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Chapter12 Bonds,Quarks,GluonsandNeutrinos Introduction:Thischapterlumpstogetherseveraldifficultsubjectsnotpreviouslycovered. Theseincludebonds,theψfunction,quarks,gluons,theweakforceandneutrinos.Mostofthese are not clearly understood in mainstream physics. This vagueness prevents plausibility calculationstotestthespacetimemodelinvolvingthesesubjects.Forexample,quarksdonot exist in isolation, so their properties are always partly hidden. Even their mass/energy is a mystery.Perhapsthemostshockingconclusionisthatthespacetimebasedmodelinitscurrent state of development does not need gluons. As previously explained, there is only one truly fundamentalforce therelativisticforce andthisforceisalwaysrepulsive.Thissingleforce appearstobecapableofgeneratingaforcewiththestrengthandbondingcharacteristicsofthe strong force. With thisbondingaccomplishedby an interaction with the spacetime field,are gluons required? Color charge is another property currently assigned to gluons, but the propertiesrequiringcolorchargecanprobablybeexplainedasaninteractionbetweenquarks rotars andthespacetimefield.Theeliminationofgluonsisapreliminaryconclusionthatneeds toberefinedandperhapsmodifieduponfurtheranalysis.Thisisthelastchapterthatdealswith particlesandforcesbeforeswitchingtocosmology.Thesubjectswiththegreatestunknowns arelumpedintothischapter. Virtual Photons Examined: The standard model considers the electromagnetic force to be transferredbetweenpointparticlesbytheexchangeofvirtualphotons.Thisraisesinteresting questions.Wheredoesthelossofenergyoccurwhenanelectronisboundtoaproton?Itisnot sufficienttosaythatthereisareductionintheelectricfield.ThevirtualphotonsAREtheelectric field.Dothevirtualphotonsthatsupposedlybondoppositelychargedparticlespossessnegative energy? nosuchthing–onlytheabsenceofpositiveenergy Doesaprotonboundinahydrogen atomhavemoreorlessvirtualphotonssurroundingitcomparedtothesameprotoninisolation? Whatisthewavelengthofavirtualphoton?Thesequestionsareintroducedtoraisesomedoubts aboutvirtualphotonsandthegenerallyacceptedexplanations. 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 rotarspossessan“externalvolume”ofstandingwavesandnon‐oscillatingstraininspacetime previously discussed. The external volumes of interacting rotars overlap. Two oppositely chargedrotarsinteractinawaythatdecreasestheComptonrotationalfrequencyofeachrotar ωcisreduced .Thelocationofthelostenergyiseasytoidentify.Alsotheoverlappingexternal volumesaffectthepressureexertedonoppositesidesofarotarbyvacuumenergy.Thispressure The Universe Is Only Spacetime ©2012 [email protected] 12-1 differencedistributedovertherotar’sareacausesanetforce.Ifarotarisfreetomove,thereis anetmigrationoftherotationalpathofeachrotartowardstheoppositelychargedrotarwith eachrotation.Weconsiderthisforceandmigrationtobeelectromagneticattraction. Electrons Bound in Atoms:IntheBohrmodelofahydrogenatom,theelectron’s1sorbital the lowestenergylevel isdescribedashavingaradiusof ao ħc/Eeα 5.3 10‐11m.Alsothe orbital angular momentum of the electron’s 1s orbital is ħ according to the Bohr model. The combinationofthisradiussizeandthisangularmomentumcorrespondstotheelectronhaving velocityof v αc about137timesslowerthanthespeedoflight .ThedeBrogliewavelength foranelectronatthisvelocityis λd 2πao.ThismeansthatthedeBrogliewavelengthequals the circumference of this Bohr orbit. This is an appealing picture, but according to quantum mechanics,theBohratommodelisanoversimplification. Figure12‐11showsthegraphandthe3dimensionalplotrepresentingtheψfunctionofthe1s orbitalofanelectroninahydrogenatom.Squaringthisψfunctiongivestheprobabilityoffinding theelectron.Forthe1satomicorbital,thepeakcorrespondstothelocationoftheprotoninthe hydrogenatom.Thecloserweprobetotheproton,thehighertheprobabilityoflocatingthe electron.Thisplot,obtainedfromtheSchrodingerequation,looksnothinglikewhatmightbe expectedfromtheBohrmodel.Thereisnoexclusiveorbitwithradiusao.Thereisnonetorbital 1 Mark J. Winter http://winter.group.shef.ac.uk/orbitron/ The Universe Is Only Spacetime ©2012 [email protected] 12-2 angularmomentum.Theonlyangularmomentumofthisorbitalisthe½ħangularmomentum oftheelectron. Figure12‐2issimilartofigure12‐1exceptfigure12‐2showstheΨfunctionandprobabilityof findinganelectronthatisinthe2porbitalofahydrogenatom.Tounderstandthesefiguresin termsofthespacetimewavemodelofrotars,itisnecessarytoexaminetheΨfunction. Ψ Function: It is an axiom of quantum mechanics that the ψ function has no physical significance;onlythesquareoftheψfunctioncanbephysicallyinterpretedasrepresentingthe probabilityoffindingaparticle.Itisproposedherethatthespacetimewavemodelofrotars doesgiveaphysicalmeaningtotheΨfunction.Thisphysicalmeaningiseasiesttoexplainby returningtothehypotheticalexampleofa“particleinabox”.Inthisexercise,studentscalculate whatwouldhappenifaparticlewasplacedinasmallcavitysurroundedbyimpenetrablewalls aninfiniteenergywell .Therearenosuchcavities,butifthereweretheparticle’squantum mechanicalpropertieswouldbeexhibited.Theparticlecanonlypossessafewspecificpositive energiescorrespondingtoafewspecifickineticenergieswhichproducewavenullsatthewalls. Furthermore, the particle can never be stationary within the cavity never have zero kinetic energy . The Universe Is Only Spacetime ©2012 [email protected] 12-3 Ifthe“particle”isarotarwiththeexternalvolumewavestructureproposedinthisbook,thenit is conceptually understandable why the “particle” must have a wave structure that produces nullsatthewalls.Inthisexample,asingleparticlemovingrelativetotheboxproducesasingle standingwavepatternwithnullsatthewalls.Thisstandingwavepatternconsistsoftwowave frequenciespropagatinginoppositedirections.Thesetwocounterpropagatingwavesalways possessmoreenergythananisolatedparticlethatisnotconfined. The“particleinabox”thoughtexperimentisanidealizedthoughtexperimentsinceinnature therearenocavitiessurroundedbyimpenetrablewallscreatinganinfiniteenergywell.Ifsuch acavityexisted,thequantummechanicalpropertiesofaparticle rotar trappedinsidewould berevealed.Inorderfortherotartomeettheseboundaryconditionsimposedbythewalls,itis necessary for the rotar to possess slightly more energy than an isolated rotar. Recall that attraction bonding involves a loss of energy and hypothetical repulsive bonding, such as a particleinabox,requiresagaininenergy.Inorderfortherotartoachievezeroamplitudeat thetwo100%reflectorsofthebox,itisnecessaryfortwospacetimewavefrequenciestobe presentratherthanthesingleComptonfrequencyofanisolatedrotar. The Universe Is Only Spacetime ©2012 [email protected] 12-4 Figure12‐3showstheconventionaldepictionofonepossibleΨfunctionofaparticletrappedin a small box with impenetrable walls. Different resonant modes are possible, so a three lobe resonanceischosenforeaseofillustration.NotethattheΨfunctionrepresentedinfigure12‐3 hasbothpositiveandnegativevalues