosuperfluidliquidheliumoraBose‐Einstein condensate. When the helium isotope 4He is cooled to about 2° K, it changes itspropertiesandpartlybecomesasuperfluid.Coolingtheliquidfurtherincreasesthepercentageoftheheliumatomsthatareinthesuperfluidstate.Coolingsomeotheratomstoatemperaturevery close to absolute zero changes their properties and a large fraction of these atoms canoccupy the lowest quantum state and exhibit superfluid properties. This is a Bose‐Einsteincondensate.SincesuperfluidliquidheliumisaspecialcaseofaBose‐Einsteincondensate,theywillbediscussedtogether.Whenagroupofatomsoccupyasinglequantumstate,thegroupmustexhibitquantizedspinona macroscopic scale. The quarks and electrons that form atoms individually are fermions.However,aBose‐Einsteincondensateorsuperfluid4Heexhibitsquantizedspinonamacroscopicscale.Thegroupoffundamentalparticlescanpossesseitherzerospinoranintegermultipleofspin units related to ħ. Ifwe have a group of atoms in a Bose‐Einstein condensate andweintroduceangularmomentum “stir” thecondensate , thenwecan form“quantizedvortices”that possess quantized angular momentum within the larger volume of Bose‐Einsteincondensatethatdoesnotpossessmacroscopicangularmomentum.Thereforeaquantumvortexisagroupofatomsthathasadifferentangularmomentumquantumstate differentspin thanthe larger group of surrounding atoms that forms the superfluid 4He or Bose‐Einsteincondensate.Thiseffectwasfirstdiscoveredwithsuperfluidliquidhelium2.DramaticpicturesarealsoavailableofmultiplequantumvorticesinaBose‐Einsteincondensate3,4.ItisproposedthatthequantumfluctuationsofspacetimeareaLorenzinvariant“fluid”thatisthemostidealsuperfluidpossible.Unlikethefundamentalparticles fermions thatformaBose‐Einsteincondensate,thevacuumfluctuationsdonotpossessanyquantizedangularmomentum.However,vacuumfluctuationsaresimilartoasuperfluidorBose‐Einsteincondensatebecauseitisolatesangularmomentumintoquantizedunits.Thesequantizedangularmomentumunitsthatexistwithinvacuumenergyareproposedtobethefermionsandbosonsofouruniverse.Thesamewaythatthequantizedvorticescannotexistwithoutthesurroundingsuperfluid,soalsothefermionsandbosonscannotexistwithoutbeingsurroundedbyaseaofvacuumenergy.ThetotalangularmomentumpresentinthequantumfluctuationsofspacetimeatthestartoftheBigBangprobablyaddeduptozero.However,eventhoughcounterrotatingangularmomentumcancancel,stillthereshouldbeoffsettingeffectsthatshouldstatisticallypreservethequantizedangularmomentumunitsfromtheBigBangtotoday calculatedinchapter13 .Dipolewavesinspacetimethatpossessangularmomentumwouldnotbethesameasthedipolewavesthat

2 E.J. Yarmchuk, M.J. Gordon and R.E. Packard, Observation of stationary vortex arrays in rotating superfluid helium, Phys. Rev. Lett. 43, 214-217 (1979) 3 K. W. Madison, F. Chevy, W. Wohlleben and J. Dalibard, Vortex lattices in a stirred Bose-Einstein condensate cond-mat/0004037[e-print arXiv]. 4Ionut Danaila, Three-dimensional vortex structure of a fast rotating Bose-Einstein condensate with harmonic-plus-quartic confinement, http://arxiv.org/pdf/cond-mat/0503122.pdf


formvacuumfluctuations. Aunitthatpossessesquantizedangularmomentumlosesitsidealsuperfluid properties because it can interact with another unit of energy that possessesquantizedangularmomentum forexample,exchangeangularmomentum .Spacetime Eddy in a Sea of Vacuum Energy: Itisproposedthatwhatweconsidertobethefundamentalparticlestoday quarksandleptons arethespacetimeequivalentofthevorticesthat carry quantized angular momentum in a superfluid. However, the quantized angularmomentumentitiesarebettervisualizedaschaoticeddiesthatexistsinthevacuumfluctuationsofthespacetimefield.Wecanonlydirectlyinteractwiththedipolewavesinthespacetimefieldthatpossessquantizedangularmomentum.Weareunawareofthevastamountofsuperfluidvacuumenergythatsurroundsusbecauseitonlyindirectlyhasanyinfluenceonus.In the spacetime based model of the universe, fundamental particles are dipole waves in spacetime that possess quantized angular momentum. They are living in a sea of superfluid vacuum fluctuations that cannot possess angular momentum. Fundamental particles cannot exist without the support provided by this sea of superfluid vacuum fluctuations.Spin and Particle Size: Before describing how fundamental particles can be formed out of the properties of spacetime, I would like to point out several problems with the vague “point particle” description of particles currently used in quantum mechanics. Molecules have experimentally observable size, so we will start there. There is experimental evidence which indicates that molecules possess physical angular momentum. For example, molecules suspended in a vacuum physically rotate at specific frequencies. Each isolated molecule has a fundamental rotational frequency and allowed rotational harmonics of that frequency. For example, a carbon monoxide molecule has a fundamental rotation frequency of 115 GHz. This molecule can only rotate at this frequency or at higher frequencies which are integer multiples of the fundamental frequency. This fundamental rotational frequency corresponds to the carbon monoxide molecule possessing ½ħ of angular momentum. The carbon monoxide molecule has physical dimensions which can be measured. The rotation can be visualized as a classical physical rotation. The quantized rotational frequencies are not classical, but even these are conceptually understandable if the molecule is visualized as existing within the superfluid spacetime field which enforces quantized angular momentum. The reason for going into this detail about the rotation of molecules is that the physical rotation of a molecule is going to be contrasted to fundamental particles which are said to possess an “intrinsic” form of angular momentum known as “spin”. The concept is that the fundamental particles somehow possess a quality with dimensions of angular momentum, but without any part of the fundamental particle undergoing a classical rotation. The problem is that the description of a fundamental particle as a point particle or a Planck length string does not allow for any physical rotation which achieves ½ ħ of angular momentum. For example, an electron has energy of 0.511 MeV. If a photon had this energy, it would have to propagate at the speed of light around a circle


