Starting Assumption: Physics today has a large body of experimental observations andmathematical equations that correspond to the experimental observations. Therefore, on asuperficiallevelitwouldappearthatwehaveagoodtheoreticalunderstandingofnatureuptoalimitthatwillbecalledthefrontierofknowledge.However,therearemanycounterintuitivephysical interpretations of themathematical equations and experimental observations. Thisbook proposes alternative physical interpretations that not only fit the equations andexperiments,butalsoofferimprovedconceptualunderstandingandnewinsights.Ifwe are looking for the fabled “theory of everything", it is best to start the questwith thesimplest possible starting assumption. Only if the simplest assumption is proven to beinadequate,shouldwereluctantlymoveontoamorecomplexassumption.WhenIexaminedthesimilaritiesbetweenlightconfinedinareflectingboxandparticles,Iwasstruckbyabigidea.Thisideais:BasicAssumption:The universe is only spacetime.This ideawill be taken as a basic assumption for the remainder of this book. If this simplestartingassumptioniscorrect,itshouldbepossibletoinventamodeloftheuniversethatusesonlythepropertiesof4dimensionalspacetime.Ultimately,allmatter,energy,forces,fieldsandlawsofphysicsshouldlogicallybeobtainablefromjust4dimensionalspacetime.Thisisalargeprojectthatencompassesallofphysics.Itgrewintothisbooklengthexplanationratherthanafewtechnicalpapers.Initially,thismightseemimpossiblebecausespacetimeappearstobejustaquietvacuumthatpossessesthreespatialdimensionsplustime.However,thequantummechanicalmodelofthevacuumhasavastenergydensityalsoknownasvacuumenergy,quantum fluctuations, zeropointenergy,etc.AsJohnArchibaldWheelersaid“Emptyspaceisnotempty…Thedensityoffieldfluctuationenergyinthevacuumarguesthatelementaryparticlesrepresentpercentage‐wisealmostcompletelynegligiblechangeinthelocallyviolentconditionsthatcharacterizethevacuum.”Thespacetimemodelthatiscapableofformingmatter,energy,forcesandfieldsisacompositeofthequantummechanicalvacuumonthemicroscopicscaleandgeneralrelativisticcharacteristicsofspacetimeonthemacroscopicscale. Besidesaspecificspeedof lightandagravitationalconstant,spacetimealsopossessesimpedance,bulkmodulus,energydensityetc.
Thecombinationofthesepropertiespermitsspacetimetobecomethebasicbuildingblockforallmatterandforces.Spacetime does have some real advantages as the basic building block of everything in theuniverse. Spacetimeisthestiffestofallpossiblemediumsthatsupportwavepropagation. Adisturbance in spacetime propagates at the speed of light. The characteristics of spacetimepermit it to support any frequency wave up to Planck frequency ~1043 Hz . This is atremendousadvantageifweareattemptingtofindamediumthatcanhypotheticallysupportthelargeenergydensityrequiredtobuildaproton,forexample.Somewavesinspacetimewillbeshowntobecapableofmodulatingthespatialandtemporalpropertiesofspacetime.Thiscanserveasthebasicbuildingblockofmatter,forcesandfields.Thesimplicityofthestartingassumptiondoeshaveoneadvantage.Itshouldberelativelyeasytoproveordisprove.Unlikestringtheory,thisstartingassumptionhardlyprovidesany“wiggleroom”. If theassumptioniswrong,theerrorshouldbequicklyevident. If theassumptioniscorrect,theextremelimitationsdefineanarrowpaththatshouldleadtobothconformationsandnewinsights.Iwillsummarizetheconclusionsofchapter#1.
Aconfinedphotoninamovingframeofreferencehasthefollowing8similaritiestoafundamentalparticlewiththesameenergyandsameframeofreference:1 thesameinertia,2 thesameweight,3 thesamekineticenergywhenmoving4 thesamedeBrogliewavelength 5 the samedeBroglie phase velocity, 6 the samedeBroglie group velocity, 7 the same relativistic length contraction, 8 the samerelativistic time dilation. It is hard to avoid the thought that perhaps a particle isactuallyawavewithcomponentsexhibitingbidirectionalpropagationatthespeedoflightbutsomehowconfinedtoaspecificvolume.Thisconfinementproducesstandingwavesthataresimultaneouslymovingbothtowardsandawayfromacentralregion.