aboveandbelowthezeroline .Quantummechanicsdoes notgiveaphysicalmeaningtotheΨfunction.OnlythesquareoftheΨfunctioncanbephysically interpretedastheprobabilityoffindingaparticle.Therotarmodelgoesagainstthisconvention andgivesaphysicalmeaningtotheΨfunction. The ψ function of a bound rotar is the wave envelope of the waves in spacetime that form the rotar. Figure12‐4showsthespacetimewaveinterpretationoftheΨfunctionofaparticleinabox.We willreinterprettheparticleinaboxtoarotartrappedbetweentwohypotheticalbarriersthat are 100% reflectors for waves in spacetime. The box is essentially a repulsive type of confinement.Placingarotarinarepulsiveconfinementrequiresthatenergybeaddedtothe rotarinexcessoftheenergythatarotarwouldhaveifitwasisolated.Thisaddedenergyshows upintherotarhavingtwofrequencies onehigherandonelowerthantheComptonfrequency . TogethertheyaveragemorethantheComptonfrequencyofanisolatedrotar. The Universe Is Only Spacetime ©2012 [email protected] 12-5 Placingarotarinsuchacavitychangestherotar’sboundaryconditionscomparedtoanisolated rotar.Inorderfortherotartomeettheconditionofzeroamplitudeateachofthetwo100% reflectors,therotarmustpossesstwofrequenciesthatarebothpropagatingtotheleftandright in figure 12‐4. These two frequencies traveling both directions produce the “stationary” standingwavepatternshowninthisfigure.ThispatternlookssimilartothedeBrogliewaves previouslyshown.However,deBrogliewaveshavethewaveenvelopemovingfasterthanthe speedoflightwhilethewaveenvelopeshowninfigure12‐4isstationaryinthesensethatits nodesandantinodesdonotmove. Next,wewillreturnbacktothehydrogenatomthathasitselectroninthe1sorbitaldepictedin figure12‐1.Theelectronandprotonareboundtogetherbyattraction.Thecombinationlost 13.6eVenergywhentheywentfrombeinganisolatedelectronandprotontobeinganelectron boundinthe1sorbitalofahydrogenatom.Newfrequencieswereintroducedtotheelectron and the proton’s quarks in this bonding process so that the average frequency of this combinationislessthanthesumoftheComptonfrequencyofanisolatedelectronandisolated proton.Alltheorbitalsofanelectroninahydrogenatomhaveawavestructurethatinvolves twoormorefrequencies.Thetotaloftheenergyisequaltothecombination’senergyinisolation minus the energy lost to form the hydrogen atom in the designated orbital. Orbital angular momentum also has a wave explanation that involves waves of slightly different frequencies propagatinginoppositerotationaldirectionsaroundtheproton.Thisisanalogoustothewaves havingarotatingframeofreference. WhiletheBohratommodelhasbeenreplacedbythequantummechanicalmodel,thepointis thatthesuperpositionofcounterpropagatingwavesinthespacetimefieldtravelingatthespeed oflightcanachievethedesiredorbitalangularmomentum.Itisproposedthatitisgoingtobe possibletocombinethespacetimewavemodelwiththequantummechanicalatomicmodelto giveaconceptuallyunderstandablemodelofanatom.Themechanismthateliminatesenergy loss radiationloss fromanatomisunknown,butpresumablyitissimilartothemechanism proposedforstabilizingisolatedrotars. Thisexplanationleavesalotofquestionsunanswered.Perhapsthemostobvious:Istherestilla rotatingdipolerotarvolumeburiedsomewherewithintheboundelectron’slobes?Theelectron retainsits ½ħangularmomentuminadditiontoorbitalangularmomentumpresentinmost atomic orbitals. Further insights clearly will involve the marriage of quantum mechanics and improvedversionsofthespacetimewavetheoryofrotars.Thedifferenceinthespectrumof hydrogenanddeuteriumisduetothedifferenceintheamountofnutationthetwodifferentmass nuclei experience. This seems to indicate that the electron retains a substantial amount of concentratedinertiawithintheelectroncloudthatiscausingthenucleustonutate. The Universe Is Only Spacetime ©2012 [email protected] 12-6 Thereasonforbringinguptheparticleinaboxexercisenowistomakeapointaboutbound particles.Thislessoncreatestheerroneousimpressionthatboundparticlesinnaturecanalso possessapositivebindingenergy theboundstateismoreenergeticthantheunboundstate . Theparticleinaboxexercisedescribeswhatwouldhappenifaparticleissurroundedbywalls thatarealwaysrepellingtheparticle.Iamproposingthatinnature,particlesarealwaysbound byattraction;notconfinedbyrepellingwalls.Electronsinanatomareboundbyattractionto thenucleus.Gravitationalattractionbindsaplanettoastar.Theseareallexamplesof“negative binding energy”. This means that bound state has lower total energy than the unbound component parts. Another way of saying this is that the bound state is an energy well. It is necessarytoaddenergytobreakthebond.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.Energyisemittedwhenrotars combine. Thisseemsveryreasonableandnotcontroversial.However,thisgoesagainstthecommonly acceptedmodelofagluonwhichisdepictedasapositiveenergybindingmechanism.Thesubject ofgluonsandquarkswillfollow,butfirstIwanttosupportthecontentionthatallotherformsof bindinginnatureisbyattractionforminganenergywell lessenergythantheunboundstate . Inchapter#3wedeterminedthataparticlehasmoreinternalenergyinzerogravitythanwhen theparticleisingravity. Eo ΓEg .Gravitationalpotentialenergyisanegativevaluethatis referencedtozeroatinfinitedistance.Supposeanobserverusingazerogravityclockmonitors theComptonfrequencyoftherotarastherotarisrestrainedandslowlyloweredtowardsalarge mass. Gravitational energy is removed by the restraining mechanism as the rotar is slowly loweredintostrongergravity.TheComptonfrequencyωcoftheloweredrotar,measuredbya zerogravityclock,decreasesasgravityincreasesandmoreenergyisremoved.Thisdecreasein frequencyisnotnoticeablelocallybecauseofthegravitationaldilationoftime.Locally,aslow clock is used to monitor a slow Compton frequency. The point is that gravitational bonding energyisnegativeenergy.TheComptonfrequencyofagravitationallyboundrotarislowerthan the same rotar not gravitationally bound when both frequencies are measured using a clock runningatzerogravityrateoftime. For another example of a bond reducing energy, an electron and a proton release a 13.6 eV photonwhentheybecomeelectromagneticallyboundtogethertoformahydrogenatomwith theelectroninthelowestenergylevel.Thisreleasedenergyrepresentsthenegativebinding energyofthehydrogenatom.Itispossibletogoonestepdeeperinunderstandingthisnegative bindingenergy.AnisolatedelectronhasaComptonfrequencyofabout1.24 1020Hzandthe Compton frequency of a proton sum of all components is about 2.27 1023 Hz. When an electronandaprotonareboundtogethertoformahydrogenatom,thesumofalltheCompton frequenciesisabout3.3 1015Hzlessthanthewhentheelectronandprotonwereisolated.This The Universe Is Only Spacetime ©2012 [email protected] 12-7 differenceof3.3 1015Hzisthefrequencyofthe13.6eVphotonreleasedwhenthehydrogen atomformed.Thereforeitispossibletoseethedifferenceinenergywhenanelectronandproton areboundtoformahydrogenatom. Tobeperfect,thisexampleneedstoalsoaccountforthe smallamountofkineticenergycarriedawaybythehydrogenatomasitrecoilsfromemitting