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Chapter12

Bonds,Quarks,GluonsandNeutrinos

Introduction: Thischapterlumpstogetherseveraldifficultsubjectsnotpreviouslycovered.Theseincludebonds,theψfunction,quarks,gluons,theweakforceandneutrinos.Mostoftheseare not clearly understood in mainstream physics. This vagueness prevents plausibilitycalculationstotestthespacetimemodelinvolvingthesesubjects.Forexample,quarksdonotexist in isolation, so their properties are alwayspartly hidden. Even theirmass/energy is amystery.Perhapsthemostshockingconclusionisthatthespacetimebasedmodelinitscurrentstateofdevelopmentdoesnotneedgluons. Aspreviously explained, there isonlyone trulyfundamental force therelativistic force andthis forceisalwaysrepulsive. Thissingleforceappearstobecapableofgeneratingaforcewiththestrengthandbondingcharacteristicsofthestrong force. With thisbondingaccomplishedbyan interactionwith thespacetime field,aregluons required? Color charge is another property currently assigned to gluons, but thepropertiesrequiringcolorchargecanprobablybeexplainedasaninteractionbetweenquarksrotars andthespacetimefield.Theeliminationofgluonsisapreliminaryconclusionthatneedstoberefinedandperhapsmodifieduponfurtheranalysis.Thisisthelastchapterthatdealswithparticlesandforcesbeforeswitchingtocosmology.Thesubjectswiththegreatestunknownsarelumpedintothischapter.Virtual Photons Examined: The standard model considers the electromagnetic force to betransferredbetweenpointparticlesbytheexchangeofvirtualphotons.Thisraisesinterestingquestions.Wheredoesthelossofenergyoccurwhenanelectronisboundtoaproton?Itisnotsufficienttosaythatthereisareductionintheelectricfield.ThevirtualphotonsAREtheelectricfield.Dothevirtualphotonsthatsupposedlybondoppositelychargedparticlespossessnegativeenergy? nosuchthing–onlytheabsenceofpositiveenergy Doesaprotonboundinahydrogenatomhavemoreorlessvirtualphotonssurroundingitcomparedtothesameprotoninisolation?Whatisthewavelengthofavirtualphoton?Thesequestionsareintroducedtoraisesomedoubtsaboutvirtualphotonsandthegenerallyacceptedexplanations.The spacetimemodel of the universe proposes that there are no virtual photonmessengerparticles. Thesearereplacedby fluctuationsof thespacetime fieldwhichexertpressure.Allrotarspossessan“externalvolume”ofstandingwavesandnon‐oscillatingstraininspacetimepreviously discussed. The external volumes of interacting rotars overlap. Two oppositelychargedrotarsinteractinawaythatdecreasestheComptonrotationalfrequencyofeachrotarωcisreduced .Thelocationofthelostenergyiseasytoidentify.Alsotheoverlappingexternalvolumesaffectthepressureexertedonoppositesidesofarotarbyvacuumenergy.Thispressure


differencedistributedovertherotar’sareacausesanetforce.Ifarotarisfreetomove,thereisanetmigrationoftherotationalpathofeachrotartowardstheoppositelychargedrotarwitheachrotation.Weconsiderthisforceandmigrationtobeelectromagneticattraction.Electrons Bound in Atoms:IntheBohrmodelofahydrogenatom,theelectron’s1sorbital thelowestenergylevel isdescribedashavingaradiusofao ħc/Eeα 5.3 10‐11m. Alsotheorbitalangularmomentumof theelectron’s1sorbital isħaccording to theBohrmodel.Thecombinationofthisradiussizeandthisangularmomentumcorrespondstotheelectronhavingvelocityofv αc about137timesslowerthanthespeedoflight .ThedeBrogliewavelengthforanelectronatthisvelocityisλd 2πao.ThismeansthatthedeBrogliewavelengthequalsthecircumferenceof thisBohrorbit. This isanappealingpicture,butaccordingtoquantummechanics,theBohratommodelisanoversimplification.

Figure12‐11showsthegraphandthe3dimensionalplotrepresentingtheψfunctionofthe1sorbitalofanelectroninahydrogenatom.Squaringthisψfunctiongivestheprobabilityoffindingtheelectron.Forthe1satomicorbital,thepeakcorrespondstothelocationoftheprotoninthehydrogenatom. Thecloserweprobetotheproton,thehighertheprobabilityoflocatingtheelectron.Thisplot,obtainedfromtheSchrodingerequation,looksnothinglikewhatmightbeexpectedfromtheBohrmodel.Thereisnoexclusiveorbitwithradiusao.Thereisnonetorbital

1 Mark J. Winter http://winter.group.shef.ac.uk/orbitron/


angularmomentum.Theonlyangularmomentumofthisorbitalisthe½ħangularmomentumoftheelectron.

Figure12‐2issimilartofigure12‐1exceptfigure12‐2showstheΨfunctionandprobabilityoffindinganelectronthatisinthe2porbitalofahydrogenatom.Tounderstandthesefiguresintermsofthespacetimewavemodelofrotars,itisnecessarytoexaminetheΨfunction.Ψ Function: It is an axiom of quantum mechanics that the ψ function has no physicalsignificance;onlythesquareoftheψfunctioncanbephysicallyinterpretedasrepresentingtheprobabilityoffindingaparticle. It isproposedherethatthespacetimewavemodelofrotarsdoesgiveaphysicalmeaningtotheΨfunction.Thisphysicalmeaningiseasiesttoexplainbyreturningtothehypotheticalexampleofa“particleinabox”.Inthisexercise,studentscalculatewhatwouldhappenifaparticlewasplacedinasmallcavitysurroundedbyimpenetrablewallsaninfiniteenergywell . Therearenosuchcavities,butifthereweretheparticle’squantummechanicalpropertieswouldbeexhibited.Theparticlecanonlypossessafewspecificpositiveenergiescorrespondingtoafewspecifickineticenergieswhichproducewavenullsatthewalls.Furthermore, theparticle canneverbe stationarywithin the cavity neverhave zerokineticenergy .


Ifthe“particle”isarotarwiththeexternalvolumewavestructureproposedinthisbook,thenitis conceptuallyunderstandablewhy the “particle”musthaveawavestructure thatproducesnullsatthewalls.Inthisexample,asingleparticlemovingrelativetotheboxproducesasinglestandingwavepatternwithnullsatthewalls.Thisstandingwavepatternconsistsoftwowavefrequenciespropagatinginoppositedirections.Thesetwocounterpropagatingwavesalwayspossessmoreenergythananisolatedparticlethatisnotconfined.The“particleinabox”thoughtexperimentisanidealizedthoughtexperimentsinceinnaturetherearenocavitiessurroundedbyimpenetrablewallscreatinganinfiniteenergywell.Ifsuchacavityexisted,thequantummechanicalpropertiesofaparticle rotar trappedinsidewouldberevealed.Inorderfortherotartomeettheseboundaryconditionsimposedbythewalls,itisnecessary for the rotar to possess slightly more energy than an isolated rotar. Recall thatattraction bonding involves a loss of energy and hypothetical repulsive bonding, such as aparticleinabox,requiresagaininenergy.Inorderfortherotartoachievezeroamplitudeatthetwo100%reflectorsof thebox, it isnecessary fortwospacetimewavefrequenciestobepresentratherthanthesingleComptonfrequencyofanisolatedrotar.


