Chapter 12 Bonds, Quarks, Gluons and Neutrinosonlyspacetime.com/Chapter_12.pdf · 2019. 10. 5. ·...
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The Universe Is Only Spacetime ©2012 [email protected] 12-1 Chapter 12 Bonds, Quarks, Gluons and Neutrinos Introduction: This chapter lumps together several difficult subjects not previously covered. These include bonds, the ψ function, quarks, gluons, the weak force and neutrinos. Most of these are not clearly understood in mainstream physics. This vagueness prevents plausibility calculations to test the spacetime model involving these subjects. For example, quarks do not exist in isolation, so their properties are always partly hidden. Even their mass/energy is a mystery. Perhaps the most shocking conclusion is that the spacetime based model in its current state of development does not need gluons. As previously explained, there is only one truly fundamental force ሺthe relativistic forceሻ and this force is always repulsive. This single force appears to be capable of generating a force with the strength and bonding characteristics of the strong force. With this bonding accomplished by an interaction with the spacetime field, are gluons required? Color charge is another property currently assigned to gluons, but the properties requiring color charge can probably be explained as an interaction between quarks ሺrotarsሻ and the spacetime field. The elimination of gluons is a preliminary conclusion that needs to be refined and perhaps modified upon further analysis. This is the last chapter that deals with particles and forces before switching to cosmology. The subjects with the greatest unknowns are lumped into this chapter. Virtual Photons Examined: The standard model considers the electromagnetic force to be transferred between point particles by the exchange of virtual photons. This raises interesting questions. Where does the loss of energy occur when an electron is bound to a proton? It is not sufficient to say that there is a reduction in the electric field. The virtual photons ARE the electric field. Do the virtual photons that supposedly bond oppositely charged particles possess negative energy? ሺno such thing – only the absence of positive energyሻ Does a proton bound in a hydrogen atom have more or less virtual photons surrounding it compared to the same proton in isolation? What is the wavelength of a virtual photon? These questions are introduced to raise some doubts about virtual photons and the generally accepted explanations. The spacetime model of the universe proposes that there are no virtual photon messenger particles. These are replaced by fluctuations of the spacetime field which exert pressure. All rotars possess an “external volume” of standing waves and non‐oscillating strain in spacetime previously discussed. The external volumes of interacting rotars overlap. Two oppositely charged rotars interact in a way that decreases the Compton rotational frequency of each rotar ሺω c is reducedሻ. The location of the lost energy is easy to identify. Also the overlapping external volumes affect the pressure exerted on opposite sides of a rotar by vacuum energy. This pressure
Transcript of Chapter 12 Bonds, Quarks, Gluons and Neutrinosonlyspacetime.com/Chapter_12.pdf · 2019. 10. 5. ·...
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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
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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/
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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 .
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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.
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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.
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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.
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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
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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
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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.
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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
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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.
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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 .
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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
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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
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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
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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.
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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
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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
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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
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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.
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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)
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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.