larger about 10-13 m in order to have ½ ħ of orbital angular momentum. Since relativistic collision experiments seem to imply that an electron is no larger than 10-18 m, this 10-13 m physical size is rejected. The angular momentum of an electron is the first of three areas that imply a size mystery. The second conflict is the implied minimum size of an electron calculated from the electric field of an electron. An electron possesses an electric field with measurable energy density. The classical radius of an electron is calculated by finding the radius where the total energy contained in the electron’s electric field equals the electron’s energy (0.511 MeV). This “classical electron radius” equals 2.8×10-15 m. This is the implied minimum size of an electron based on our knowledge of electric fields. Since this is much larger than the previously mentioned 10-18 m, this is another size mystery. If an electron is actually approximately Planck length in radius as in some models, then the energy of the electron’ electric field should be about 1020 times larger than 0.511 MeV. Rather than admit that there is a possible problem with the point particle model, the calculated maximum size of an electron is dubbed the “classical” electron radius. The word “classical” is the kiss of death to any quantum mechanical explanation. A third problem occurs in quantum electrodynamics calculations. When the size of an electron is required for a calculation, then the analysis gives a ridiculous answer of infinity if the electron is assumed to be a point particle. The process of renormalization is required to eliminate the infinity. However, this is an artificial adjustment of the answer so that it is no longer a faithful extension of the starting assumptions. An analysis of this problem shows that in order to obtain a reasonable answer (not infinity), the radius of the electron must be assumed to be larger than the classical electron radius. This also implies a size mystery. These three examples are given here because they illustrate some of the problems with the point particle model used in quantum mechanics. The explanation usually given to students is that the point particle model is correct, but quantum mechanics is a mathematical subject. Physical explanations are simply beyond human understanding. How is it possible to conceptually understand a point particle possessing “intrinsic” angular momentum with nothing actually rotating? How is it possible for an electron to be much smaller than its classical radius? Will we ever be able to understand an electric field in terms of something more fundamental? Will we ever be able to understand how a fundamental particle causes curved spacetime? All of these questions will be answered in this book. The first step is to examine the proposed spacetime particle model which solves all of the size mysteries and many other related mysteries. Rotar: Thesimplest formofquantizedangularmomentumthatcanexist inaseaofdipolewaves in spacetime would be a rotating dipole wave that forms a closed loop that is onewavelengthincircumference.Adipolewaveinspacetimeisalwayspropagatingatthespeedoflight,evenifitformsaclosedloop.ThisagreeswiththehighlysuccessfulDiracequationwhichrequiresthatafundamentalparticlesuchasanelectronisalwayspropagatingatthespeedof


light.Diracexpressedthisrequirementmathematicallyas csoanelectroncanhaveanaveragevelocityofzerowhilehavingawavemovinginaconfinedvolumeataspeedofc.ThisrotatingdipolewaveinspacetimeisstillsubjecttothePlancklength/timelimitation,soitcanbethoughtofasbeingatthelimitofcausality.Itsrotationischaoticratherthanbeinginasingleplane.Ithasadefinableangularmomentum,butallrotationdirectionsarepermittedwithdifferentprobabilitiesofobservation. Theexactoppositeoftheexpectationdirectionhaszeroprobability .Therefore,theproposedmodelofanisolatedfundamentalparticleisadipolewaveinthespacetimefieldthatformsarotatingclosedloopthatisonewavelengthincircumference.Thisobviouslyisadrasticdeparturefromthestandarddefinitionoftheword“particle”. Thestandardmodelofa fundamentalparticle isamass thathasnodiscerniblephysicalsize,butsomehowexhibitswaveproperties,angularmomentumandinertia.Itisanaxiomofquantummechanicsthattheψfunctionhasnophysicalinterpretation.Thisvaguenesswillbereplacedwithatangiblephysicalmodelthatexplainsmanyofthepropertiesexhibitedbyfundamentalparticles.Anewnameisrequiredtodistinguishbetweenthestandardconceptofafundamentalparticleandtheproposedmodelofarotatingdipolewaveinspacetime.Thenewnameforthespacetimemodelofafermionwillbe:“rotar”. It iswithgreatreluctancethatanewwordiscoined,butthisisnecessaryforclarityandbrevityintheremainderofthisbook.Thenamerotarrefersspecificallytothespacetimedipolemodelofafundamentalparticlethatexhibitsrestmass afermion .Thismodel,anditsvariations,isdescribedindetaillater.Bosonswithoutrestmass,suchasaphoton,haveadifferentmodelandarenotcoveredbytheterm“rotar”.Therewillbeaspacetimemodelofaphoton,butthatwillbeintroducedlater.Theword“particle”willbeusedwheneverthecommondefinitionofaparticleisappropriateorwhenitisnot necessary to specifically refer to the spacetime particlemodel. For example, the name“particleaccelerator”doesnotneedtobechanged.Eventheterm“fundamentalparticle”willoccasionallybeused in theremainderof thisbookwhen theemphasis isondistinguishingaquarkorleptonfromcompositeobjectssuchashadronsormolecules.Trial and Error:TheangularmomentumpresenttodayintheformoffermionsandbosonswaspresentattheBigBangintheformofphotonswiththehighestenergypossiblewhichisPlanckenergy.Thisstartingconditionwillbediscussedmoreinthechaptesoncosmology.Eventhoughphotonsmakeupasmallpercentageoftheenergyintheuniversetoday,thephotonsofthe cosmic microwave background still possess the vast majority of the quantized angularmomentumintheuniverse.Theearlyuniversewasradiationdominated,butenergeticphotonscancombinetoformmatter/antimatterpairs.However,thereisaslightpreferenceformatteraboutonepartinabillion .Astheearlyuniverseexpanded transformed ,thechaoticdipolewavesinspacetimeexploredeveryallowedcombinationoffrequencyandamplitudeinaneffortto find themostsuitable formtohold theunwantedangularmomentum. By trialanderror,relatively long lived spacetime resonances were found that both held quantized angular