Figure12‐3showstheconventionaldepictionofonepossibleΨfunctionofaparticletrappedina smallboxwith impenetrablewalls. Different resonantmodesarepossible, soa three loberesonanceischosenforeaseofillustration.NotethattheΨfunctionrepresentedinfigure12‐3hasbothpositiveandnegativevalues aboveandbelowthezeroline .QuantummechanicsdoesnotgiveaphysicalmeaningtotheΨfunction.OnlythesquareoftheΨfunctioncanbephysicallyinterpretedastheprobabilityoffindingaparticle.TherotarmodelgoesagainstthisconventionandgivesaphysicalmeaningtotheΨfunction.

The ψ function of a bound rotar is the wave envelope of the waves in spacetime that form the rotar. Figure12‐4showsthespacetimewaveinterpretationoftheΨfunctionofaparticleinabox.Wewillreinterprettheparticleinaboxtoarotartrappedbetweentwohypotheticalbarriersthatare 100% reflectors for waves in spacetime. The box is essentially a repulsive type ofconfinement. Placingarotarinarepulsiveconfinementrequiresthatenergybeaddedtotherotarinexcessoftheenergythatarotarwouldhaveifitwasisolated.Thisaddedenergyshowsupintherotarhavingtwofrequencies onehigherandonelowerthantheComptonfrequency .TogethertheyaveragemorethantheComptonfrequencyofanisolatedrotar.


Placingarotarinsuchacavitychangestherotar’sboundaryconditionscomparedtoanisolatedrotar.Inorderfortherotartomeettheconditionofzeroamplitudeateachofthetwo100%reflectors,therotarmustpossesstwofrequenciesthatarebothpropagatingtotheleftandrightin figure 12‐4. These two frequencies traveling both directions produce the “stationary”standingwavepatternshowninthisfigure.ThispatternlookssimilartothedeBrogliewavespreviouslyshown.However,deBrogliewaveshavethewaveenvelopemovingfasterthanthespeedoflightwhilethewaveenvelopeshowninfigure12‐4isstationaryinthesensethatitsnodesandantinodesdonotmove.Next,wewillreturnbacktothehydrogenatomthathasitselectroninthe1sorbitaldepictedinfigure12‐1. Theelectronandprotonareboundtogetherbyattraction. Thecombinationlost13.6eVenergywhentheywentfrombeinganisolatedelectronandprotontobeinganelectronboundinthe1sorbitalofahydrogenatom.Newfrequencieswereintroducedtotheelectronand the proton’s quarks in this bonding process so that the average frequency of thiscombinationislessthanthesumoftheComptonfrequencyofanisolatedelectronandisolatedproton.Alltheorbitalsofanelectroninahydrogenatomhaveawavestructurethatinvolvestwoormorefrequencies.Thetotaloftheenergyisequaltothecombination’senergyinisolationminus the energy lost to form thehydrogenatom in thedesignated orbital. Orbital angularmomentumalsohasawaveexplanation that involveswavesof slightlydifferent frequenciespropagatinginoppositerotationaldirectionsaroundtheproton.Thisisanalogoustothewaveshavingarotatingframeofreference.WhiletheBohratommodelhasbeenreplacedbythequantummechanicalmodel,thepointisthatthesuperpositionofcounterpropagatingwavesinthespacetimefieldtravelingatthespeedoflightcanachievethedesiredorbitalangularmomentum.Itisproposedthatitisgoingtobepossibletocombinethespacetimewavemodelwiththequantummechanicalatomicmodeltogiveaconceptuallyunderstandablemodelofanatom.Themechanismthateliminatesenergyloss radiationloss fromanatomisunknown,butpresumablyitissimilartothemechanismproposedforstabilizingisolatedrotars.Thisexplanationleavesalotofquestionsunanswered.Perhapsthemostobvious:Istherestillarotatingdipolerotarvolumeburiedsomewherewithintheboundelectron’slobes?Theelectronretains its½ħangularmomentuminadditiontoorbitalangularmomentumpresent inmostatomicorbitals.Further insightsclearlywill involve themarriageofquantummechanicsandimprovedversionsofthespacetimewavetheoryofrotars. Thedifferenceinthespectrumofhydrogenanddeuteriumisduetothedifferenceintheamountofnutationthetwodifferentmassnuclei experience. This seems to indicate that the electron retains a substantial amount ofconcentratedinertiawithintheelectroncloudthatiscausingthenucleustonutate.


Thereasonforbringinguptheparticleinaboxexercisenowistomakeapointaboutboundparticles.Thislessoncreatestheerroneousimpressionthatboundparticlesinnaturecanalsopossessapositivebindingenergy theboundstateismoreenergeticthantheunboundstate .Theparticleinaboxexercisedescribeswhatwouldhappenifaparticleissurroundedbywallsthatarealwaysrepellingtheparticle.Iamproposingthatinnature,particlesarealwaysboundbyattraction;notconfinedbyrepellingwalls.Electronsinanatomareboundbyattractiontothenucleus.Gravitationalattractionbindsaplanettoastar.Theseareallexamplesof“negativebinding energy”. This means that bound state has lower total energy than the unboundcomponentparts. Anotherwayofsaying this is that theboundstate isanenergywell. It isnecessarytoaddenergytobreakthebond.Fromthis,thefollowingstatementcanbemade:Rotars bound by attraction always possess less energy than the same rotar when it is isolated. Attraction binding energy can be thought of as negative energy.Energyisemittedwhenrotarscombine.Thisseemsveryreasonableandnotcontroversial. However, thisgoesagainstthecommonlyacceptedmodelofagluonwhichisdepictedasapositiveenergybindingmechanism.Thesubjectofgluonsandquarkswillfollow,butfirstIwanttosupportthecontentionthatallotherformsofbindinginnatureisbyattractionforminganenergywell lessenergythantheunboundstate .Inchapter#3wedeterminedthataparticlehasmoreinternalenergyinzerogravitythanwhentheparticleisingravity. Eo ΓEg .Gravitationalpotentialenergyisanegativevaluethatisreferencedtozeroatinfinitedistance.SupposeanobserverusingazerogravityclockmonitorstheComptonfrequencyoftherotarastherotarisrestrainedandslowlyloweredtowardsalargemass. Gravitational energy is removed by the restrainingmechanism as the rotar is slowlyloweredintostrongergravity.TheComptonfrequencyωcoftheloweredrotar,measuredbyazerogravityclock,decreasesasgravityincreasesandmoreenergyisremoved.Thisdecreaseinfrequencyisnotnoticeablelocallybecauseofthegravitationaldilationoftime.Locally,aslowclock isused tomonitor a slowCompton frequency. Thepoint is that gravitationalbondingenergyisnegativeenergy.TheComptonfrequencyofagravitationallyboundrotarislowerthanthe same rotarnot gravitationallyboundwhenboth frequencies aremeasuredusinga clockrunningatzerogravityrateoftime.For another example of a bond reducing energy, an electron and aproton release a 13.6 eVphotonwhentheybecomeelectromagneticallyboundtogethertoformahydrogenatomwiththeelectroninthelowestenergylevel. Thisreleasedenergyrepresentsthenegativebindingenergyofthehydrogenatom.Itispossibletogoonestepdeeperinunderstandingthisnegativebindingenergy.AnisolatedelectronhasaComptonfrequencyofabout1.24 1020HzandtheCompton frequencyof aproton sumof all components is about2.27 1023Hz. Whenanelectronandaprotonareboundtogethertoformahydrogenatom,thesumofalltheComptonfrequenciesisabout3.3 1015Hzlessthanthewhentheelectronandprotonwereisolated.This