thephoton. A more extreme example is the bonding of anelectron toa uranium nucleus which has been strippedofallelectrons.Thisbondingissostrongthatthebondingenergyisequivalenttoabout ¼ the mass/energy of an electron. The energy lost when this bonding first takes place is removed by the emission of one or more gamma ray photons. Isolated particles are more energeticthanboundparticles.Thisconceptwilllaterbeappliedtoboundquarkswithsome surprisingimplications. BindingEnergyinChemicalBonds:Next,anexamplefromchemistry.Thereareafewmolecules suchasozone O3 andacetylene C2H2 whicharecommonlydescribedasbeing“endothermic”. Thismeansthatstartingwithastandardizedsetofconditionsfromchemistry,ittakesaninput ofenergy heat toformthemolecule.Thiswouldseemtoimplythatallendothermicmolecules formpositiveenergybonds.Theimplicationisthatthisisanexamplewheretheboundstateis moreenergeticthantheunboundstate.Forexample,ozonerequiresaninputofenergywhenit isformedfrommolecularoxygenO2understandardizedconditions.However,weareprobinga fundamental question about the nature of bonds. We must compare the bound state to the unboundstatewhichinthiscasewouldbeindividualatoms.Ittakes1½moleculesofO2toform 1moleculeofO3 writtenas:3O2→2O3 .ToseparateoneoftheO2moleculesintotwooxygen atomstakesabout2.6eV/moleculeor249kJ/mole.Thisgivestheerroneousimpressionofthe boundstatecanbemoreenergeticthantheunboundstate.However,ifweformedozonestarting with3atomicoxygenatoms,thenthisreactionreleasesenergywhenamoleculeofO3isformed. Similarly, the formation of acetylene is an endothermic reaction if the standardized starting components of graphite and molecular hydrogen H2 are used. However, the formation of acetyleneisanexothermicchemicalreactionifthestartingcomponentsareatomiccarbonand atomichydrogen.Infact,therearenoendothermicchemicalreactionsifthestartingmaterialis individual atoms. Therefore, even chemistry supports the contention that bonds in nature reducetheenergyofthecomponentparts.Inthiscasemoleculesalways possess less energy than the component atoms when the atoms are isolated. Binding Energy of Nucleons:Whileitisverydifficulttomakeenergyandforcemeasurements insideaprotonorneutron,wecanobtainahintofwhatisgoingoninsideprotonsandneutrons bylookingatthebindingthatoccursbetweennucleons.Whenprotonsandneutronsarebound togethertoformatomicnuclei,isthereagainorlossofenergy?Theanswerisobvious.Ahelium atom 4He haslessmass/energythan2deuteriumatoms.Thebindingenergyofnucleonsisa negativeformofenergy energyreductioncomparedtothesumoftheunboundcomponents . Thereisadecreaseinmass lossofenergy whenhydrogennucleifusetoformnucleiofheavier The Universe Is Only Spacetime ©2012 [email protected] 12-8 atoms.Atfirstitmightappearthat235Uandotherheavyatomsareanexceptiontothisrule,but thisisincorrect.Thestrongestboundatomicnucleolusis56Fewithabindingenergyof8.79MeV pernucleon. 235Uhasabindingenergyof7.79MeVpernucleonandthisiscomparabletothe bindingenergypernucleonofcarbonornitrogen.Breaking235Uapartreleasesenergybecause thetwolighternucleiformedhaveagreaterbindingenergypernucleonthan 235U.Agreater bindingenergymeansthatexcessenergymustbereleaseduponformation.Thepointisthat even 235U has less mass/energy than the energy of the protons and neutrons that form the uraniumnucleus. Itisproposedthatquarksareboundtogethertoformhadronsbynegativeenergy.Thehadrons wouldhavelessenergythanthetotalenergyofthecomponentquarksifthequarkswerestable inisolationsothattheirenergyinisolationcouldbeexperimentallymeasured. Gluons,QuarksandHadrons Background: The previous discussion asserted that in nature the bound state was always a lower energy condition that the individual components in the unbound state bound state is alwaysanenergywell .Thisconceptisgoingtobeimportantinthefollowingdiscussionabout quarksandgluons.Theproblemisthatifwefaithfullydevelopamodeloftheuniversestarting withtheassumptionthattheuniverseisonlyspacetime,weobtainthestrongforcefromthe pressureexertedbythespacetimefield.Thereisnoneedtopostulategluons!Sincegluonsare verymuchapartofmodernparticlephysics,thisseemstopresentaproblemforthespacetime modeloftheuniverse.However,itwillbearguedherethatallthefunctionscurrentlyattributed to gluons color charge, etc. can be converted to functions attributed to the rotar model of quarksexistinginthepressureexertedbythespacetimefield. Previously we rejected virtual photons as the “messenger particles” that carried the electromagnetic force and rejected gravitons as the “messenger particles” that carried the gravitationalforce.Thenextremainingvirtualmessengerparticleisthegluonandthisisgoing tobequestioned.Thereisnoexperimentalobservationsthatcanbeinterpretedasbeingproof thatvirtualphotonsorgravitonsexistbutthereissomeexperimentsthatseemtoimplythat gluonsexistalthoughtheyhaveneverbeendirectlyobserved.Alsothereisavastamountof theoretical calculations that are modeling effects that are attributed to gluons. Therefore the discussionaboutgluonsisgoingtobemorenuanced.Theanalysisofquarksandgluonswill beginwithadiscussionaboutthemass/energyofquarks. The Universe Is Only Spacetime ©2012 [email protected] 12-9 Mass/EnergyofQuarks:Sincequarksdonotexistintheunboundstate,itisnotpossibleto simplycomparetheenergyofanunboundquarktoaboundquark.Thefollowingisaquotefrom anarticleonquarkmasseswrittenbyA.V. Manohar and C.T. Sachrajda2 “Quark masses therefore cannot be measured directly, but must be determined indirectly through their influence on hadronic properties. Although one often speakslooselyofquarkmassesasonewouldofthemassoftheelectronormuon, any quantitative statement about the value of a quark mass must make careful reference to the particular theoretical framework that is used to define it. It is important to keep this scheme dependence in mind when using the quark mass valuestabulatedinthedatalistings.Historically,thefirstdeterminationsofquark masseswereperformedusingquarkmodels.Theresultingmassesonlymakesense in the limited context of a particular quark model, and cannot be related to the quarkmassparametersoftheStandardModel.” I will expand on this thought somewhat. Suppose that there is an experiment which collides protonsandanti‐protonstogetherathighenergy.Thecollisionproducesacomplicatedshower ofparticlesthatishardtointerpret.Ifprotonsareassumedtoconsistofpointparticlequarks plus gluonsand virtual particlepairs forming and annihilating, then the interpretation of the resultswillbedifferentthaniftheprotonsareassumedtobetherotar‐modelquarkspossessing quantizedangularmomentumcollidinginseaofdipolewavesdesignatedasthespacetimefield. Withthisbeingsaid,wewillfirstlookatthewidelyacceptedinterpretationsofthesecomplicated experimentalresults. Thedescriptionofaprotondiffersgreatlydependingontheexperiment.Forexample,inlow energy collisions, a proton seems to be made of 3 quarks with each quark possessing approximately1/3oftheproton’senergy.Inhighenergycollisionsaprotonseemstohavemany quarks over10 witheachquarkpossessingenergyofonlyafewMeV.Wewillexamineeach model. Atthelowenergylimitaprotonappearstohaveatotalof3quarks‐twoupquarksandone downquark.Inthelowenergyconditionthese3quarksarereferredtoas“constituentquarks”. Thetwoconstituent“up”quarksofaprotonappeartohaveenergyof336MeVeach3.Thesingle downconstituentquarkappearstohaveenergyof340MeV.Hereisanotherdescriptionofthe constituentquarks. Nonrelativisticquarkmodelsuseconstituentquarkmasses,whichareoforder350 MeVfortheuanddquarks.Constituentquarkmassesmodeltheeffectsofdynamical chiralsymmetrybreaking…Constituentmassesareonlydefinedinthecontextofa particularhadronicmodel."