momentumandalsowerecompatiblewiththepropertiesofthevacuumenergydipolewavesinspacetime. These spacetime resonances are proposed to be the fundamental particlesfundamentalrotars .Itwillbeshownlaterthattheknownfundamentalrotarsareresonancesthathavefrequenciesbetweenabout1020and1025Hz.In theproposedearlystagesof theBigBang, themostenergeticspacetimeparticles rotars formed first. Forexample, tauons tau leptons formedbeforemuons. Thesewerepartiallystable resonances. They survived for perhaps 1011 cycles, but not indefinitely. They thendecayed into other energetic rotars and photons. The radiation dominated universe wasundergoinga large redshift. Energywasbeing removed fromphotonsand transformed intovacuumenergy. Thisloweredthetemperatureoftheobservableportionoftheuniversethatpossessesangularmomentum photons,neutrinosandrotars .Eventually,otherfundamentalspacetimeresonances rotars wereformedatlowerfrequencies lowerenergy . Eventually,trulystableresonancesformedandthesewereelectronsandtheupanddownquarksthatfoundstabilitybyformingprotonsandneutrons.Wave-Particle Duality: Before launching intoamoredetaileddescriptionandanalysisof arotar, it is interesting to initially stand back and look at the philosophical difference inperspectiverequiredtoimagineaparticlemadeentirelyofdipolewavesinspacetime.Atfirst,theideaofaparticlemadeoutofwavesinspacetimeseemstobeintuitivelyunappealing.Theessenceofaparticleissomethingthatactsasaunit.Waves,ontheotherhand,areimaginedtobeinfinitelydivisible. Whenaparticleundergoesacollision, itrespondsasasingleunit inacollision.Thispropertyseemsincompatiblewitharotarmadeentirelyofawave.Thesuperfluidpropertiesofthespacetimefieldmakesangularmomentumintoquantizedunitsof ½ ħ or ħ. The same way that a superfluid Bose Einstein condensate isolates angularmomentumintodiscretevorticies,eachwithħofangularmomentum,soalsospacetimeisolatesangular momentum into isolated units possessing quantized angular momentum.. It is notpossibletointeractwithjust1%ofaquantizedunitofangularmomentum.Itisallornothing.Therefore, dipole waves in spacetime possessing ½ ħ of angular momentum appear to beparticlesbecausetheyrespondtoapertibationasaunit.LaterinthisbookIwillpostulateanewpropertyofnaturecalled“unity”.Thispropertyiscloselyrelatedtoentanglement.Itpermitsadipolewavepossessingquantizedangularmomentumtocommunicateinternallyfasterthanthespeedoflightandrespondtoaperturbationasasingleunit. This property would impart a “particle like” property to a quantized dipole wave inspacetime. However, the quantized wave would not exhibit classical particle properties.“Finding”theparticlewouldbecomeaprobabilisticeventbecausewearereallydealingwithinteractingwithawavecarryingquantizedangularmomentumthatisdistributedoverafinitevolume.AquantizedwaveinthespacetimefieldcanexhibitbothangularmomentumandgiveaphysicalinterpretationtothepathintegralofQED.Thereisactuallyagreatdealofappealto


fundamentalparticlesbeingmadeofquantizedwavesinspacetime,providedthatthemodelisplausible.Anotherobjection to a rotarmodelmade entirely ofwaves is that our experiencewith lightseems to imply that waves do not interact with each other. Light does have a very weakgravitational interaction, but overall lightwaves exhibit almost no interaction. Thewaves inspacetimethatareproposedtobethebuildingblocksofallmatterandforcesmustbeabletointeractwitheachother.Any wave that exhibits nonlinearity will interact to some degree with a similar wave. Forexample,soundwaveshaveaslightnonlinearity.Thereisatemperaturedifferencebetweenthecompressionandrarefactionpartsofasoundwave.Thisslighttemperaturedifferenceproducesaslightperiodicdifferenceinthespeedofsound.Thisslightnonlinearityinasinglesoundwavemeansthattwosuperimposedsoundwavesdointeract. However,atcommonlyencounteredsoundintensities,theinteractionbetweentwosoundwavesisverysmall.Gravitational waves also have a slight interaction because general relativity shows thatgravitationalwavesarenonlinear.Oneoftheappealsofdipolewavesinspacetimeisthattheyexhibittherequiredabilitytointeractwitheachother.Infact,dipolewavesinteractsostronglythat they would cause a violation of the conservation of momentum without the quantummechanicalPlancklength/timelimitationpreviouslydiscussed.Theinteractionsbetweendipolewavesinspacetimewillbeshowntoberesponsibleforalltheforcesincludinggravity.Thespacetimefieldisthestiffestpossiblemedium.TheincrediblylargeimpedanceofspacetimeZs c3/G 4 1035kg/s permitsawavewithsmalldisplacementtohavetheveryhighenergydensityforagivenfrequency. Whenwehavefrequenciesinexcessof1020Hz,thenwavesinspacetimearecapableofachievingtheenergydensityoffundamentalparticles.WhenwepermitthefrequencytoreachPlanckfrequency,wecanachievetheenergydensityrequiredatthestartof the Big Bang Planck energy density . Also, a universe made only of spacetime andperturbationsofspacetimehasanappealingsimplicity.Particle Design Criteria:Everythingthathaspreviouslybeensaidinthisbookhassetthestageforthetaskofattemptingtodesignandanalyzeaplausiblemodelofafundamentalrotar. Indesigningarotarfromdipolewavesinspacetime,thereisonefactorthatwillbetemporarilyignored.Thisistheexperimentalevidencethatseemstoindicatethatfundamentalparticlesarepointswithnophysicalsize.Therotarmodelwillbeshowntoexhibitthisproperty,butthiswillbeanalyzedlater.Itshouldbeexpectedthatthefirstmodeloffundamentalparticleswillbeoverlysimplified.Forexample,thisfirstgenerationrotarmodelwillmakenodistinctionbetweenleptonsandquarks.Subsequentgenerationsof the rotarmodel shouldmakesuchadistinctionandexhibitother


refinements.Thehopeisthatthefirstgenerationrotarmodelwillpassenoughplausibilityteststhatotherswillbeencouragedtoimproveonthismodel.Thereare6considerationsthatwillbebroughttogetherinanattempttodesignafundamentalparticle.Theseare:

1 The universe is only spacetime. The energetic spacetime field contains waves inspacetime. Thewaves canbedipolewaves with thePlanck length/time limitation ,quadrupolewaves forexample,gravitationalwaves orhigherorderwaves.Ofthese,onlydipolewavesinspacetimemodulatetherateoftimeandmodulatevolume.Thesearethecharacteristicsrequiredtobethebuildingblocksofrotars.