differenceof3.3 1015Hzisthefrequencyofthe13.6eVphotonreleasedwhenthehydrogenatomformed.Thereforeitispossibletoseethedifferenceinenergywhenanelectronandprotonareboundtoformahydrogenatom. Tobeperfect,thisexampleneedstoalsoaccountforthesmallamountofkineticenergycarriedawaybythehydrogenatomasitrecoilsfromemittingthephoton. Amoreextremeexample is thebondingofanelectrontoauraniumnucleuswhichhasbeenstrippedofallelectrons.Thisbondingissostrongthatthebondingenergyisequivalenttoabout¼ the mass/energy of an electron. The energy lost when this bonding first takes place isremoved by the emission of one or more gamma ray photons. Isolated particles are moreenergeticthanboundparticles.Thisconceptwilllaterbeappliedtoboundquarkswithsomesurprisingimplications.BindingEnergyinChemicalBonds:Next,anexamplefromchemistry.Thereareafewmoleculessuchasozone O3 andacetylene C2H2 whicharecommonlydescribedasbeing“endothermic”.Thismeansthatstartingwithastandardizedsetofconditionsfromchemistry,ittakesaninputofenergy heat toformthemolecule.Thiswouldseemtoimplythatallendothermicmoleculesformpositiveenergybonds.Theimplicationisthatthisisanexamplewheretheboundstateismoreenergeticthantheunboundstate.Forexample,ozonerequiresaninputofenergywhenitisformedfrommolecularoxygenO2understandardizedconditions.However,weareprobingafundamental question about the nature of bonds. Wemust compare the bound state to theunboundstatewhichinthiscasewouldbeindividualatoms.Ittakes1½moleculesofO2toform1moleculeofO3 writtenas:3O2→2O3 .ToseparateoneoftheO2moleculesintotwooxygenatomstakesabout2.6eV/moleculeor249kJ/mole.Thisgivestheerroneousimpressionoftheboundstatecanbemoreenergeticthantheunboundstate.However,ifweformedozonestartingwith3atomicoxygenatoms,thenthisreactionreleasesenergywhenamoleculeofO3isformed.Similarly, the formation of acetylene is an endothermic reaction if the standardized startingcomponents of graphite andmolecular hydrogen H2 are used. However, the formation ofacetyleneisanexothermicchemicalreactionifthestartingcomponentsareatomiccarbonandatomichydrogen.Infact,therearenoendothermicchemicalreactionsifthestartingmaterialisindividual atoms. Therefore, even chemistry supports the contention that bonds in naturereducetheenergyofthecomponentparts.Inthiscasemoleculesalways possess less energy than the component atoms when the atoms are isolated. Binding Energy of Nucleons:Whileitisverydifficulttomakeenergyandforcemeasurementsinsideaprotonorneutron,wecanobtainahintofwhatisgoingoninsideprotonsandneutronsbylookingatthebindingthatoccursbetweennucleons.Whenprotonsandneutronsareboundtogethertoformatomicnuclei,isthereagainorlossofenergy?Theanswerisobvious.Aheliumatom 4He haslessmass/energythan2deuteriumatoms.Thebindingenergyofnucleonsisanegativeformofenergy energyreductioncomparedtothesumoftheunboundcomponents .Thereisadecreaseinmass lossofenergy whenhydrogennucleifusetoformnucleiofheavier


atoms.Atfirstitmightappearthat235Uandotherheavyatomsareanexceptiontothisrule,butthisisincorrect.Thestrongestboundatomicnucleolusis56Fewithabindingenergyof8.79MeVpernucleon.235Uhasabindingenergyof7.79MeVpernucleonandthisiscomparabletothebindingenergypernucleonofcarbonornitrogen.Breaking235Uapartreleasesenergybecausethetwolighternucleiformedhaveagreaterbindingenergypernucleonthan235U. Agreaterbindingenergymeansthatexcessenergymustbereleaseduponformation. Thepointisthateven 235U has lessmass/energy than the energy of the protons and neutrons that form theuraniumnucleus.Itisproposedthatquarksareboundtogethertoformhadronsbynegativeenergy.Thehadronswouldhavelessenergythanthetotalenergyofthecomponentquarksifthequarkswerestableinisolationsothattheirenergyinisolationcouldbeexperimentallymeasured.

Gluons,QuarksandHadronsBackground: Thepreviousdiscussionasserted that innature theboundstatewasalwaysalowerenergycondition that the individual components in theunboundstate boundstate isalwaysanenergywell .Thisconceptisgoingtobeimportantinthefollowingdiscussionaboutquarksandgluons.Theproblemisthatifwefaithfullydevelopamodeloftheuniversestartingwiththeassumptionthattheuniverseisonlyspacetime,weobtainthestrongforcefromthepressureexertedbythespacetimefield.Thereisnoneedtopostulategluons!Sincegluonsareverymuchapartofmodernparticlephysics,thisseemstopresentaproblemforthespacetimemodeloftheuniverse.However,itwillbearguedherethatallthefunctionscurrentlyattributedto gluons color charge, etc. can be converted to functions attributed to the rotarmodel ofquarksexistinginthepressureexertedbythespacetimefield.Previously we rejected virtual photons as the “messenger particles” that carried theelectromagnetic force and rejected gravitons as the “messenger particles” that carried thegravitationalforce.Thenextremainingvirtualmessengerparticleisthegluonandthisisgoingtobequestioned.Thereisnoexperimentalobservationsthatcanbeinterpretedasbeingproofthatvirtualphotonsorgravitonsexistbutthereissomeexperimentsthatseemtoimplythatgluonsexistalthoughtheyhaveneverbeendirectlyobserved. Alsothereisavastamountoftheoretical calculations thataremodelingeffects thatareattributed togluons.Therefore thediscussionaboutgluonsisgoingtobemorenuanced. Theanalysisofquarksandgluonswillbeginwithadiscussionaboutthemass/energyofquarks.


Mass/EnergyofQuarks: Sincequarksdonotexistintheunboundstate,it isnotpossibletosimplycomparetheenergyofanunboundquarktoaboundquark.ThefollowingisaquotefromanarticleonquarkmasseswrittenbyA.V. Manohar and C.T. Sachrajda2

“Quarkmasses therefore cannot bemeasured directly, butmust be determinedindirectly through their influence on hadronic properties. Although one oftenspeakslooselyofquarkmassesasonewouldofthemassoftheelectronormuon,any quantitative statement about the value of a quarkmassmustmake carefulreference to the particular theoretical framework that is used to define it. It isimportant tokeep this schemedependence inmindwhenusing thequarkmassvaluestabulatedinthedatalistings.Historically,thefirstdeterminationsofquarkmasseswereperformedusingquarkmodels.Theresultingmassesonlymakesensein the limited context of a particular quarkmodel, and cannot be related to thequarkmassparametersoftheStandardModel.”

Iwill expandon this thought somewhat. Suppose that there is anexperimentwhich collidesprotonsandanti‐protonstogetherathighenergy.Thecollisionproducesacomplicatedshowerofparticlesthatishardtointerpret.Ifprotonsareassumedtoconsistofpointparticlequarksplusgluonsandvirtualparticlepairs formingandannihilating, thenthe interpretationof theresultswillbedifferentthaniftheprotonsareassumedtobetherotar‐modelquarkspossessingquantizedangularmomentumcollidinginseaofdipolewavesdesignatedasthespacetimefield.Withthisbeingsaid,wewillfirstlookatthewidelyacceptedinterpretationsofthesecomplicatedexperimentalresults.Thedescriptionofaprotondiffersgreatlydependingontheexperiment.Forexample,inlowenergy collisions, a proton seems to be made of 3 quarks with each quark possessingapproximately1/3oftheproton’senergy.Inhighenergycollisionsaprotonseemstohavemanyquarks over10 witheachquarkpossessingenergyofonlyafewMeV.Wewillexamineeachmodel.Atthelowenergylimitaprotonappearstohaveatotalof3quarks‐twoupquarksandonedownquark.Inthelowenergyconditionthese3quarksarereferredtoas“constituentquarks”.Thetwoconstituent“up”quarksofaprotonappeartohaveenergyof336MeVeach3.Thesingledownconstituentquarkappearstohaveenergyof340MeV.Hereisanotherdescriptionoftheconstituentquarks.