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 4 Griffiths, D., (2008) Introduction to Elementary Particles p. 135, Wiley-Vch "Note on Quark Masses":http://pdg.lbl.gov/2010/reviews/rpp2010-rev-quark-masses.pdf The Universe Is Only Spacetime ©2012 [email protected] 12-10 Thisname“constituentquarks”isusedwhendescribingthemodelthatemergesfromlowenergy experiments.Thename“currentquarks”isusedtorepresentthequarkmodelwhichisobtained inhighenergycollisionexperiments.Inhighenergycollisionexperimentsthereappearstobe many more than 3 quarks and each of these appears to have energy of only a few MeV. To reconcile this difference the difference between the low energy and high energy collision experiments,the3constituentquarksobservedinlowenergycollisionsareoftenvisualizedas beingcomposedofacorecurrentquarkwithenergyofafewMeVwhichissurroundedbyeither aclusterofvirtualparticle‐antiparticlepairsorsurroundedbygluons.Ineithercase,thetotal energyofwhatisinterpretedtobeaclusterisapproximately1/3oftheprotonenergy. According to the proposed spacetime model, the problem comes in interpreting high energy collisions.Intherotarmodelofahighenergycollision,oneormoreofthe3quarksmomentarily absorbsfarmoreenergythantherestenergyofthequark.Recallthepreviousdiscussionofthe difficultydeterminingthesizeofanelectronfromenergeticcollisionsoftherotarmodelofan electron.Thekineticenergyofthecollisionismomentarilyconvertedintotheinternalenergy oftheelectron rotarmodel .Thiscausestheelectron’sradiustomomentarilydecreasesothat itwasalwaysbelowthedetectablelimitoftheexperiment. Thecollisionofprotonsismorecomplicated,butonethingisclear.Theenergeticconditions whichprevailatthemomentofcollisionarenotthesameasanisolatedproton.Ifthemodelof aquarkisapointparticle,thenthereisnointernalstructureanditisvalidtoassumethatthe quarkretainsitspropertieseveninaviolentcollision.However,ifeachquarkisassumedtohave a rotarmodel, then this is three “fluffy” rotating dipolewaves existing in thespacetime field. They each are a rotating dipole wave in spacetime possessing a quantized unit of angular momentum.Thisrotatingwaveisdistributedoveravolumeofspace.Addingthekineticenergy ofthecollisionmomentarilydecreasesthesizeofaquark.Thischangesthebondingconditions butretainsaconstantangularmomentum.Therotarmodelofprotonsisinanearlystageof developmentandcannotpredicttheresultswhichwouldbeexpectedinanenergeticcollision. However, it is possible to imply that the complicated results of energetic collisions can be misinterpretedifpointparticlequarksandgluonmessengerparticlesareerroneouslyassumed. Thequarksobservedinhighenergycollisionsappeartobeverydifferentfromtheconstituent quarksatthelowenergylimit.Thethree“currentquarks”thatformaprotonappeartohave energylessthan10MeV.Inthispictureobtainedfromhighenergycollisions,onlyabout1%of therestmassofaprotonappearstobeintheformthequarks.Inthiscaseabout99%ofthe mass/energy of a proton is therefore assigned primarily to the energy of gluons with some contributionfromthekineticenergyofquarks.Inotherwords,thegluonsmustpossesspositive energyinthismodel.Morewillbesaidaboutgluonslater. The Universe Is Only Spacetime ©2012 [email protected] 12-11 AlternativeExplanation:Theproposedalternativeexplanationofthemassofaquarkisthatup anddownquarkswouldbeintrinsicallyhighenergyrotatingdipolewavesiftheywerestablein isolation.Theyarestronglyboundtogetherbyaninteractionwiththespacetimefieldwhenthey formhadrons.Therearenoisolatedfirstorsecondgenerationquarksbecausetheysimplydo notattainstabilityasisolatedrotars. Thetopquarkwillbediscussedlater .Whenthismodel ofaquarkisboundintoahadronitisinalowenergystate,andeepenergywell.Attemptingto removequarksfromahadronagainstthestrongforceincreasesthequark’senergy Compton frequency towardsthehigherenergystatewhichwouldexistifaquark rotarmodel could existinisolation.Theenergyexertedinattemptingtoremoveaquarkfromahadronrequires somuchenergythatanewmeson pion isformedbeforeanisolatedquarkisobtained.When new mesons are formed, the binding force between former components of the split hadron decreasestonearzero.Singlefirstorsecondgenerationquarksareneverproduced. However,toillustratetheconcepts,wewillimaginewhatitwouldbelikeifisolatedquarkswere allowed.Itisproposedhere justifiedlater thatifisolatedupanddownquarksexisted,they would be rotating dipoles with energy substantially greater than 400 MeV. If up and down quarksexistedasisolatedrotars,thentheywouldshedenergywhentheybondtoformaproton orneutron.Hadronscomeintoexistencealreadyformedsincethisisthelowestenergystate andtheonlyformthathasstability.However,itisinformativetoimaginethestepsthatwould occurifahadronwasformedfromisolatedquarks. Energy of Bound Quarks:Theworkingproposalisthatalltheenergyofaprotoniscontained initsthreeboundquarkrotars rotatingdipolewavesinspacetime .However,themodelofthe interactionofquantizedwavesshouldnotbeequatedtotheexpectedinteractionifthequarks werehardshelledparticles.Furthermore,itisproposedthatthebindingenergyissogreatthat theboundquarkshavemuchlessenergythantheywouldhaveashypotheticalisolatedrotars. We will first survey the hadrons that are made of only up and down quarks to compare the energyoftheupanddownquarksundervariousboundconditions.Thenucleons protonsand neutrons havealmostthe same energy ~938MeV. If we assume that all this energy can be tracedtotheenergyof3rotatingspacetimedipoles 3quarks thentheimplicationisthatup anddownquarkshaveaboutthesameenergy.Therearedifferentproportionsofupanddown quarks, yet approximately the same total energy. We will assume that bound up and down quarksinanucleonhasenergyofabout313MeV ~1/3ofthetotal . Therearetwootherfamiliesofhadronsthatconsistofonlyupanddownquarks.Thesearethe pimesons pions andthedeltabaryons.ThedeltabaryonshavespinofJ 3/2ratherthanthe spinof½forthenucleons.Thereare4deltabaryons.Theseare: Δ uuu ;Δ uud ;Δo udd andΔ‐ ddd . The Universe Is Only Spacetime ©2012 [email protected] 12-12 Theseallhaveaboutthesameenergy 1,232MeV thereforetheupanddownquarksboundin thishadronhaveenergyofabout1/3ofthisvalue:~411MeV. Thepionsconsistofaquarkandananti‐quarksuchasanupquarkandananti‐downquark.The netspinofthepionsiszero counterrotatingdipoles .Theenergyofthepionsis139.5MeVfor thetwochargedpions π