2 The rotar model should exhibit inertia. As shown in chapter 1, this requires energytraveling at the speed of light, but confined to a limited volume in a way that themomentumvectorsgenerallycancel.

3 Therotarmodelshouldexhibitangularmomentum.Thiswillbeinterpretedasimplyingacirculation rotation ofthedipolewavesinspacetime.Furthermore,thereshouldbealogicalreasonwhyfundamentalrotars fermions withdifferentenergyallpossessthesameangularmomentum.

4 TherotarmodelshouldexhibitdeBrogliewaveswhenmovingrelativetoanobserver.Thisimpliesbidirectionalwavemotion,atleastinthe“externalvolume”.ThefrequencyoftheconfineddipolewavesinspacetimecanbecalculatedbyanalogytothedeBrogliewavesgeneratedbyconfinedlightdescribedinchapter1.

5 The rotarmodel should exhibit action at a distance without resorting tomysteriousexchangeparticles. Bothgravityandanelectric fieldshould logically follow fromtherotardesign.Toaccomplishthis,partoftherotar’sdipolewaveinspacetimemustextendintowhatweregardasemptyspacesurroundingtherotar.

6 Therotarmodelshould logicallyexplainhow it ispossible forparticles toexploreallpossiblepathsbetweentwoeventsinspacetime pathintegralofQED .

NotetoReader:Therestofthischapterpresentsthespacetime‐basedmodelofafundamentalparticle.Inthese11pagestheemphasiswillbeondescribingtheparticlemodelandtherewillbenoattempttojustifythismodel.Thisspacetime‐basedparticlemodelwillincludeunfamiliarconceptsthatmaybedifficulttoinitiallyvisualize.Chapters6,8and10aredevotedtotestingthisparticlemodel.Forexample,chapter6willsubjecttheparticlemodeltotestsofitsangularmomentum,inertia,energyandthegenerationofforces includinggravity .Thesetestswillalsohelptoexplainthemodelfurther.


ParticleModelFourthStartingAssumption:A fundamental particle is a dipole wave in spacetime that forms a rotating spacetime dipole, one wavelength in circumference. Inertia is a natural property of this particle design.Arotatingdipoleinthespacetimefieldcanbementallythoughtofasadipolewaveinspacetimethathasbeenformedintoaclosedloop,onewavelengthincircumference.Recallthatadipolewaveinspacetimeoscillatesboththerateoftimeandpropervolume.Forexample,oneportionofthewave,whichwewillnamethespatialmaximum,expandspropervolumeandslowstherateoftimerelativetolocalflatspacetime.Theoppositeportionofthewave,whichwewillnamethespatialminimumhasareductionofpropervolumeandanincreasedrateoftimerelativetolocalflatspacetime.Ifadipolewaveinspacetimepossessesquantizedangularmomentumof½ħ,itformsaclosedloopthatisonewavelengthincircumference.To visualize this, a single cyclewave has been given angularmomentum so that the spatialmaximumandminimuminaplanewavehavenowbecomethetwooppositepolaritylobesoftherotatingdipolewave.Thewaveisstilltravelingatthespeedoflight;itisjusttravelingatthespeedoflightaroundaclosedloop. Suchawaveisconfinedenergytravelingatthespeedoflight.Whilethereisangularmomentum,thenettranslationalmomentumofthisquantizedwaveis zero p 0 because of opposing vectors . Therefore, just like confined light or confinedgravitationalwaves,adipolewaverotatingatthespeedoflightsatisfiestheconditionrequiredforittoexhibitrestmassandinertia.Thisrotatingdipolemustbepicturedasan isolatedrotatingdipolewaveexisting inaseaofvacuumenergy/pressure that consists of other non‐rotating dipolewaves in spacetime. Therotarmodel implies internal pressure explained later .The vacuumenergy/pressure of thesurrounding spacetime field is capableof exerting a far greaterpressure than is required toconfine the energydensity of a rotar. For now the important point is that a rotar rotatingspacetime dipole can achieve stability by interacting with the surrounding sea of vacuumenergy thesurroundingspacetimefield .Therotatingdisturbanceisonlyaquantizedunitofangularmomentumthatcaneffortlesslymovethroughthesuperfluidspacetimefield.Illustrations of a Rotar:Figures5‐1and5‐2aretwodifferentwaysofdepictingtherotatingdipoleportionoftherotarmodel.ThespacetimedipoledepictedinFigure5‐1showstwodiffuselobesrepresentingstrainedvolumesofspacetimethatarerotatingintheseaofvacuumenergy.Theselobesaredesignated“dipolelobeA”and“dipolelobeB”.Eachlobeexhibitsbothaslightspatialandatemporaldistortionofthespacetimefield.Forexample,lobeAcanbeconsideredthe lobe that exhibits a proper volume slightly larger than the Euclidian norm the spatialmaximumlobe andarateoftimethatisslightlyslowerthanthelocalnorm.LobeBhastheoppositecharacteristics smallerpropervolumeandfasterrateoftime .Theselobesarealways


movingatthespeedoflight,soitisonlypossibletoinfertheireffectontimeorspacebywaveamplitudes.Also, the rotarmodelextendsbeyond thevolumeshown,but thatportion isnotillustratedhere.