Nonrelativisticquarkmodelsuseconstituentquarkmasses,whichareoforder350MeVfortheuanddquarks.Constituentquarkmassesmodeltheeffectsofdynamicalchiralsymmetrybreaking…Constituentmassesareonlydefinedinthecontextofaparticularhadronicmodel."4

2 Quark Masses Updated Jan 2012 by A.V. Manohar (University of California, San Diego) and C.T. Sachrajda (University of Southampton) http://pdg.lbl.gov/2013/reviews/rpp2012-rev-quark-masses.pdf 3 Griffiths, D., (2008) Introduction to Elementary Particles p. 135, Wiley-Vch 4 "Note on Quark Masses":http://pdg.lbl.gov/2010/reviews/rpp2010-rev-quark-masses.pdf


Thisname“constituentquarks”isusedwhendescribingthemodelthatemergesfromlowenergyexperiments.Thename“currentquarks”isusedtorepresentthequarkmodelwhichisobtainedinhighenergycollisionexperiments.Inhighenergycollisionexperimentsthereappearstobemanymore than3quarks andeachof theseappears tohaveenergyof only a fewMeV. Toreconcile this difference the difference between the low energy and high energy collisionexperiments,the3constituentquarksobservedinlowenergycollisionsareoftenvisualizedasbeingcomposedofacorecurrentquarkwithenergyofafewMeVwhichissurroundedbyeitheraclusterofvirtualparticle‐antiparticlepairsorsurroundedbygluons.Ineithercase,thetotalenergyofwhatisinterpretedtobeaclusterisapproximately1/3oftheprotonenergy.According to theproposed spacetimemodel, theproblemcomes in interpretinghigh energycollisions.Intherotarmodelofahighenergycollision,oneormoreofthe3quarksmomentarilyabsorbsfarmoreenergythantherestenergyofthequark.Recallthepreviousdiscussionofthedifficultydeterminingthesizeofanelectronfromenergeticcollisionsoftherotarmodelofanelectron.Thekineticenergyofthecollisionismomentarilyconvertedintotheinternalenergyoftheelectron rotarmodel .Thiscausestheelectron’sradiustomomentarilydecreasesothatitwasalwaysbelowthedetectablelimitoftheexperiment.Thecollisionofprotonsismorecomplicated,butonethingisclear. Theenergeticconditionswhichprevailatthemomentofcollisionarenotthesameasanisolatedproton.Ifthemodelofaquarkisapointparticle,thenthereisnointernalstructureanditisvalidtoassumethatthequarkretainsitspropertieseveninaviolentcollision.However,ifeachquarkisassumedtohavearotarmodel, thenthis is three“fluffy”rotatingdipolewavesexisting in thespacetime field.They each are a rotating dipole wave in spacetime possessing a quantized unit of angularmomentum.Thisrotatingwaveisdistributedoveravolumeofspace.Addingthekineticenergyofthecollisionmomentarilydecreasesthesizeofaquark.Thischangesthebondingconditionsbutretainsaconstantangularmomentum.Therotarmodelofprotonsisinanearlystageofdevelopmentandcannotpredicttheresultswhichwouldbeexpectedinanenergeticcollision.However, it is possible to imply that the complicated results of energetic collisions can bemisinterpretedifpointparticlequarksandgluonmessengerparticlesareerroneouslyassumed.Thequarksobservedinhighenergycollisionsappeartobeverydifferentfromtheconstituentquarksatthelowenergylimit.Thethree“currentquarks”thatformaprotonappeartohaveenergylessthan10MeV.Inthispictureobtainedfromhighenergycollisions,onlyabout1%oftherestmassofaprotonappearstobeintheformthequarks.Inthiscaseabout99%ofthemass/energy of a proton is therefore assigned primarily to the energy of gluonswith somecontributionfromthekineticenergyofquarks.Inotherwords,thegluonsmustpossesspositiveenergyinthismodel.Morewillbesaidaboutgluonslater.


AlternativeExplanation:Theproposedalternativeexplanationofthemassofaquarkisthatupanddownquarkswouldbeintrinsicallyhighenergyrotatingdipolewavesiftheywerestableinisolation.Theyarestronglyboundtogetherbyaninteractionwiththespacetimefieldwhentheyformhadrons.Therearenoisolatedfirstorsecondgenerationquarksbecausetheysimplydonotattainstabilityasisolatedrotars. Thetopquarkwillbediscussedlater .Whenthismodelofaquarkisboundintoahadronitisinalowenergystate,andeepenergywell.Attemptingtoremovequarksfromahadronagainstthestrongforceincreasesthequark’senergy Comptonfrequency towardsthehigherenergystatewhichwouldexist ifaquark rotarmodel couldexistinisolation.Theenergyexertedinattemptingtoremoveaquarkfromahadronrequiressomuchenergythatanewmeson pion isformedbeforeanisolatedquarkisobtained.Whennewmesons are formed, the binding force between former components of the split hadrondecreasestonearzero.Singlefirstorsecondgenerationquarksareneverproduced.However,toillustratetheconcepts,wewillimaginewhatitwouldbelikeifisolatedquarkswereallowed.Itisproposedhere justifiedlater thatifisolatedupanddownquarksexisted,theywould be rotating dipoleswith energy substantially greater than 400MeV. If up and downquarksexistedasisolatedrotars,thentheywouldshedenergywhentheybondtoformaprotonorneutron.Hadronscomeintoexistencealreadyformedsincethisisthelowestenergystateandtheonlyformthathasstability.However,itisinformativetoimaginethestepsthatwouldoccurifahadronwasformedfromisolatedquarks.Energy of Bound Quarks:Theworkingproposalisthatalltheenergyofaprotoniscontainedinitsthreeboundquarkrotars rotatingdipolewavesinspacetime .However,themodeloftheinteractionofquantizedwavesshouldnotbeequatedtotheexpectedinteractionifthequarkswerehardshelledparticles.Furthermore,itisproposedthatthebindingenergyissogreatthattheboundquarkshavemuchlessenergythantheywouldhaveashypotheticalisolatedrotars.Wewill first survey thehadrons that aremadeofonlyupanddownquarks to compare theenergyoftheupanddownquarksundervariousboundconditions.Thenucleons protonsandneutrons havealmostthesameenergy~938MeV. Ifweassumethatall thisenergycanbetracedtotheenergyof3rotatingspacetimedipoles 3quarks thentheimplicationisthatupanddownquarkshaveaboutthesameenergy.Therearedifferentproportionsofupanddownquarks, yetapproximately the same totalenergy. Wewill assume thatboundupanddownquarksinanucleonhasenergyofabout313MeV ~1/3ofthetotal .Therearetwootherfamiliesofhadronsthatconsistofonlyupanddownquarks.Thesearethepimesons pions andthedeltabaryons.ThedeltabaryonshavespinofJ 3/2ratherthanthespinof½forthenucleons.Thereare4deltabaryons.Theseare:Δ uuu ;Δ uud ;Δo udd andΔ‐ ddd .