andπ‐ andabout135MeVfortheneutralpion πo .Thismeansthat theupanddownquarksinapionhaveaverageenergyofabout70MeVforthechargedpions π andπ‐ andabout68MeVforaneutralpionπo. Thereforewehaveexampleswhereupanddownquarkshaveenergyrangingfrom411MeVto 68MeV.Thestandardmodeldealswiththisdifferencebyassumingthatanisolatedupordown quarkhasenergyofonlyafewMeV.Theextraenergyrequiredtoreach68MeV,313MeVor 411MeVisassumedtobepredominatelyintheenergyofthegluons. Energy of a Hypothetical Isolated Quark: The proposed spacetime wave model of quarks offersadifferentanswer.Itsaysthatanisolatedrotarupordownquarkwouldhaveenergy substantially greater than 411 MeV. When quarks are bound into a hadron, the bonds are so strongthatalargepercentageofthehypotheticalisolatedenergyislost.Itwouldberadiated awayifitwaspossibletodothisexperiment.Thedifferencebetweenthe68MeV,313MeVor 411MeVreflectsdifferentamountsofbindingenergy. Thebindingenergypernucleonin 56Ferepresentsapproximately1%ofaproton’senergy.An electronboundtoauraniumatom’snucleolusstrippedofallotherelectronshasabindingenergy thatisabout25%ofanisolatedelectron’senergy.Inorderforanelectrontoattachtoastripped uraniumatomnucleolus,ithastoemitoneormoregammarayphotonstoshedatotalofabout 25% of the electron’s energy. Actually part of the lost energy comes from the protons in the nucleus,butthatisoffthesubject. Itisproposedthatthebindingenergyofquarksinahadronismuchgreaterthantheseexamples. Toillustratethisconcept,wewillchooseanenergysubstantiallylargerthan411MeVforthe energyofahypotheticalunboundupordownquark.Forillustration,wewillusethenumberof about600MeVfortheenergyofisolatedupanddownquarks.Withthisassumption,anisolated upordownquarkwouldloseabout1/3ofitsenergywhenitformsadeltabaryon 411MeV . Itwouldloseabout½ofitsenergywhenitformsanucleon 313MeV anditwouldloseabout 89%ofitsenergywhenitformsaneutralpimeson 68MeV . Electron vs. Proton Size:Beforeproceedingtoofar,itisdesirabletodoacalculationtoseeif theideasproposedhereareplausible.Wewillattempttocalculatethesizeofaproton.However, firstitisnecessarytorecognizewhyaprotonhasameasurablesizeandanelectrondoesnot.A protonhasameasurablesizebecauseaprotonismadeupof3fundamentalrotars.Thethree quarks of a proton do not respond to a high energy collision as a single quantized unit. The The Universe Is Only Spacetime ©2012 [email protected] 12-13 propertyofunityonlyexistswithinasinglequantizedwave rotar .Acollisionwithaproton involves speed of light communication of forces between the three quarks of a proton. This meansthattheprotonexhibitsaphysicalsizeinacollisioneventhoughthissizedoesnotexhibit ahardboundary. Whenanelectroncollideswithoneofthethreequarksinaproton,itappearsasifthereisa collision between two point particles. The reason is the same as previously explained for a collisionbetweentwoelectrons.Boththeelectronandthequarkarequantizedrotatingdipoles inthespacetimefield.Inadirecthit,theybothconvertthekineticenergyofthecollidingelectron to internal energy of the rotating dipole. This happens fasterthan the speed of light because preserving the quantized angular momentum results in the previously explained property of unity.TheconversionofkineticenergymomentarilyincreasestheComptonfrequencyofeach rotar. In order for angular momentum to be conserved, the rotar radius of each rotar momentarily decreases. The amount of decrease in size makes each rotar experimentally indistinguishablefromapointparticlebecause aspreviouslyexplained themomentaryradius islessthantheresolutionlimitsetbytheuncertaintyprinciple.Theothertwoquarksthatwere partoftheprotononlylearnaboutthecollisionthroughspeedoflightcommunication. Calculation of Proton Radius:Thepresenceofonlythreequantizedwavesmeansthataproton stillexhibitssubstantialquantummechanicalpropertiessuchasnodefiniteshapeandthelack ofahardedge.Alsotheshapeofaprotondependsonthealignmentofthespinsofthequarks. Ananalysis5ofallmeasurementsoftheprotonradiusconcludesamostprobablechargeradius foraprotonis:0.877 10‐15meter 0.15 10‐15meter Wewilldoaplausibilitycalculationtoseeiftheproposedrotarmodelofaprotongivesroughly the correct size. This calculation will assume that the proton is made of 3 rotars, each with energyof313MeV 5 10‐11J .Wemustdecidehowthesethreerotatingdipolesfittogether. Aretherevoidsorexcessiveoverlaps?Itisknownthatprotonsarenotnecessarilyspherical depending on the alignment of the spins of the up and down quarks. Still, the simplest assumptionisasphericalprotonwithquarksthataresointimatelyboundthattheprotonhas threetimesthevolumeofanindividualrotarquarkwithradius .Theplausibilitycalculation willassumethissimplifiedmodel. Wewillfirstcalculatetherotarradius ofarotarwithenergyof5 10‐11Joule 313MeV . Thenwewillincreasethisradiusbyafactorof31/3toobtaintheradiusofaspherewith3times thevolumeofanindividualrotarquark. 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 The Universe Is Only Spacetime ©2012 [email protected] 12-14 Theexperimentallydeterminedradiusofaprotonis:8.77 10‐16 1.5 10‐16meter,therefore thecalculatedradiusof9 10‐16meteragreeswithintheexperimentalerror.Thisdegreeof accuracyisprobablymorethanwedeserveconsideringthecrudenessofthecalculation.Infact, therotarmodelcouldbecorrectforchargedleptonsandtoosimplifiedtobeappliedtoquarks whicharetightlyboundwithveryrestrictiveboundaryconditions.Still,thecalculationdoesgive areasonableanswerandcannotbeignored.Thiscalculationcouldeasilyhavebeenoffbymany ordersofmagnitudeiftherotarmodelwascompletelywrong. Itisalsointerestingtonotethatthedensityofthequarksintheabovecalculationisroughly 5.9 1017kg/m3.Thedensityofthenucleusofanatomwithmanyboundnucleonsissubjectto someinterpretation,butisroughly2.3 1017kg/m3.Therefore,thedensityofanatomicnucleus isroughlyhalfthedensityofindividualquarks.Thisisfardifferentfromthestandardmodel that depicts quarks as point particles and therefore infinitely more dense than an atomic nucleolus. To summarize, the rotar model of quarks implies that if quarks could exist in isolation, they wouldhavesubstantiallymoreenergythantheyhavewhenboundtogethertoformhadrons.In thiscase,thequarkswouldloseenergy emitphotons whentheyareboundtogethertoform hadrons. This results in an energy well, just like all other bonds in nature. Therotar model dependsoftheexistenceofthespacetimefieldtostabilizetherotars.Aspreviouslystated,the spacetime‐based model of the universe has only one truly fundamental force the relativistic force andthatforceisalwaysrepulsive.Thebondingofthequarksisultimatelytraceableto pressureexertedbythespacetimefield. Gluon Background:Next,wewillexaminegluons.Accordingtothestandardmodel,gluonsare exchangeparticlesthatcarrythestrongforce thestronginteraction betweenquarks.Gluons carry the color charge and also participate in the strong interaction in addition to being a mediatingexchangeparticle.The8typesofgluonshavecolorcharge.Whilethereare3color charges red,greenandblue ,gluonscarrycomplexcombinationsofthesecolorcharges.For example,adescriptionofoneofthe8possiblegluonsis: red‐antiblue blue‐antired .Gluons arealsodescribedasmasslessvectorbosonswithspinof1whichhavetwopolarizationstates. The standard model description of gluons is very complex and quantum electrodynamics calculationsinvolvinggluonsarealsocomplex. According to theory, bonds between quarks become weaker as the distance decreases. Thereforequarksboundinhadronsareinastateof“asymptoticfreedom”.Whenquarksarein their unperturbed state, they can migrate within the hadron as if they are not tightly bound. However, the asymptotic freedom state only occurs when quarks maintain the prescribed distance relative to each other. If the distanceis increased,the strong force increases. As the separationdistanceisincreased,energyisbeingaddedtothehadronandtherestoringforce The Universe Is Only Spacetime ©2012 [email protected] 12-15 increases. The added energy supposedly goes into the energy of the gluons. The quarks supposedly maintain a constant energy of less than 10 MeV. When the separation distance betweenquarksreachesroughly10‐15m,enoughenergyhasbeenaddedtothegluonstoforma newmeson quark–antiquarkpair andtherestoringforcedropstonearlyzero.Therearethree problemswiththis. 1 This gluon bond model does not follow the example of the particles possessing less energyintheboundstatethantheyhaveinisolation.Itistruethatwecannotobtainan isolatedquarkforcomparison,butthepointisthatthemodelisthateachquarkretains aconstantenergyasthequarksarebeingseparated.Theworkbeingdonedoesnotgo intoincreasingtheenergyofthequarks.Thisisnotatypicalenergywell. 2 The gluons possess positive energy and are traveling at the speed of light. Since the protonhasenergydensityofabout3 1035J/m3,ifalmostalltheenergyisattributedto gluons this implies that the gluons should exert pressure of at least 1035 N/m2. The pressure of this high gluon energy density should destroy protons, not bind them together.Howdothegluonsachieveattraction? 3 Why does the force start at zero and increase with distance? This is “explained” by physicistspostulatingthatasthequarksareseparated,thegluonsform“fluxtubes”and thisconcentrationactuallyincreasestheforceofattractioneventhoughthedistanceis increasing.Whatisthephysicsbehindthisconcept?Whatsuppliestheforcetoconstrain thesizeofthefluxtubes?Dependingonthevolumeofthefluxtubes,theconfinedgluons should exert even more pressure than 1035 N/m2. All of this is so far removed from anythingelseinnaturethatitspeakstotheproblemscreatedtheconceptofgluons. The experimental evidence for the existence of gluons is that very energetic collisions of electrons and positrons sometimes produce “three jet events” a jet is a narrow shower of particles .Theexplanationforthesethreejeteventsisthatatleastoneofthethreejetsresulted fromagluon“hadronize”intonormalparticles colorlesshadrons whichresultsinthenarrow showerofparticlesknownasajet. TheRelativisticForce:Aspreviouslystated,thespacetimemodelhasonlyonetrulyfundamental force:therelativisticforce.Thisforceisgeneratedwhenenergy,travelingatthespeedoflight, isdeflectedinsomeway.Forexample,theabsorption,emissionorreflectionofaphotonresults inthetransferoflinearmomentum.Therelativisticforce Fristhenamegivenwhenmultiple linearmomentumtransferscanbeconsideredtobeacontinuousforce.TheequationisFr Pr/c where Prisrelativisticpowerpropagatingatthespeedoflight.Therelativisticforceisalways repulsive.Aspreviouslyexplainedtherelativisticforcecanappeartobeanattractingforcewhen the spacetime field exerts the relativistic force in a way that brings particles together. For example,theelectrostaticorgravitationalattractionisactuallytheresultofthespacetimefield applyingunequalpressureonrotarsproducinganetforceofattraction.Thisisanintroduction of how the relativistic force also produces what we perceive to be the strong force without gluons. The Universe Is Only Spacetime ©2012 [email protected] 12-16 All rotars possess energy density which implies that they have internal pressure. The rotar pressureis:ℙr ωc4ħ/c3 Ei/ .Tostabilizethisinternalpressurethespacetimefieldmust exertanopposingpressure.Ifthispressureisbalancedonallsides,thenthereisnonetforce. However,otherrotarsinthevicinityresultinadistortionofthespacetimefieldandthisinturn resultsinanunbalancedpressure anetforce exertedontherotar.Whenthisnetforceisin thedirectionoftheotherrotar,thenwesaythatthereisaforceofattractionbetweenthetwo rotars. Themaximumforce Fm thatarotarcanexertwaspreviouslyshowntobeFm ℙr / . CaremustbeusedinapplyingthisequationbecauseEiistheinstantaneousinternalenergyand λc is the instantaneous rotar radius. For example, in a collision, the kinetic energy gets temporarilyaddedtotherotar’sinternalenergyEi.Thereforeattheinstantofthecollisionthe valueofEiincreasesandthevalueofλcdecreases.TheresultisthatthevalueofFmisgreaterin acollisionthanthetheoreticalvalueforarotarnotundergoingacollision. Itispossibletodoaroughcalculationofthevalueofthemaximumforcethatthe3quarksthat makeupaprotoncanexert.Wewillstartbyassumingthattheproton’senergyof938MeVis evenlydistributedamongits3quarks rotars .Ifeachquarkhasenergyofabout313MeVor 5 10‐11J,thenthevalueofthemaximumforceavailabletothethreequarksintheunperturbed stateofasymptoticfreedomisabout Fm 80,000N.Thismaximumforcecalculationdoesnot attempt to identify whether the rotar can actually exert this maximum force, it is merely the upperlimit. In chapter 7 the section titled “Asymptotic Freedom” gave the explanation of how the strong forcecanbezeroattheasymptoticfreedomseparationdistance.Recallthatatthisseparation distance opposing forces between the spacetime field and the repulsion of adjacent particles offseteachothersothenetforceonaquarkattheasymptoticfreedomseparationdistanceis zero.However,displacingaquarkineitherdirection closerorfurtherfromtheotherquarks produces a net force which attempts to restore the separation to the asymptotic freedom separation. The energy required to change the separation distance is stored in the quark increasingitsrotationalfrequency.Recallthehypotheticalassumptionthatanupordownquark inaprotonhasabout313MeVbutitwouldhaveenergyofabout600MeVifitcouldexistasa stableisolatedparticle.Thisistheenergywellpreviouslydiscussed.Inthisexample,removing aquarkfromaprotonwouldrequireabout300MeVbutapionformsat135MeV,sothishappens firstandtherestoringforcefallstonearlyzero. Wecandoaroughcalculationtoseeifthismodelisreasonable.Weknowthattheradiusofa protonisabout8.8 10‐16mandpionsareformedwhenaquarkisdisplacedbyroughlythis distance.Itispossibletodoaroughcalculationtoseehow faraquarkwouldhavetomove againstagainstaconstant80,000Nforcebeforeenoughenergywouldbestoredtomakeapion The Universe Is Only Spacetime ©2012 [email protected] 12-17 withenergyof135MeV Ei 2.2 10‐11J ?Theanswerisabout2.7 10‐16m.Thiscalculation representsanunrealisticlowerlimitbecausetheforcewouldnotgofromzeroattheasymptotic