Download Chapter 12 Bonds, Quarks, Gluons and Neutrinos

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
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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/
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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 .
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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.
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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.
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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.
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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
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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
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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.
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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
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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.
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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 .
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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
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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
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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
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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.
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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
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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
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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
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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.
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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)
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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.
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