Theseallhaveaboutthesameenergy 1,232MeV thereforetheupanddownquarksboundinthishadronhaveenergyofabout1/3ofthisvalue:~411MeV.Thepionsconsistofaquarkandananti‐quarksuchasanupquarkandananti‐downquark.Thenetspinofthepionsiszero counterrotatingdipoles .Theenergyofthepionsis139.5MeVforthetwochargedpions π andπ‐ andabout135MeVfortheneutralpion πo .Thismeansthattheupanddownquarksinapionhaveaverageenergyofabout70MeVforthechargedpionsπ andπ‐ andabout68MeVforaneutralpionπo.Thereforewehaveexampleswhereupanddownquarkshaveenergyrangingfrom411MeVto68MeV.ThestandardmodeldealswiththisdifferencebyassumingthatanisolatedupordownquarkhasenergyofonlyafewMeV.Theextraenergyrequiredtoreach68MeV,313MeVor411MeVisassumedtobepredominatelyintheenergyofthegluons.Energy of a Hypothetical Isolated Quark: Theproposed spacetimewavemodelofquarksoffersadifferentanswer. Itsaysthatanisolatedrotarupordownquarkwouldhaveenergysubstantiallygreater than411MeV.Whenquarksarebound intoahadron, thebondsaresostrongthatalargepercentageofthehypotheticalisolatedenergyislost.Itwouldberadiatedawayifitwaspossibletodothisexperiment.Thedifferencebetweenthe68MeV,313MeVor411MeVreflectsdifferentamountsofbindingenergy.Thebindingenergypernucleonin56Ferepresentsapproximately1%ofaproton’senergy.Anelectronboundtoauraniumatom’snucleolusstrippedofallotherelectronshasabindingenergythatisabout25%ofanisolatedelectron’senergy.Inorderforanelectrontoattachtoastrippeduraniumatomnucleolus,ithastoemitoneormoregammarayphotonstoshedatotalofabout25%of theelectron’senergy.Actuallypartof the lostenergycomes fromtheprotons in thenucleus,butthatisoffthesubject.Itisproposedthatthebindingenergyofquarksinahadronismuchgreaterthantheseexamples.Toillustratethisconcept,wewillchooseanenergysubstantiallylargerthan411MeVfortheenergyofahypotheticalunboundupordownquark.Forillustration,wewillusethenumberofabout600MeVfortheenergyofisolatedupanddownquarks.Withthisassumption,anisolatedupordownquarkwouldloseabout1/3ofitsenergywhenitformsadeltabaryon 411MeV .Itwouldloseabout½ofitsenergywhenitformsanucleon 313MeV anditwouldloseabout89%ofitsenergywhenitformsaneutralpimeson 68MeV .Electron vs. Proton Size:Beforeproceedingtoofar,itisdesirabletodoacalculationtoseeiftheideasproposedhereareplausible.Wewillattempttocalculatethesizeofaproton.However,firstitisnecessarytorecognizewhyaprotonhasameasurablesizeandanelectrondoesnot.Aprotonhasameasurablesizebecauseaprotonismadeupof3fundamentalrotars.Thethreequarksof aprotondonot respond to ahigh energy collision as a singlequantizedunit. The


propertyofunityonlyexistswithinasinglequantizedwave rotar .Acollisionwithaprotoninvolves speedof light communicationof forcesbetween the threequarksof aproton. Thismeansthattheprotonexhibitsaphysicalsizeinacollisioneventhoughthissizedoesnotexhibitahardboundary.Whenanelectroncollideswithoneofthethreequarksinaproton, itappearsasifthereisacollision between twopoint particles. The reason is the same as previously explained for acollisionbetweentwoelectrons.Boththeelectronandthequarkarequantizedrotatingdipolesinthespacetimefield.Inadirecthit,theybothconvertthekineticenergyofthecollidingelectronto internalenergyof therotatingdipole.Thishappens faster than thespeedof lightbecausepreserving thequantizedangularmomentumresults in thepreviouslyexplainedpropertyofunity.TheconversionofkineticenergymomentarilyincreasestheComptonfrequencyofeachrotar. In order for angular momentum to be conserved, the rotar radius of each rotarmomentarily decreases. The amount of decrease in size makes each rotar experimentallyindistinguishablefromapointparticlebecause aspreviouslyexplained themomentaryradiusislessthantheresolutionlimitsetbytheuncertaintyprinciple.Theothertwoquarksthatwerepartoftheprotononlylearnaboutthecollisionthroughspeedoflightcommunication.Calculation of Proton Radius:Thepresenceofonlythreequantizedwavesmeansthataprotonstillexhibitssubstantialquantummechanicalpropertiessuchasnodefiniteshapeandthelackofahardedge.Alsotheshapeofaprotondependsonthealignmentofthespinsofthequarks.Ananalysis5ofallmeasurementsoftheprotonradiusconcludesamostprobablechargeradiusforaprotonis:0.877 10‐15meter 0.15 10‐15meterWewilldoaplausibilitycalculationtoseeiftheproposedrotarmodelofaprotongivesroughlythe correct size. This calculationwill assume that theproton ismadeof3 rotars, eachwithenergyof313MeV 5 10‐11J .Wemustdecidehowthesethreerotatingdipolesfittogether.Aretherevoidsorexcessiveoverlaps? It isknownthatprotonsarenotnecessarilysphericaldepending on the alignment of the spins of the up and down quarks. Still, the simplestassumptionisasphericalprotonwithquarksthataresointimatelyboundthattheprotonhasthreetimesthevolumeofanindividualrotarquarkwithradius .Theplausibilitycalculationwillassumethissimplifiedmodel.Wewillfirstcalculatetherotarradius ofarotarwithenergyof5 10‐11Joule 313MeV .Thenwewillincreasethisradiusbyafactorof31/3toobtaintheradiusofaspherewith3timesthevolumeofanindividualrotarquark. ħc/Eisubstitute:Ei 313MeV 5 10‐11J 6.3 10‐16meterradiusofonequarkwithenergyof313MeV 31/3 9 10‐16metercalculatedprotonradius 3quarks

5 http://arxiv.org/abs/hep-ph/0008137v1


Theexperimentallydeterminedradiusofaprotonis:8.77 10‐16 1.5 10‐16meter,thereforethecalculatedradiusof9 10‐16meteragreeswithintheexperimentalerror. Thisdegreeofaccuracyisprobablymorethanwedeserveconsideringthecrudenessofthecalculation.Infact,therotarmodelcouldbecorrectforchargedleptonsandtoosimplifiedtobeappliedtoquarkswhicharetightlyboundwithveryrestrictiveboundaryconditions.Still,thecalculationdoesgiveareasonableanswerandcannotbeignored.Thiscalculationcouldeasilyhavebeenoffbymanyordersofmagnitudeiftherotarmodelwascompletelywrong.It isalsointerestingtonotethatthedensityofthequarksintheabovecalculationisroughly5.9 1017kg/m3.Thedensityofthenucleusofanatomwithmanyboundnucleonsissubjecttosomeinterpretation,butisroughly2.3 1017kg/m3.Therefore,thedensityofanatomicnucleusisroughlyhalfthedensityofindividualquarks. Thisisfardifferentfromthestandardmodelthat depicts quarks as point particles and therefore infinitely more dense than an atomicnucleolus.To summarize, the rotarmodelofquarks implies that if quarks couldexist in isolation, theywouldhavesubstantiallymoreenergythantheyhavewhenboundtogethertoformhadrons.Inthiscase,thequarkswouldloseenergy emitphotons whentheyareboundtogethertoformhadrons. Thisresults inanenergywell, just likeallotherbonds innature. Therotarmodeldependsoftheexistenceofthespacetimefieldtostabilizetherotars.Aspreviouslystated,thespacetime‐basedmodelof theuniversehasonlyone truly fundamental force therelativisticforce andthatforceisalwaysrepulsive.Thebondingofthequarksisultimatelytraceabletopressureexertedbythespacetimefield.Gluon Background:Next,wewillexaminegluons.Accordingtothestandardmodel,gluonsareexchangeparticlesthatcarrythestrongforce thestronginteraction betweenquarks.Gluonscarry the color charge and also participate in the strong interaction in addition to being amediatingexchangeparticle.The8typesofgluonshavecolorcharge.Whilethereare3colorcharges red,greenandblue ,gluonscarrycomplexcombinationsofthesecolorcharges.Forexample,adescriptionofoneofthe8possiblegluonsis: red‐antiblue blue‐antired .Gluonsarealsodescribedasmasslessvectorbosonswithspinof1whichhavetwopolarizationstates.The standard model description of gluons is very complex and quantum electrodynamicscalculationsinvolvinggluonsarealsocomplex.According to theory, bonds between quarks become weaker as the distance decreases.Thereforequarksboundinhadronsareinastateof“asymptoticfreedom”.Whenquarksareintheirunperturbedstate, theycanmigratewithin thehadronas if theyarenot tightlybound.However, the asymptotic freedom state only occurs when quarks maintain the prescribeddistancerelative toeachother. If thedistance is increased, thestrong force increases.As theseparationdistanceis increased,energyisbeingaddedtothehadronandtherestoringforce