freedom separation distance to the full maximum force of 80,000 N abruptly. Instead, there wouldbeagradualincreasestartingatzeroandendingatsomeforceprobablylessthan80,000 N.Anothersimplifiedcalculationoftheseparationdistancerequiredtomakeapionwouldstart atzeroforceattheasymptoticfreedomseparationandlinearlyincreasetheforceto80,000Nat thetotalenergyrequiredtomakeapion.Inthiscasetheseparationdistancewhereapionis formedwouldberoughly5.5 10‐16m.Eventhisoversimplifiedassumptionclearlygivesan answerintherangeofprotonradius.Again,thiscalculationcouldhavebeenoffbymanyorders ofmagnitude. GluonsNotNeededforBonding:Thepointofthisdiscussionistosupportthecontentionthatthe spacetime‐based model of the universe can explain the strong force using only the single universal force: the relativistic force. The spacetime‐based model of the universe is not developed sufficiently to make predictions about the properties of specific fundamental particles.Inparticular,itisnotpossibletosaywhetheragluon‐likeparticlewithspinof1exists. Themainreasonforpostulatingtheexistenceofagluon amessengerparticlethatconveysthe strongforce hasbeenremoved.However,somethingcauses3jeteventsinenergeticcollisions ofelectronsandpositrons.Quantumchromodynamicsassignsadditionalfunctionstogluons besidesbeingamessengerparticleandtheseadditionalfunctionsarestillrequired.Therulesof thecolorforcewhichcurrentlyrequire8gluonsmaystillrequire8bosonsbutwithredefined wave‐basedcharacteristics.Thereforegluonsarenotneededforbonding,butsomeoftheother functionscurrentlyassignedtogluonswillneedtobereinterpreted. Stability of Hadrons:Supposethatweimaginestartingwiththesuperfluidspacetimefieldthat lacks angular momentum, then we introduce one unit of ½ħ quantized angular momentum. Merely stating the amount of angular momentum does not specify the energy, frequency, amplitude,rotationalsize,etc.thatthisangularmomentummighttake.Thespacetimefieldhas characteristicsthatdeterminewhatcombinationachieveslongtermstabilitysuchasanelectron andwhatissemi‐stablesuchasamuonortauon.Thereisaninfinitenumberofotherpossible combinations of frequency, amplitude, rotational size that do not possess any stabilizing characteristicsfromthesurroundingspacetimefield.Thesetotallyunstablecombinationslast foronlyaunitoftimeequalto 1/ωc whereωcisthehypotheticalComptonangularfrequency. Forfrequenciesinthegeneralrangeoftheknownparticles,thesurvivaltimewouldberoughly intherangeof10‐25to10‐20seconds.Thefewcombinationsofangularmomentum,frequency, amplitude,etc.thatachievestabilityaretherareexception. Thisismentionedasanintroductiontoadiscussionofthestabilityofhadrons.Whiletheleptons arestableorsemi‐stableasindividualrotars,thequarksarenot.Somehowtwoorthreequarks acting together can find stability where individual quarks do not. Do the hadrons that find stabilityachievethisstabilitybyexhibitingthestandingwavepropertiesofasingleunit?Itis The Universe Is Only Spacetime ©2012 [email protected] 12-18 possibletoanswerthisquestionbylookingatthediffractionpatternofneutronspassingthrough a crystal. The diffraction pattern produced by a neutron 3 quarks implies a de Broglie wavelengththatischaracteristicoftheneutron’stotalmass λd h/mv ratherthanthemassof thethreeindividualquarkswithapproximatelyonethirdthistotalmass. Apparentlythestabilityconditionrequiredforvacuumenergytostabilizeaneutronresultsin frequency summation in the external volume. In other words, the 3 quarks present in the neutronlosetheirindividualityattheboundaryoftheneutron.Externally,thevacuumenergy stabilizesaneutronbytreatingitasasingleunit.Thestandingwavesgeneratedinthevacuum energyapparentlyareequivalenttoaComptonfrequencycharacteristicoftheentireenergyof the neutron. The de Broglie waves generated by a neutron imply a single wavelength of the bidirectional standing waves in the neutron’s external volume. Besides neutrons, larger compositeparticlessuchasalphaparticlesandevenentiremoleculesexhibitdiffractionpatterns characteristic of the total energy. An improved rotar model should address the issue of frequencysummationfurther. Formation of the First Hadrons: The formation of rotars in the Big Bang was previously described as a trial and error process where a few combinations of angular momentum, frequency,andamplitudecondensedoutofthechaoticenergeticwavesinspacetimepresentin the early stages of the Big Bang. It is now proposed that besides single rotating spacetime dipoles,naturealsofoundafewcombinationsofrotatingdipolesthatcouldachievestability. These also condensed out of the energetic waves in the spacetime field as already formed hadrons.Thesourceoftheangularmomentumrequiredtoformquarks,leptonsandphotons willbeaddressedinchapters13and14.Itwillbeshownthateventhestartingconditionofthe universe Planckspacetime musthavepossessedquantizedangularmomentum. Presumablythefirsthadronsthatcondensedoutoftheenergeticwavesinspacetimecreatedby the Big Bang were highly energetic hadrons made from generation III and II quarks. The probable sequence that eventually arrives at the dominance of protons and neutrons in the universetodaywillhavetobedevelopedbyothers. W and Z Bosons:SofarthisanalysishasnotmentionedW ,W‐andZbosons.Thereisclearlya large body of experimental observations that support these particles in the standard model. However, like gluons, it is proposed that these bosons have a wave explanation. W and Z particleshaveħspincharacteristicwhichisnormallyassociatedwithaboson.HoweverWand Zparticlesalsohaverestmasswhichisnormallyassociatedwithafermion spin½ħ .Clearly thisismorecomplicatedthanpreviouslyencounteredwithotherfermionsorbosons. Isthereanyothercasediscussedinthisbookwhereaboson spinħ possessesrestmass?The answeris:yes.Inthefirstchapterwediscussedthecaseofphotonsconfinedinareflectingbox. Photonshave ħspinyetwhentheyareconfinedinsomewaytheyareforcedtohaveaspecific The Universe Is Only Spacetime ©2012 [email protected] 12-19 frameofreferenceandtheyacquirerestmass.Infact,itwaspointedoutthatanytimeaphoton hasenergyof E pc,thephotonwillhaverestmass.Whenaphotonisconfinedbetweentwo reflectors it can be thought of as propagating in both directions simultaneously. Since momentumisavector,thetwovectorscanceland p 0.Thisconditiongivesthephotonrest masseventhoughthephotonisaboson.Thereforeevenaphotonpropagatingthroughglassis propagatingatlessthanthespeedoflightinavacuumandE pc. Thepointofthisexampleisthatbosons,withspin ħ,canhaverestmassiftheyinteractwith fermions rotars inawaythatresultsinE pc.Apparentlyspacetimeandthehadronstructure musthaveatypeofresonancethatoccursat1.22 1026s‐1 Wboson80,38GeV and1.39 1026 s‐1 Zboson91.19GeV . ImaginetwoquarksactingsomethinglikemirrorsmomentarilyconfiningaWorZboson.With Comptonwavelengthsof1.54 10‐17mand1.36 10‐17m WandZrespectively thesearethe sizerangethatplausiblycouldinteractwiththerotarstructureofhadrons.TheWandZbosons