Rotar Radius and Rotar Volume : This cross sectional view inFigure5‐1 showsa circledesignated“imaginaryboundaryoftherotatingdipolewave”.ThiscirclewhichisoneComptonwavelengthincircumference.Thiscirclewillsometimesbecalledthe“Comptoncircle”andthevolume within this circle will be called the “quantum volume”. The radius is equal to thefundamentalparticle’sComptonwavelengthdividedby2πwhichwillbedesignatedthereducedComptonwavelength λc . This circle and radius λc should not be considered as hard edgedphysicalentities.Instead,theyshouldbeconsideredasconvenientmathematicalreferencesforarotar.Thisissimilartothewaythatthecenterofmassisaconvenientmathematicalconceptformechanicalanalysis.Figure 5‐1 depicts spatial nd temporal variuations in the properties of the spacetime field.Missing from this figure is all the higher frequency dipolewaves in spacetime that are alsopresentinspacetime.Forexample,themodelofthespacetimefieldisdipolewaveswhichlackangular momentum primarily at Planck frequency with wavelength predominantly equal toPlancklength.Iffigure5‐1representsanelectron,thenadipolewavewithwavelengthofPlancklengthwouldbeabout1022timessmallerthantheradiusdepictedinfigure5‐1.Therefore,thevariationsshowninfigure5‐1canbethoughtofasmadefromavastnumberofsmallerwaveswhichhaveslightdifferencesindensityresultinginthecharacteristicsshowninthisfigure.Sincethedipolelobesarequantummechanicalentities,theycannotbeaccuratelydescribedbystaticpictures.Whilefigure5‐1depictsarotationinasingleplane,theintendedrepresentationisasemi‐chaoticrotationthathasanexpectationdirectionofrotation,butalsootherplanesofrotation occur with a probabilistic distribution. Also, this is merely quantized angularmomentumintheseaofpredominantlyhighfrequencydipolewavesthatmakeupthespacetimefield.Thischaoticenvironmentisatthelimitofcausality.Ithasanexpectationrotationalaxis,butthischaoticenvironmentcreatesthequantummechanicalspincharacteristicsofaparticle.ThecircledepictedinFigure5‐1shouldbeconsideredthecrosssectionofanimaginaryspherebecausethechaoticrotationalcharacteristicsallowallrotationalaxisexcepttheoppositeoftheexpectationaxis..Thevolumeofthisimaginaryspherewillbedesignatedthe“rotarvolumeVr”.Whilethisvolumeshouldbe 4/3 πλc3,oftenwearedroppingnumericalfactorsnear1inthisplausibilitystudy,sotherotarvolumewillbeconsideredVr λc3.Rotating Rate of Time Gradient: The presence of these lobes also implies that there is agradient in therateof timeandagradient inpropervolumebetween these lobes andevenoutsidetheselobes .IflobeAhasarateoftimethatisslowerthanthelocalnormandlobeBhasa rate of time that is faster than the local norm, then this implies that the rotarmodel alsocontainsavolumeofspacewithagradientintherateoftimethatisrotatingwiththelobes.Any


gradientintherateoftimeproducesacceleration.Inchapter2weshowedthattheaccelerationofgravitywasdirectlyrelatedtothegradientintherateoftime:

g c2 –

For example, a 1 m/s2 acceleration is produced by a rate of time gradient of: 1.11 10‐17seconds/secondpermeter.Therateoftimegradientintherotarmodelthereforeproducesavolumeofspacetimethatexhibitsaccelerationsimilartogravitybuttherearealsoimportantdifferencesexplainedbelow.Figure5‐2isintendedtoillustratetherotatingrateoftimegradientpresentintherotarmodel.In figure 5‐2 the lobes A and B have been replaced with a dashed outline showing theirapproximatelocation.Insteadofillustratingthelobes,figure5‐2showstherateoftimegradientthatexistsbetweenthelobes. Onlytherateoftimegradientinsidetherotarvolumeisshown .Thearrowsshowthedirection vector oftherateoftimegradientandthelengthofthearrowsisacruderepresentationoftheamountofrateoftimegradient.Thedirectionoftherateoftimegradientrotateswiththelobes,soFigure5‐2shouldbeconsideredasdepictingamomentintime.Rotating “Grav” Field: Anewnameisrequiredtodescribethisrotatingaccelerationfieldcausedbytherotatingrateoftimegradientillustratedinfigure5‐2.Thename“rotatinggrav field”willbeusedtodescribethisrotatingrateoftimefield.Itwillbeshownlaterthatthisisafirst order effect capable of exerting a force comparable to the maximum force of a rotar.Howeverthisforcevectorisrapidlyrotatingthereforewearenotawareofitseffect.Thegravityproducedbyarotarisavastlyweakerforce. However,thegravityvectorisnotrotatingandthereforeitisadditive.This“rotatinggravfield”fillingthecenteroftherotarvolumewillbeshowntohaveanenergydensitycomparabletotheenergydensityoftherotatingdipolewavewhich is concentrated closer to the circumference of the rotar volume. Therefore, the twodifferent types of energetic spacetime approximately fill the entire rotar volume with anapproximatelyuniformtotalenergydensity.Lobe A as described above produces an effect in spacetime that is similar to the effect onspacetimeproducedbyordinarymass verysnall slowing in the rateof timeandverysmallincreaseinvolume .LobeB,ontheotherhand,producesaneffectthatissimilartotheeffectofahypotheticalanti‐gravitymass.Itproducesaverysmallincreaseintherateoftimerelativetothelocalnormandaverysmalldecreaseinvolume.InlobeB,theverysmallincreaseintherateoftimeneverreachestherateoftimethatwouldoccurinahypotheticalemptyuniverse.Thiswill be discussed later, but it will be proposed that the entire universe has a backgroundgravitationalgammaГthatresultsintheentireuniversehavingarateoftimethatisslowerthanahypotheticalemptyuniverse.ItisthereforepossibleforlobeBtohavearateoftimethatis


faster than the surrounding spacetime field without having a rate of time faster than ahypotheticalemptyuniverse.Compton Frequency: We will return to figures later, but first we want to calculate therotational frequency of the rotating dipole. If we presume that a rotar is a confined wavetravelingatthespeedoflight,itisnecessarytoassignafrequencytothiswave.Isitpossibletoobtainanimpliedfrequencyfromaparticle’sdeBrogliewavecharacteristics?Inchapter#1weshowedthatconfinedlightexhibitsmanypropertiesofaparticle.TheseincludetheappearanceoftheopticalequivalentofdeBrogliewaveswhentheconfinedlightismovingrelativetoanobserver.IfwewereonlyabletodetecttheopticaldeBrogliewavespresentinamovinglaser,itwouldbepossibletocalculatethefrequencyofthelightinthemovinglaser.Similarly,wecanattempt to calculate a rotar’s frequency from its de Brogliewaves.We know a particle’s deBrogliewavelength λd h/mv andthedeBrogliewave’sphasevelocity wd c2/v . Fromtheseweobtainthefollowingangularfrequencyω.