The assumption that theuniverse is only spacetime causesus to explore thepossibility thatwavesinspacetime dynamicallycurvedspacetime arethebasicbuildingblocksofparticles,forces and fields. It also offers the opportunity to give a physical description of quantummechanicaloperationssuchasthecollapseofthewavefunctionormakingameasurementofaquantummechanicalstate.Theultimatetestiswhetherthisassumptionlogicallyleadstogravityandcompatibilitywithquantummechanics.The starting assumption that the universe is only spacetime requires that the reader change perspective about what is a cause and what is an effect. The standard physical interpretation of general relativity is that matter causes curved spacetime. The reverse perspective would be that curved spacetime causes matter. In this perspective spacetime is the single universal field responsible for everything in the universe including matter. Waves in spacetime can be
thought of as dynamically curved spacetime. Static curved spacetime and particles will both be shown to be the result of dynamically curved spacetime.Creative Challenge: Istartedwithtwopositionsthatarecurrentlynotconnected.Ontheonehand,thereisthecurrentunderstandingofthefundamentalparticles,forcesandphysicallaws.Ontheotherhand,thereisthebasicassumptionthattheuniverseisonlyspacetime.Anattemptto bring these two disconnected positions together requires a creative look at both theproperties of spacetime and the properties of particles, forces and physical laws. Theexperimentally verified physical facts and equations are assumed to be correct, but it is notnecessary to adopt the physical interpretations currently used to explain these facts andequations.Forexample,theequationsofgeneralrelativityaccuratelydescribegravityandtheuniverse. However, the accuracy of these equations does not guarantee the accuracy of thephysicalinterpretationscurrentlyassociatedwiththeseequations.Theideathatgravityisnotaforce,buttheresultofthegeometryofspacetimeisaphysicalinterpretationoftheequationsofgeneralrelativity.Ratherthanfocusingonexplaininggravityorunitingquantummechanicsand general relativity, I merely start with what I believe is the simplest possible startingassumption the universe is only spacetime and attempt to reconcile this assumptionwitheverythingknowntoexistintheuniverse.Planck Units:In1899MaxPlanckproposedasystemofunitsbasedonlyonconstantsofnature.HeusedthereducedPlanckconstantħ 1.055 10‐34kgm2/s, theNewtoniangravitationalconstantG 6.672 10‐11m3/s2kg,thespeedoflightc 2.998 108m/sandtheCoulombconstant1/4πεo 8.987 109m3kg/s2C2.Thiscombinationofconstantscanbeusedtomakeunitsoflength,time,mass,andcharge.Extrapolatingfurther,itispossibletomakeallotherunitssuchasunitsofforce,energy,momentum,power,electricfield,etc.ItwasimmediatelyrecognizedthatPlanckunitswerefundamentalbecausetheywerederivedfromconstantsofnature.However,itlaterbecamerecognizedthatPlanckunitsheldanevenmorespecialplaceinphysics.Planckunitswereactuallybasedonthepropertiesofspacetimeandtheyrepresentedthelimitingvalues maximumorminimum forasinglefermionorboson.Forexample,agroupofparticlescanhavemassinexcessofPlanckmass mp 2.176 10‐8kg .However,thetheoreticallimitforasinglefundamentalparticle asinglefermion isPlanckmass.IftherewasafermionwithPlanckmassitwouldformablackhole.TheinverseofPlancktimeisthemaximumpossiblefrequencyforaphoton.Plancklengthlp 1.616 10‐35mrepresentsthe theoretical limiting value device independent of any length measurement. Similarly,Plancktimetp 5.301 10‐44srepresentsthelimitingaccuracyofanytimemeasurement.Whenweareattemptingtobuildtheuniverseoutofonlyspacetime,Planckunitsbecomethenaturalunitsforthisanalysis.