wouldhaveastandingwavestructurewhichwouldlooklikestandingwavesinteractingwith thewavestructureofthetwoquarks.ThiswouldgivetheseWorZbosonsrestmassandthe short range properties normally associated with the weak force. This is not a complete explanation,butitdoesshowhowthespacetimemodelofforcesandparticlescanaccommodate WandZbosons.Hopefullyotherswillanalyzethisfurther. TheconceptoftheHiggsfieldandHiggsbosonwasoriginallydevelopedto“explain”howWand Zbosonsacquiredrestmass inertia .WhileIfavorthepreviousexplanationofhowWandZ bosonsacquireinertia,therestofthescientificcommunitycurrentlybelievesthattheHiggsfield interactswithWandZbosonsandthatinteractiongivesthemrestmass.Inthespacetimemodel oftheuniverse,thespacetimefieldistheonlyonetrulyfundamentalfield.Multipleresonances within the spacetime field are responsible for all the various particles. These multiple resonancescanbethoughtofasseparatefields.Inthatsense,itispossibletosaythatthereisa Higgs field the same way that all other particles can be considered to have their own fields resonances .Sincethespacetimemodeloftheuniversehasnotbeendevelopedsufficientlyto makepredictionsaboutWandZparticles,itisnotpossibletoconclusivelysayhowWandZ bosonsobtaintheirinertia.Thereforeitishypotheticallypossiblethatthemechanismmight includeaninteractionwiththeHiggsresonance Higgsfield .However,aspreviouslyexplained, fermionsexhibitrestmassthroughthesamemechanismthatconfinedphotonsexhibitrestmass. FermionsdonotrequireaHiggsfieldtoobtaininertia. The Universe Is Only Spacetime ©2012 [email protected] 12-20 Neutrinos Neutrino Introduction: Neutrinos are the least understood of the “fundamental particles”. There are three types or “flavors” of neutrinos electron neutrinos, muon neutrinos and tau neutrinos . These are three flavors are sometimes designated m1, m2 and m3 respectively. Previouslythestandardmodelconsideredneutrinostobemasslessparticlesbutexperiments prove that neutrinos can change from one type of neutrino to another type of neutrino as a neutrinopropagatesthroughspace.This“neutrinoflavoroscillation”isinterpretedasindicating thatneutrinosmusthavesomerestmass.Thereasoningisthatanythingtravelingatthespeed oflightcannotexperiencetimeandthereforeneutrinoflavoroscillationimpliesthatneutrinos must be traveling at less than the speed of light. The flavor oscillation data could not give absolutevaluesforneutrinomass,butthedatacouldgiveanindicationofthedifferencebetween 7.6 10 thesquareofthemasses6.Forexample,thisdifferencecanbeexpressedas:Δ 2 2 2.4 10 eV . Now there has been the first experimental results which eV and Δ purporttogiveanabsolutevalueofthesumoftherestmassofthethreeflavorsofneutrinos7as 0.32 0.08 eV. I will interpret this as the average rest mass since the flavor oscillation is sequential. This was not a direct measurement of mass. Instead it combined cosmological measurements and a theory of the effect neutrino mass should have on these cosmological measurements.Therefore,thismeasurementcouldbewrongifthetheoryiswrong.Still,this mass/energyisreasonableandwillbeusedinfurtherdiscussionofneutrinosbothhereandin chapter13.Forexample,usingavalueof0.32eVforthemassofthemuonneutrinoandusing the previously mentioned values of the difference in the square of the masses we obtain the following:Anelectronneutrinoshouldbeabout1.2 10‐4eVlessthanamuonneutrinoanda tauneutrinoshouldbeabout3.7 10‐3eVlargerthanamuonneutrino.Thereforethisestimate impliesthatthetauneutrinoisabout1%moreenergeticthantheelectronandmuonneutrinos. Thespacetimewavemodeloftheuniversecanaccommodateneutrinosthathaveasmallrest mass.Thestartingassumption theuniverseisonlyspacetime issorestrictivethatitgreatly narrowsthepossibilitiesforphysicalmodels.Allparticlesthatexhibitrestmassareproposedto generallyhavetherotarmodel.Besidesthedifferenceinmass,thereisobviouslyabigdifference inpropertiesbetweenanelectronandanelectronneutrino.Thisimpliesthatthereshouldbea tangibledifferenceinthemodelsofthesetwospacetimeparticles.Thisdifferenceisunknown atthepresenttime.However,sincethemechanismforgivinganeutrinorestmass,energyand angular momentum is the same asan electron, we will start by using the same general rotar modelforanisolated,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) The Universe Is Only Spacetime ©2012 [email protected] 12-21 Modeling a Neutrino:Ifweassumethatthethreeneutrinoshaveenergyintherangeof0.32 eV,thisimpliesthatanisolatedneutrinoinitsrestframehasaComptonangularfrequencyof ωc 5 1014s‐1andarotarradiusofabout6 10‐7m.Thislargesizeandlowfrequencyforrotars wouldseemtopresentaproblemfortherotarmodelthatcanbeillustratedwithanexample.A muondecaysintoanelectron,anelectronantineutrinoandamuonneutrino.Themuonhasa rotarradiusofabout1.9 10‐15mandaComptonangularfrequencyofabout1.6 1023s‐1.If neutrinoshaverestmass,howisitpossibleforthedecayofamuontoproduceneutrinosthat areabout108timeslargerradiusthanthemuon? ~10‐7mcomparedto~10‐15m This apparent incompatibility occurs because we are erroneously comparing the size and frequencyofisolatedrotarsinarestframewhenweshouldbelookingatthesecharacteristics whenrotarsareintheverycloseproximitytootherrotarsatthemomentofdecay.Recallthat when an electron collides with a proton or another electron, there is a moment when all the kineticenergyoftheelectronisconvertedtointernalenergyoftheelectron.Thismomentarily increasestheelectron’sComptonfrequencyandmomentarilycontractsitsrotarradius.A50 GeVelectroncollisioncausestheelectrontomomentarilydecreaseitsrotarradiusbyafactorof about100,000andincreaseitsfrequencybythesamefactor. Itisproposedthataneutrinocreatedinaparticledecay amuondecayforexample isinitially createdinthehighenergy,compressedconditioncharacteristicofacollision.Thisextraenergy isconvertedtotheultra‐relativisticvelocitiesofthethreedecayproductsproducedbythemuon decay. This can be seen from the following example: Suppose that we imagine reversing the decay process. The decay products consisting of an electron, an electron antineutrino and a muon neutrino would reverse directions and produce a collision that forms a muon. This collisionwouldbehighlyrelativisticandmomentarilyreturnthethreedecayproductstotheir energetic,compressedstatepresentwhenthemuoninitiallydecayed.Infact,thesumofthe frequenciesofthethreedecayproductsinthecompressedstate beforeseparation wouldequal themuon’sComptonfrequency.Inthisexplanation,theneutrinoswouldnotdevelopthelarge sizeandlowerfrequencyuntiltheyseparatefromtheotherrotarsandeachisviewedinitsrest frame. Almost all the quantized angular momentum in the universe is contained in neutrinos and photons.Alltheotherleptonsandquarkstogethercontainlessthanonepartin108compared toquantizedangularmomentumofphotonsandneutrinos.Thismakesneutrinosanimportant consideration when examining the evolution of the universe. Therefore, neutrinos will be discussedagaininchapters13and14oncosmology. The Universe Is Only Spacetime ©2012 [email protected] 12-22