increases. The added energy supposedly goes into the energy of the gluons. The quarkssupposedly maintain a constant energy of less than 10 MeV.When the separation distancebetweenquarksreachesroughly10‐15m,enoughenergyhasbeenaddedtothegluonstoformanewmeson quark–antiquarkpair andtherestoringforcedropstonearlyzero.Therearethreeproblemswiththis.

1 This gluon bondmodel does not follow the example of the particles possessing lessenergyintheboundstatethantheyhaveinisolation.Itistruethatwecannotobtainanisolatedquarkforcomparison,butthepointisthatthemodelisthateachquarkretainsaconstantenergyasthequarksarebeingseparated.Theworkbeingdonedoesnotgointoincreasingtheenergyofthequarks.Thisisnotatypicalenergywell.

2 The gluons possess positive energy and are traveling at the speed of light. Since theprotonhasenergydensityofabout3 1035J/m3,ifalmostalltheenergyisattributedtogluons this implies that the gluons should exert pressure of at least 1035N/m2. Thepressure of this high gluon energy density should destroy protons, not bind themtogether.Howdothegluonsachieveattraction?

3 Why does the force start at zero and increasewith distance? This is “explained” byphysicistspostulatingthatasthequarksareseparated,thegluonsform“fluxtubes”andthisconcentrationactuallyincreasestheforceofattractioneventhoughthedistanceisincreasing.Whatisthephysicsbehindthisconcept?Whatsuppliestheforcetoconstrainthesizeofthefluxtubes?Dependingonthevolumeofthefluxtubes,theconfinedgluonsshould exert evenmorepressure than1035N/m2. All of this is so far removed fromanythingelseinnaturethatitspeakstotheproblemscreatedtheconceptofgluons.

The experimental evidence for the existence of gluons is that very energetic collisions ofelectrons and positrons sometimes produce “three jet events” a jet is a narrow shower ofparticles .Theexplanationforthesethreejeteventsisthatatleastoneofthethreejetsresultedfromagluon“hadronize”intonormalparticles colorlesshadrons whichresultsinthenarrowshowerofparticlesknownasajet.TheRelativisticForce:Aspreviouslystated,thespacetimemodelhasonlyonetrulyfundamentalforce:therelativisticforce.Thisforceisgeneratedwhenenergy,travelingatthespeedoflight,isdeflectedinsomeway.Forexample,theabsorption,emissionorreflectionofaphotonresultsinthetransferoflinearmomentum.TherelativisticforceFristhenamegivenwhenmultiplelinearmomentumtransferscanbeconsideredtobeacontinuousforce.TheequationisFr Pr/cwherePrisrelativisticpowerpropagatingatthespeedoflight.Therelativisticforceisalwaysrepulsive.Aspreviouslyexplainedtherelativisticforcecanappeartobeanattractingforcewhenthe spacetime field exerts the relativistic force in a way that brings particles together. Forexample,theelectrostaticorgravitationalattractionisactuallytheresultofthespacetimefieldapplyingunequalpressureonrotarsproducinganetforceofattraction.Thisisanintroductionof how the relativistic force also produceswhatwe perceive to be the strong forcewithoutgluons.


All rotars possess energy densitywhich implies that they have internal pressure. The rotarpressureis:ℙr ωc4ħ/c3 Ei/ .Tostabilizethisinternalpressurethespacetimefieldmustexertanopposingpressure.Ifthispressureisbalancedonallsides,thenthereisnonetforce.However,otherrotarsinthevicinityresultinadistortionofthespacetimefieldandthisinturnresultsinanunbalancedpressure anetforce exertedontherotar.Whenthisnetforceisinthedirectionoftheotherrotar,thenwesaythatthereisaforceofattractionbetweenthetworotars.Themaximumforce Fm thatarotarcanexertwaspreviouslyshowntobeFm ℙr / .CaremustbeusedinapplyingthisequationbecauseEiistheinstantaneousinternalenergyandλc is the instantaneous rotar radius. For example, in a collision, the kinetic energy getstemporarilyaddedtotherotar’sinternalenergyEi.ThereforeattheinstantofthecollisionthevalueofEiincreasesandthevalueofλcdecreases.TheresultisthatthevalueofFmisgreaterinacollisionthanthetheoreticalvalueforarotarnotundergoingacollision.Itispossibletodoaroughcalculationofthevalueofthemaximumforcethatthe3quarksthatmakeupaprotoncanexert.Wewillstartbyassumingthattheproton’senergyof938MeVisevenlydistributedamongits3quarks rotars .Ifeachquarkhasenergyofabout313MeVor5 10‐11J,thenthevalueofthemaximumforceavailabletothethreequarksintheunperturbedstateofasymptoticfreedomisaboutFm 80,000N.Thismaximumforcecalculationdoesnotattempt to identifywhether therotarcanactuallyexert thismaximumforce, it ismerely theupperlimit.Inchapter7 thesection titled“AsymptoticFreedom”gave theexplanationofhowthestrongforcecanbezeroattheasymptoticfreedomseparationdistance.Recallthatatthisseparationdistanceopposing forcesbetween thespacetime fieldand the repulsionof adjacentparticlesoffseteachothersothenetforceonaquarkattheasymptoticfreedomseparationdistanceiszero.However,displacingaquarkineitherdirection closerorfurtherfromtheotherquarks produces a net force which attempts to restore the separation to the asymptotic freedomseparation. The energy required to change the separation distance is stored in the quarkincreasingitsrotationalfrequency.Recallthehypotheticalassumptionthatanupordownquarkinaprotonhasabout313MeVbutitwouldhaveenergyofabout600MeVifitcouldexistasastableisolatedparticle.Thisistheenergywellpreviouslydiscussed.Inthisexample,removingaquarkfromaprotonwouldrequireabout300MeVbutapionformsat135MeV,sothishappensfirstandtherestoringforcefallstonearlyzero.Wecandoaroughcalculationtoseeifthismodelisreasonable.Weknowthattheradiusofaproton isabout8.8 10‐16mandpionsare formedwhenaquark isdisplacedbyroughlythisdistance. It ispossibletodoaroughcalculationtoseehowfaraquarkwouldhavetomoveagainstagainstaconstant80,000Nforcebeforeenoughenergywouldbestoredtomakeapion