SpacetimeModelsSpacetime: The Quantum Mechanical Model: Quantum mechanics does not specifically have a model of spacetime. However, quantum mechanics does describe the properties of the energetic vacuum which we will be defining as the properties of spacetime on the microscopic scale. For comparison, the general relativity description of spacetime will be characterized as the macroscopic properties of spacetime. Thequantummechanicalviewofthevacuum includingQEDandQCD isalocallyviolentmediumfilledwithvacuumfluctuations.Atthebasisoftheuncertainty principle there is energetic spacetime that is in a continuous state of flux. Thedistancebetweentwopointscanonlybespecifiedtoalimitedaccuracy Plancklength becauseof the effect of these fluctuations on spatial measurement. Similarly the energy at a pointundergoeswild fluctuations. This isusuallyconsideredas justificationforthe formationandannihilationofvirtualparticlepairs,butthisenergyfluctuationcanalsobeconsideredmerelyanenergeticdistortionofspacetime.Eventherateoftimeatadjacentpointsin“flat”spacetimenogravitationalacceleration canfluctuateslightlyproducingvariations differencesbetweenclocks thatcandifferbyPlancktime.Thesefluctuationsproducemeasurableresults.Forexample,theCasimireffectproducesaforceon two closely spacedmetal plateswhich have beenmeasured to an accuracy of 5% of thetheoreticalprediction.Inahydrogenatomthereisaninteractionbetweentheelectronandthevacuum fluctuations thatproducesa small shift in theenergyof the 2S1/2 energy level. This“Lambshift”hasbeenaccuratelypredictedandexperimentallymeasured.InQED,thevacuumfluctuationscanmixwiththeexcitedstatesofanatomresultingintheinitiationofspontaneousemissionofaphoton fromtheatom1 2.Also, thesevacuum fluctuationscanproducevacuumpolarizationwhichchangesCoulomb’slawnearanelectricallychargedparticle.
An electron has a magnetic moment which would be precisely equal to 2 except for theanomalousmagneticdipolemomentcausedbyvacuumfluctuations.Thiselectronsping‐factorgs has been predicted by QED calculations and experimentally verified to better than 10significant figures for the anomalous contribution. The result is: gs 2.00231930436. Thismeansthatthemagneticmomentofanelectronisthemostaccuratepredictioninallofphysics.Thisaccuracydependsontheaccuracyofthequantummechanicalmodelofthefluctuationsinspacetime.Alloftheseexamplesaremeanttoillustratethatquantummechanicsrequiresthatvacuumhasvacuumfluctuationsataverylargeenergydensity.
1 Hiroyuki Yokoyama & Ujihara K (1995). Spontaneous emission and laser oscillation in microcavities. Boca Raton: CRC Press. p. 6. ISBN 0-8493-3786-0. 2 Marian O Scully & M. Suhail Zubairy (1997). Quantum optics. Cambridge UK: Cambridge University Press. p. §1.5.2 pp. 22–23. ISBN 0-521-43595-1
Onewayofquantifyingthesefluctuationsistovisualizeavacuumasbeingfilledwithharmonicoscillatorsatatemperatureofabsolutezero.Fromfieldtheory,thelowestquantummechanicalenergyofeachoscillator3isE ½ħω ½ħc/λ wherec ωλandλispronouncedlambdabar .Thisisthefamouszeropointenergy.EachoscillatorcanbevisualizedasoccupyingavolumeofV kλ3wherekisanumericalfactornear1.Forexample,awavecanbeconfinedinareflectingcavitythatis½wavelengthonaside.Thewaveamplitudeiszeroatthewallsandmaximuminthecenterforthissizecavity.Sincewearestandardizingontheuseofωforfrequencyandλforwavelength,itispossibletosaythatthewavehasbeenconfinedtoavolumeofλ3ifweignorenumericalfactorsnear1.Usingthisvolumedesignation,thismeansthattheenergydensityUatfrequencyωis:Uω ħω/λ3 ħc/λ4 ħω4/c3.Whatisthetotalenergydensityofzeropointenergyatallfrequenciesuptoacutofffrequencyofω?Whenall