υ frequency

2 ħ

ω ωc ħ ħ

Comptonangularfrequency

This calculation says that a rotar’s angular frequency is equal to a rotar’s Compton angularfrequencyωc.Wewillpresumethatthisisarotar’sfundamentalfrequencyofrotation.WhilethedeBrogliewavelengthandphasevelocitydependonrelativevelocity, thevelocity termscancel in the above equation yielding a fundamental frequency Compton frequency that isindependentofrelativemotion.Thereasoninginthiscalculationcanbeconceptuallyunderstoodbyanalogytotheexampleinchapter1ofthebidirectionalwavesinthemovinglaser.Arotar’sComptonwavelengthwillbedesignatedλc.Theconnectionbetweenarotar’sComptonwavelengthanddeBrogliewavelengthλdisverysimple.λc λd v/c where isthespecialrelativitygamma: 1– v/c 2 ‐1/2λc λd Ultrarelativisticapproximationwhenv/c 1Thesimplicityoftheseequationsshowtheintimaterelationshipbetweenarotar’sdeBrogliewavelengthandComptonwavelength. Foranotherexample,imagineageneric“particle”thatmightbeacompositeparticlesuchasanatomormolecule.This“particle”isatrestinourframeof reference. Suppose that this particle emits a photon of wavelength λγ. This photon hasmomentump h/λγ. Therefore the emission of this photon imparts the samemagnitude ofmomentum to the emitting particle but in the opposite vector direction recoil . Now, the


particleismovingrelativetoourframeofreference.WhatisthedeBrogliewavelengthoftherecoilingparticleinourframeofreference?λd h/psetp h/λγλd λγTherefore,weobtaintheveryinterestingresultthatthedeBrogliewavelengthoftherecoilingparticleequalsthewavelengthoftheemittedphoton.InAppendixAofchapter1itwasproventhataconfinedphotonwithaspecificenergyexhibitsthesameinertiaasafundamentalparticlewiththesameenergy.AnotherwayofsayingthisisthataparticlewithdeBrogliewavelengthλd exhibits the same magnitude of momentum as a photon with the same wavelength.Furthermore,inchapter1wesawthesimilaritybetweendeBrogliewaveswithwavelengthλdand the propagating interference patterns with modulation wavelength λm. Impartingmomentump h/λγtoeitherafundamentalparticlewithComptonwavelengthλcoraconfinedphotonwiththesamewavelengthwillproducetheresult:λd λm λγ.Therefore,itisproposedthatthisoffersadditionalsupporttothecontentionthatfundamentalparticlesarecomposedofaconfinedwaveinspacetimewithawavelengthequaltotheparticle’sComptonwavelengthλc.Intheremainderofthisbookwewilloftenuseanelectroninnumerousexamples.AnelectronhasthefollowingComptonfrequency,ComptonangularfrequencyandComptonwavelength:Electron’sComptonfrequencyνc 1.24 1020HzElectron’sComptonangularfrequencyωc 2πνc 7.76 1020s‐1Electron’sComptonwavelengthλc 2.43 10‐12mElectron’sreducedComptonwavelengthλc 3.86 10‐13m λc c/ωc Radius of a Rotar:Onceweknowtherotar’sfrequencyofrotation,wecancalculatetherotar’sradiusassuming speedof lightmotion.Thecircle inFigure5‐1 is an imaginarycirclewithacircumferenceoneComptonwavelength.TheradiusofthecircleoneComptonwavelengthincircumferenceisequaltotherotar’sreducedComptonwavelengthλc.λc c/ωc λc/2π ħ/mc ħc/EiWhere:,λc reducedComptonwavelength rotar’sradius;λc Comptonwavelength,Ei rotar’sinternalenergyInquantummechanics,thisdistanceλcisthelogicaldivisionwhereaparticle’squantumeffectsbecomedominant. Forexample,afundamentalparticleofmassmcanmovediscontinuouslyoveradistanceλc.Aparticlecangooutofexistence,orcomeintoexistence,foratimeequaltoλc/c.Essentially,thedistanceλcisarotar’snaturalunitoflengthand1/ωcisarotar’snaturalunitoftime.Inchapters6and8itwillbeshownthatthegravitationalandelectrostaticforceexerted by a fundamental particle become much easier to understand when the distancebetweenparticlesisexpressedanthenumberofreducedComptonwavelengthsratherthanthenumberofmeters.


Analysis of the Lobes:Supposethatitwaspossibletofreezethemotionoftherotatingdipoleandexaminethedifferencebetweenthetwolobes.Theslowtimelobe lobeA canbethoughtof as having a proper volume that exceeds the anticipated Euclidian volume as previouslyexplained.Thefasttimelobe lobeB canbethoughtofashavinglesspropervolumethantheanticipatedEuclidianvolume thespatialminimumlobe .Thisconnectionbetweenvolumeandtherateoftimeiswellestablishedfortheeffectsofgravity.However,gravityisastaticeffectonspacetime.Thiseffectonspaceproducedbyarotar’sdipolewaveinspacetimeresultsinthedistancebetweentwopointsontheComptoncirclechangingslightlyasthedipolerotates.


Similarly,ifitwaspossibletofreezetherotationwewouldfindadifferentrateoftimebetweenthetwolobes.Sincethelobesarealwaysmovingatthespeedoflight,theeffectisthattherateoftimefluctuatesatapointontheComptoncircle radius λc andthedistancebetweentwopointsontheComptoncirclealsofluctuates.Allquantizeddipolewaveshavemaximumspatialdisplacementamplitudeequal to Plancklength Lp as the quantumdipole rotates. To illustrate this concept, imagine two pointslocatedontheComptoncircleofFigure5‐1separatedbyacircumferentialdistanceequaltoλcseparatedbyoneradian .AsthelobesrotatetheymodulatevolumeandresultintheseparationdistancebetweenthesetwopointsincreasinganddecreasingbyPlancklength Lp .Figure5‐3isagraphofthespatialeffectproducedbytherotatingspacetimedipole.Infigure5‐3the“Y”axisisthespatialdisplacementproducedbytherotatingdipolebetweenthesetwopointsLp .The“X”axisislengthinunitsofλc.Itshouldbenotedthatthe“Y”axisisaboutafactorof