withenergyof135MeV Ei 2.2 10‐11J ?Theanswerisabout2.7 10‐16m.Thiscalculationrepresentsanunrealisticlowerlimitbecausetheforcewouldnotgofromzeroattheasymptoticfreedomseparationdistance to the fullmaximum forceof80,000Nabruptly. Instead, therewouldbeagradualincreasestartingatzeroandendingatsomeforceprobablylessthan80,000N.Anothersimplifiedcalculationoftheseparationdistancerequiredtomakeapionwouldstartatzeroforceattheasymptoticfreedomseparationandlinearlyincreasetheforceto80,000Natthetotalenergyrequiredtomakeapion.Inthiscasetheseparationdistancewhereapionisformedwouldberoughly5.5 10‐16m. Eventhisoversimplifiedassumptionclearlygivesananswerintherangeofprotonradius.Again,thiscalculationcouldhavebeenoffbymanyordersofmagnitude.GluonsNotNeededforBonding:Thepointofthisdiscussionistosupportthecontentionthatthespacetime‐based model of the universe can explain the strong force using only the singleuniversal force: the relativistic force. The spacetime‐based model of the universe is notdeveloped sufficiently to make predictions about the properties of specific fundamentalparticles.Inparticular,itisnotpossibletosaywhetheragluon‐likeparticlewithspinof1exists.Themainreasonforpostulatingtheexistenceofagluon amessengerparticlethatconveysthestrongforce hasbeenremoved.However,somethingcauses3jeteventsinenergeticcollisionsofelectronsandpositrons. Quantumchromodynamicsassignsadditional functionstogluonsbesidesbeingamessengerparticleandtheseadditionalfunctionsarestillrequired.Therulesofthecolorforcewhichcurrentlyrequire8gluonsmaystillrequire8bosonsbutwithredefinedwave‐basedcharacteristics.Thereforegluonsarenotneededforbonding,butsomeoftheotherfunctionscurrentlyassignedtogluonswillneedtobereinterpreted.Stability of Hadrons:Supposethatweimaginestartingwiththesuperfluidspacetimefieldthatlacks angularmomentum, thenwe introduce one unit of½ħ quantized angularmomentum.Merely stating the amount of angular momentum does not specify the energy, frequency,amplitude,rotationalsize,etc.thatthisangularmomentummighttake.Thespacetimefieldhascharacteristicsthatdeterminewhatcombinationachieveslongtermstabilitysuchasanelectronandwhatissemi‐stablesuchasamuonortauon.Thereisaninfinitenumberofotherpossiblecombinations of frequency, amplitude, rotational size that do not possess any stabilizingcharacteristicsfromthesurroundingspacetimefield.Thesetotallyunstablecombinationslastforonlyaunitoftimeequalto1/ωcwhereωcisthehypotheticalComptonangularfrequency.Forfrequenciesinthegeneralrangeoftheknownparticles,thesurvivaltimewouldberoughlyintherangeof10‐25to10‐20seconds.Thefewcombinationsofangularmomentum,frequency,amplitude,etc.thatachievestabilityaretherareexception.Thisismentionedasanintroductiontoadiscussionofthestabilityofhadrons.Whiletheleptonsarestableorsemi‐stableasindividualrotars,thequarksarenot.Somehowtwoorthreequarksacting together can find stabilitywhere individual quarks do not. Do the hadrons that findstabilityachievethisstabilitybyexhibitingthestandingwavepropertiesofasingleunit?Itis


possibletoanswerthisquestionbylookingatthediffractionpatternofneutronspassingthrougha crystal. The diffraction pattern produced by a neutron 3 quarks implies a de Brogliewavelengththatischaracteristicoftheneutron’stotalmass λd h/mv ratherthanthemassofthethreeindividualquarkswithapproximatelyonethirdthistotalmass.Apparentlythestabilityconditionrequiredforvacuumenergytostabilizeaneutronresultsinfrequency summation in the external volume. In other words, the 3 quarks present in theneutronlosetheirindividualityattheboundaryoftheneutron.Externally,thevacuumenergystabilizesaneutronbytreatingitasasingleunit.ThestandingwavesgeneratedinthevacuumenergyapparentlyareequivalenttoaComptonfrequencycharacteristicoftheentireenergyoftheneutron. ThedeBrogliewavesgeneratedbyaneutron implyasinglewavelengthof thebidirectional standing waves in the neutron’s external volume. Besides neutrons, largercompositeparticlessuchasalphaparticlesandevenentiremoleculesexhibitdiffractionpatternscharacteristic of the total energy. An improved rotar model should address the issue offrequencysummationfurther.Formation of the First Hadrons: The formation of rotars in the Big Bangwas previouslydescribed as a trial and error process where a few combinations of angular momentum,frequency,andamplitudecondensedoutofthechaoticenergeticwavesinspacetimepresentinthe early stages of the Big Bang. It is now proposed that besides single rotating spacetimedipoles,naturealsofoundafewcombinationsofrotatingdipolesthatcouldachievestability.These also condensed out of the energetic waves in the spacetime field as already formedhadrons.Thesourceoftheangularmomentumrequiredtoformquarks,leptonsandphotonswillbeaddressedinchapters13and14.Itwillbeshownthateventhestartingconditionoftheuniverse Planckspacetime musthavepossessedquantizedangularmomentum.Presumablythefirsthadronsthatcondensedoutoftheenergeticwavesinspacetimecreatedbythe Big Bang were highly energetic hadrons made from generation III and II quarks. Theprobable sequence that eventually arrives at the dominance of protons and neutrons in theuniversetodaywillhavetobedevelopedbyothers.W and Z Bosons:SofarthisanalysishasnotmentionedW ,W‐andZbosons.Thereisclearlyalarge bodyof experimental observations that support these particles in the standardmodel.However, like gluons, it is proposed that these bosons have a wave explanation. W and Zparticleshaveħspincharacteristicwhichisnormallyassociatedwithaboson.HoweverWandZparticlesalsohaverestmasswhichisnormallyassociatedwithafermion spin½ħ .Clearlythisismorecomplicatedthanpreviouslyencounteredwithotherfermionsorbosons.Isthereanyothercasediscussedinthisbookwhereaboson spinħ possessesrestmass?Theansweris:yes.Inthefirstchapterwediscussedthecaseofphotonsconfinedinareflectingbox.Photonshaveħspinyetwhentheyareconfinedinsomewaytheyareforcedtohaveaspecific