1023 smaller scale than the “X” axis ifwe presume that λc is an electron’s reducedComptonwavelength λc 3.86 10‐13mandLp 1.6 10‐35m .Figure5‐4isagraphofthetemporaleffectoftherotatingspacetimedipole.ItwaspreviouslystatedthatinFigure5‐1wecanconsiderlobe“A”asexhibitingarateoftimeslowerthanthelocalnormandlobe“B”asexhibitingarateoftimefasterthanthelocalnorm.Toillustratethisconceptfurther,wewill imagineathoughtexperimentwhereweplaceahypotheticalperfectclockatapointonthecircumferencepreviouslydesignatedthe“Comptoncircle”inFigure5‐1.Previouslyweimaginedfreezingtherotationofthedipole.Nowinfigure5‐4weimaginehavingthedipolerotateandwearemonitoringthetimeatonlyonepointontheimaginaryComptoncircleandcomparingthistoa“coordinateclock”atanotherlocationinflatspacetime.Theclockmonitoringapointontheedgeofthedipolewillbecalledthe“dipoleclock”.AslobesAandBrotatepastthedipoleclocklocation,thedipoleclockwouldspeedupandslowdownrelativetothecoordinateclockthatisunaffectedbytherotatingdipole.Bothclocksarestartedatthesamemoment.Inflatspacetime,wewouldexpectbothclockstoperfectlytrackeachother.Figure5‐4plotsthetemporaldisplacementofspacetimeproducedbytherotatingdipolewave Yaxis versustimeasexpressedinunitsof1/ω Xaxis .Forexample,anelectronhasangularfrequencyofωc 7.76 1020s‐1.Therefore,foranelectron1/ωc 1.29 10‐21s.Ascanbeseeninfigure5‐4thedipoleclockspeedsupandslowsdownrelativetothecoordinateclock. The maximum time difference between the two clocks is plus or minus PlancktimeTp ~5 10‐44 s .Thismaximumtimedifference isaquantummechanical limit foradisplacementofspacetimethatisundetectable.Thisoscillationoftherateoftimeiswhathasbeencalled“dynamicPlancktimeTp”.Figure5‐4onlyshowswhathappensduringashorttimeperiod ~10‐20s afterstartingthedipoleandcoordinateclocks. Thetimedifferenceoveralongertimewillbediscussedinalaterchapterandshowntoresultinanetreductionintherateoftime.


Strain Amplitude – Aβ:Thestrainamplitudeofthewavedepictedinfigures5‐3and5‐4isjustthemaximumslopeofthesewaves.Thedashedlineinfigure5‐3representsthemaximumslopewhichoccurswhen thesinewavecrosseszero.Thismaximumslopecanbeadimensionlessnumberif the“X”and“Y”axishavethesameunitswhichcancelwhenexpressingslope. Forexample,infigure5‐3boththe“X”and“Y”axishaveunitsoflength.Themaximumdisplacementis one unit of Planck length Lp 1.6 10‐35m . The “X” axis is length units expressed asmultiplesofλc.Foranelectronλc 3.86 10‐13m.ThemaximumslopeoccursatY 0.Themaximumslopeinfigure5‐3isLp/λc.Thisdimensionlessmaximumslopewillbedesignatedthe“rotar’sstrainamplitude”anddesignatedwiththesymbolAβ.Therefore,onewayofexpressingarotar’sstrainamplitudeiswiththeratiooflengths:Aβ Lp/λc strainamplitudeexpressedwithlengthratioFigure5‐4issimilartofigure5‐3exceptthat5‐4ischaracterizingtheeffectontherateoftime.TheYaxisofthisfiguredepictsthedifferencebetweenthedipoleclockandthecoordinateclockshortlyafterwestartbothclocks.Thisdifferencebetweenclockscanreach Plancktime Tp .The “X” axis of figure 5‐4 is in units of time expressed as 1/ωc which for an electron is1/ωc 1.29 10‐21s.ThestrainamplitudeAβofthedipolewavecanalsobeexpressedusingtimerelatedsymbols:

Aβ ωc/ωp TpωcstrainamplitudeexpressedusingfrequencyandtimeThereforethedipolewavesstrainamplitudecanbeexpressedeitherasastrainofspace Lp/λc or as a strain in the rate of time ωc/ωp Tpωc . For an electron λc 3.86 10 ‐13m andωc 7.76 1020s‐1.Therefore,anelectron’sdimensionlessstrainamplitudeis:Aβ 4.18 10‐23.Thiswillbediscussedinmoredetailinthenextchapter. OtherrotarshavedifferentstrainamplitudesbecausetheyhavedifferentComptonangularfrequenciesanddifferentvaluesofλc.Notethatthesinewavesinfigures5‐3and5‐4areshiftedbyπradians 180° .Thisisbecausethelobewithmaximumpropervolumecorrespondstothelobewiththeminimumrateoftimeandviceversa.Conceptual Examples of Wave Amplitude: Therotarmodelisbasedontheseaofvacuumfluctuationsthatformspacetimebeingdynamicallystrained.Itisimportanttohaveamentalpictureof the incrediblysmalldisplacementsof timeandspacerequired for thismodel. Forexample,foranelectronAβ 4.18 10‐23whichistheratioofLp/λcorTpωc.Thisspatialstrainofthespacetimefieldcausestheorbitsofthetwolobestoexhibitdifferencesincircumferenceand radius comparable to Planck length. This is really equivalent to having one of the lobesexceed theelectron’s rotar radiusbyPlanck lengthand theother lobe is less than theRotarradiusbyPlancklength.Thismeansthatthelobesarenotexactlysymmetrical.Actually,theveryconceptofadipoleimpliesthattheremustbetwodifferent opposite propertiesthatare


interacting. With electromagnetic radiation, a dipole oscillator has a positive and negativeelectricalcharge.Similarly,aspacetimedipolehastwolobeswhichproduceanoppositetypeofspatialdistortion bigandsmall ofthepropertiesofspacetimeortheoppositetypeoftemporaldistortion fastandslow ofthepropertiesofspacetime.Plancklengthissosmallthatitishardtoimaginetheverysmalldistortionofspacetimerequiredtomakeanelectronaccordingto theproposedmodel. Wewilluse the followingexample toillustrate this incredibly small difference between the two lobes. Suppose we compare anelectron’stotheradiusofJupiter’sorbit.StretchingspacebyPlancklengthoveradistanceequaltoanelectron’sRotarradiusproducesastrainofabout4.2 10‐23. 1.6 10‐35/3.9 10‐13 410‐23 . StretchingJupiter’sorbitalradius 7.8 1011m by3.3 10‐11mwouldproducea

comparablestraininspace.Toputthisinperspective,theBohrradiusofahydrogenatomis~5.3 10‐11m.NowimagineaspherethesizeofJupiter’sorbit,exceptthatonehemispherehasstrained spacetime such that the radius exceeds theprescribed radiusbyadistance roughlyequaltotheradiusofahydrogenatom.Theotherhemisphereislessthantheprescribedamountby the radius of a hydrogenatom a4 10‐23 volumedifference . Of course, the transitionbetweenthetwolobesisnotanabruptstep.Thissimplifiedexampleismeanttoillustratethevery small distortion of the spacetime field involved in the spacetime‐based model of afundamentalparticle.Continuingwiththeexample,supposethatweweretocomparetherateoftimebetweenthetwolobesofanelectron. Suppose that itwaspossible tostop therotationand insertaperfectlyaccurateclockintothefastlobeofanelectron atdistanceλc andinsertasecondperfectclockintotheslowlobe.Therateoftimedifferenceissosmallthatitwouldtakeabout50,000timeslongerthantheageoftheuniversebeforethetwoclocksdifferedintimebyonesecond.Thisratiointherateoftimeisalsoabout4 10‐23.Inchapter6wewillanalyzethisspacetime‐basedmodeloffundamentalparticlestoseeifthemodelplausiblyyieldsthecorrectenergy,angularmomentum,gravity,etc.However,theaboveexamplesbegintogiveafeelforhowparticlescanappeartobenebulousentitieswhichresultintheir counter intuitive quantum mechanical properties. Rotars made from small amplitudewavesinthespacetimefieldcanbedifficulttolocateexactly.Furthermore,apropertywillbeproposedlaterthatpermitsquantizedwavesinthespacetimefieldtorespondtoaperturbationasasingleunit.Thisgives“particle‐like”propertiestoaquantizedwaveinspacetimeandgivesrisetothefamouswave‐particlepropertiesinnature.Solitons: Whydo a few combinations of frequency and amplitudeproduce resonances thatresult in fundamental particles and all other frequencies and amplitudes not producefundamentalparticles?Theremustbeacombinationofpropertiesofspacetimewhichachievestabilitybycancelinglossatthefewfrequenciesthatformfundamentalparticles.Thereappearstobeasimilaritybetweentheconditionsthatformastablerotarandtheconditionsthatforma


stableopticalsoliton.Anopticalsolitonisformedwhenaveryshortpulseoflaserlightisfocusedintoatransparentmaterialthatexhibitsasetofcomplementaryopticalcharacteristics.OneofthesecharacteristicsistheopticalKerreffect.Aspreviouslymentioned,thisisanonlineareffectinalltransparentmaterialswherethespeedoflightisdependentonintensity.Thisnonlineareffectisalsowavelengthdependent.InsomeopticalmaterialsthedispersionoftheopticalKerreffect can be offset against the optical dispersion of the transparent material. These twopropertiescaninteractinawaythatconfinesratherthandispersestheenergyinthepulseoflaserlight.Thedispersionisalossmechanismforapulseoflaserlight.Thecombinationofthetwodifferenttypesofdispersionplustheintensitydependencetogethercancreateastabilitycondition.Apulseoflaserlightformsapropagatingwavethatfulfillsthisstabilityconditionandthiscombinationofeffectsshapethepulseoflightintoan“opticalsoliton”.Theterm“soliton”isaself‐reinforcingwavethatmaintains itsshapeas itpropagates. Thefirst identifiedsolitonswerewaterwaves propagating in a channel. Optical solitons can exhibitmany particle‐likeproperties.Forexample,twoopticalsolitonspropagatingneareachothercanattractorrepeleachotherdependingontherelativephaseofthelight. Awonderfulvideoisavailableatthefollowingwebsiteshowingparticle‐likeinteractionsofopticalsolitons5.Thecharacteristicsof thespacetime fieldappear to formasimilar losscancellation for the3chargedleptons.Thesearefundamentalparticleswithrestmassthatcanexistinisolation.Thestability of any rotars depends on the existence of vacuum energy, but theremust be a fewfrequenciesandconditionswherethestabilizationisoptimum.Thisisequivalenttoapulseoflightsatisfyingthesolitonconditioninatransparentmaterial.Theanalogytoopticalsolitonscanbeextendedifafundamentalparticleisvisualizedaspropagatingalongthegeodesicatthespeedoflight.DiracEquation:Inhis1933NobelPrizelecture,PaulDiracsaidthefollowing:“Itisfoundthatanelectronwhichseemstoustobemovingslowly,mustactuallyhaveaveryhighfrequencyoscillatorymotionofsmallamplitudesuperposedontheregularmotionwhichappearstous.Asaresultofthisoscillatorymotion,thevelocityoftheelectronatanytimeequalsthevelocityoflight.Thisisapredictionwhichcannotbedirectlyverifiedbyexperimentsincethefrequencyoftheoscillatorymotionissohighandtheamplitudeissosmall.”PerhapswhenDiracgavehislecturehewasvisualizingapointparticleundergoinganoscillatorymotionatthespeedoflightandattheComptonfrequency.However,theDiracequationdoesnotspecifyapointparticle.ItisproposedthattherotarmodelofanelectronactuallyisabetterfittotheDiracequation.Aparticlewithrestmasscannotpropagateatthespeedoflight.Also,suchamovingparticlewouldexceedtheconditionsoftheuncertaintyprincipleanditshouldbepossibletodoanexperimentthatwouldrevealthisinternalstructure.Theproposedmodelisadipolewaveinspacetimewhichnaturallypropagatesatthespeedoflight.ThedisplacementamplitudeofthiswaveisPlancklengthandPlancktimewhichmeets

5 http://www.sfu.ca/~renns/lbullets.html


theconditionofbeinganundetectableamplitudeeventhoughthephysicalsizeofthemotionhastherelativelylargeradiusofλc.Finally,thedipolewaveinspacetimeismodulatingtherateoftime and proper volume which gives it the ability to produce curved spacetime in thesurroundingvolume discussedlater .

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Chapter 5 Spacetime Particle Modelonlyspacetime.com/Chapter_5.pdf · This is the structure of the spacetime ... Even though 10113 J/m3 is an incredibly large ... electrons and quarks