frameofreferenceandtheyacquirerestmass.Infact,itwaspointedoutthatanytimeaphotonhasenergyofE pc,thephotonwillhaverestmass.Whenaphotonisconfinedbetweentworeflectors it can be thought of as propagating in both directions simultaneously. Sincemomentumisavector,thetwovectorscancelandp 0.Thisconditiongivesthephotonrestmasseventhoughthephotonisaboson.ThereforeevenaphotonpropagatingthroughglassispropagatingatlessthanthespeedoflightinavacuumandE pc.Thepointofthisexampleisthatbosons,withspinħ,canhaverestmassiftheyinteractwithfermions rotars inawaythatresultsinE pc.Apparentlyspacetimeandthehadronstructuremusthaveatypeofresonancethatoccursat1.22 1026s‐1 Wboson80,38GeV and1.39 1026s‐1 Zboson91.19GeV .ImaginetwoquarksactingsomethinglikemirrorsmomentarilyconfiningaWorZboson.WithComptonwavelengthsof1.54 10‐17mand1.36 10‐17m WandZrespectively thesearethesizerangethatplausiblycouldinteractwiththerotarstructureofhadrons.TheWandZbosonswouldhaveastandingwavestructurewhichwouldlooklikestandingwavesinteractingwiththewavestructureofthetwoquarks.ThiswouldgivetheseWorZbosonsrestmassandtheshort range properties normally associated with the weak force. This is not a completeexplanation,butitdoesshowhowthespacetimemodelofforcesandparticlescanaccommodateWandZbosons.Hopefullyotherswillanalyzethisfurther.TheconceptoftheHiggsfieldandHiggsbosonwasoriginallydevelopedto“explain”howWandZbosonsacquiredrestmass inertia .WhileIfavorthepreviousexplanationofhowWandZbosonsacquireinertia,therestofthescientificcommunitycurrentlybelievesthattheHiggsfieldinteractswithWandZbosonsandthatinteractiongivesthemrestmass.Inthespacetimemodeloftheuniverse,thespacetimefieldistheonlyonetrulyfundamentalfield.Multipleresonanceswithin the spacetime field are responsible for all the various particles. These multipleresonancescanbethoughtofasseparatefields.Inthatsense,itispossibletosaythatthereisaHiggs field the sameway that all other particles can be considered to have their own fieldsresonances .SincethespacetimemodeloftheuniversehasnotbeendevelopedsufficientlytomakepredictionsaboutWandZparticles, it isnotpossibletoconclusivelysayhowWandZbosonsobtaintheir inertia. Thereforeit ishypotheticallypossiblethatthemechanismmightincludeaninteractionwiththeHiggsresonance Higgsfield .However,aspreviouslyexplained,fermionsexhibitrestmassthroughthesamemechanismthatconfinedphotonsexhibitrestmass.FermionsdonotrequireaHiggsfieldtoobtaininertia.


NeutrinosNeutrino Introduction: Neutrinos are the least understood of the “fundamental particles”.There are three types or “flavors” of neutrinos electronneutrinos,muonneutrinos and tauneutrinos . These are three flavors are sometimes designated m1, m2 and m3 respectively.Previouslythestandardmodelconsideredneutrinostobemasslessparticlesbutexperimentsprove thatneutrinos can change fromone type of neutrino to another type of neutrino as aneutrinopropagatesthroughspace.This“neutrinoflavoroscillation”isinterpretedasindicatingthatneutrinosmusthavesomerestmass.Thereasoningisthatanythingtravelingatthespeedoflightcannotexperiencetimeandthereforeneutrinoflavoroscillationimpliesthatneutrinosmust be traveling at less than the speedof light. The flavor oscillation data could not giveabsolutevaluesforneutrinomass,butthedatacouldgiveanindicationofthedifferencebetweenthesquareofthemasses6.Forexample,thisdifferencecanbeexpressedas:Δ 7.6 10 eV2 and Δ 2.4 10 eV2. Now there has been the first experimental results whichpurporttogiveanabsolutevalueofthesumoftherestmassofthethreeflavorsofneutrinos7as0.32 0.08 eV. I will interpret this as the average rest mass since the flavor oscillation issequential. This was not a directmeasurement ofmass. Instead it combined cosmologicalmeasurements and a theory of the effect neutrinomass should have on these cosmologicalmeasurements.Therefore,thismeasurementcouldbewrongifthetheoryiswrong.Still,thismass/energyisreasonableandwillbeusedinfurtherdiscussionofneutrinosbothhereandinchapter13.Forexample,usingavalueof0.32eVforthemassofthemuonneutrinoandusingthepreviouslymentionedvaluesof thedifference in the squareof themassesweobtain thefollowing:Anelectronneutrinoshouldbeabout1.2 10‐4eVlessthanamuonneutrinoandatauneutrinoshouldbeabout3.7 10‐3eVlargerthanamuonneutrino.Thereforethisestimateimpliesthatthetauneutrinoisabout1%moreenergeticthantheelectronandmuonneutrinos.Thespacetimewavemodeloftheuniversecanaccommodateneutrinosthathaveasmallrestmass.Thestartingassumption theuniverseisonlyspacetime issorestrictivethatitgreatlynarrowsthepossibilitiesforphysicalmodels.Allparticlesthatexhibitrestmassareproposedtogenerallyhavetherotarmodel.Besidesthedifferenceinmass,thereisobviouslyabigdifferenceinpropertiesbetweenanelectronandanelectronneutrino.Thisimpliesthatthereshouldbeatangibledifferenceinthemodelsofthesetwospacetimeparticles.Thisdifferenceisunknownatthepresenttime.However,sincethemechanismforgivinganeutrinorestmass,energyandangularmomentumis thesameasanelectron,wewillstartbyusingthesamegeneralrotarmodelforanisolated,stationaryneutrinoasforanisolated,stationaryelectron.

6 K. Nakamura et al. (2010). "Review of Particle Physics". Journal of Physics G 37: 1. 7Battye, R. A., Moss, A., Evidence for Massive Neutrinos from Cosmic Microwave Background and Lensing Observations, Phys. Rev. Lett. 112, 051303 (2014)


Modeling a Neutrino:Ifweassumethatthethreeneutrinoshaveenergyintherangeof0.32eV,thisimpliesthatanisolatedneutrinoinitsrestframehasaComptonangularfrequencyofωc 5 1014s‐1andarotarradiusofabout6 10‐7m.Thislargesizeandlowfrequencyforrotarswouldseemtopresentaproblemfortherotarmodelthatcanbeillustratedwithanexample.Amuondecaysintoanelectron,anelectronantineutrinoandamuonneutrino.Themuonhasarotarradiusofabout1.9 10‐15mandaComptonangularfrequencyofabout1.6 1023s‐1.Ifneutrinoshaverestmass,howisitpossibleforthedecayofamuontoproduceneutrinosthatareabout108timeslargerradiusthanthemuon? ~10‐7mcomparedto~10‐15m This apparent incompatibility occurs because we are erroneously comparing the size andfrequencyofisolatedrotarsinarestframewhenweshouldbelookingatthesecharacteristicswhenrotarsareintheverycloseproximitytootherrotarsatthemomentofdecay.Recallthatwhenanelectroncollideswithaprotonoranotherelectron, there isamomentwhenall thekineticenergyoftheelectronisconvertedtointernalenergyoftheelectron.Thismomentarilyincreasestheelectron’sComptonfrequencyandmomentarilycontractsitsrotarradius. A50GeVelectroncollisioncausestheelectrontomomentarilydecreaseitsrotarradiusbyafactorofabout100,000andincreaseitsfrequencybythesamefactor.Itisproposedthataneutrinocreatedinaparticledecay amuondecayforexample isinitiallycreatedinthehighenergy,compressedconditioncharacteristicofacollision.Thisextraenergyisconvertedtotheultra‐relativisticvelocitiesofthethreedecayproductsproducedbythemuondecay. Thiscanbeseen fromthe followingexample:Supposethatwe imaginereversingthedecayprocess. Thedecayproducts consistingof anelectron, anelectronantineutrinoandamuon neutrino would reverse directions and produce a collision that forms a muon. Thiscollisionwouldbehighlyrelativisticandmomentarilyreturnthethreedecayproductstotheirenergetic,compressedstatepresentwhenthemuoninitiallydecayed. Infact, thesumofthefrequenciesofthethreedecayproductsinthecompressedstate beforeseparation wouldequalthemuon’sComptonfrequency.Inthisexplanation,theneutrinoswouldnotdevelopthelargesizeandlowerfrequencyuntiltheyseparatefromtheotherrotarsandeachisviewedinitsrestframe.Almost all the quantized angular momentum in the universe is contained in neutrinos andphotons.Alltheotherleptonsandquarkstogethercontainlessthanonepartin108comparedtoquantizedangularmomentumofphotonsandneutrinos.Thismakesneutrinosanimportantconsideration when examining the evolution of the universe. Therefore, neutrinos will bediscussedagaininchapters13and14oncosmology.