frequenciesarepresentwiththecharacteristicsoftheharmonicoscillatorsofspacetime,Milonni previousreference hasshownthatthereareinteractionswhichresultonthetotalenergydensityisequaltoUt ħω/λ3 ħω4/c3.Thisisthesameasbeforeexceptthatnowthefrequencyrangesfromzerotoamaximumofω.Ifωisassumedtohavenolimit infinitefrequency thentheimpliedenergydensitywouldalsobeinfinite.Ifweassumethatzeropointenergy is associated with the properties of spacetime proven later then the maximumfrequencythatspacetimecansupportisPlanckfrequencyωpwhichistheinverseofPlancktimeωp 1/Tp c5/ħG 1/2 1.85 1043s‐1. AssumingPlanck frequencyωp, the impliedenergydensityofthequantummechanicalmodelofspacetimeisapproximatelyequaltoPlanckenergydensityUp ħωp4/c3 4 10113J/m3. anumericalconstantisbeingignored .Thisshockinglargenumberwillbeextensivelyanalyzedseveraldifferentplaceslaterinthisbook.Fornowwewillmerelyrecognizethatthisispartofthequantummechanicalmodelofspacetime.Spectral Energy Density:Thenormalwayoftreatingenergydensityataparticularfrequencyistodesignatethe“spectralenergydensity”whichisenergydensityperunitfrequencyinterval.Wewilldesignatethisspectralenergydensityas:U ω dω.EverypointinspacetimeistreatedlikeitisaquantizedharmonicoscillatorwithenergyE ½ħω.ThisconceptleadstoaspectralenergydensityU ω dωthatis:
U ω dω kħ
dω
“Thisspectrumwithitsω3dependenceofspectralenergydensityisuniqueinasmuchasmotionthroughthisspectraldistributiondoesnotproduceadetectableDopplershift. ItisaLorentzinvariantrandomfield.Allinertialobserversareequivalent.Anyparticularspectralcomponentundergoes a Doppler shift, but other components compensate so that all components takentogetherdonotexhibitaDopplershift.Thereforethisspectralenergydistributionsatisfiesthe
3 Milonni, P. W.: The quantum vacuum: an introduction to quantum electrodynamics. p. 49 Academic Press Inc., San Diego (1994)
requirementthatitshouldnotbepossibletodetectanydifferenceinthelawsofphysicsinanyframeofreference atleastuptothecutoffatPlanckfrequency .Itshouldalsobenotedthatneithercosmologicalexpansionnorgravityaltersthisspectrum”4.Theimplicationsofhavingafinitecutofffrequencyarediscussedaspartofthecosmologicalanalysisinchapter14.Quantum Foam:In1955,JohnWheelerproposedthatspacetimeishighlyturbulentatthescaleofPlancklength.HeproposedthatasthescaleoftimeandlengthapproachesPlancktimeandPlancklength,theenergyfluctuationsinspacetimeincrease.Thesefluctuationsonthesmallestscale possible cause spacetime to depart from its smooth macroscopic characteristic. JohnWheelersuggestedtheterm“quantumfoam”todescribespacetimeonthissmallestscale.Inthebook“Einstein'sVision”,JohnWheelerproposedthatelementaryparticleswereexcitedenergystates resonances of the vacuum energy fluctuations. He pointed out that the density of anucleuswas~1018kg/m3andthisdensityisnegligiblysmallcomparedtotheequivalentdensityof spacetime ~ 1097 kg/m3 or an energy density of ~ 10113 J/m3 . While John Wheeler’sdescriptionofspacetimehasthesamebasiccomponentsasthespacetimemodelproposedinthisbook,hisconceptofhowspacetimeformsparticlesandforcesisdifferent.Tosummarize,thequantummechanicalmodelofvacuum,spacetimeisaseaofenergeticactivitythat can be visualized several different ways. The uncertainty principle has distance,momentum, time and energy undergoing fluctuations. Field theory has a sea of harmonicoscillators,eachwithzeropointenergyofE ½ħω.Particlephysicshasvirtualparticlepairsandvirtualphotonscomingintoexistenceandgoingoutofexistence.QCDhasvirtualparticleswith both color charge and electrical charge producing vacuum polarization. The quantummechanicalmodelofvacuumrequiresaminimumvacuumenergydensityofatleast1050J/m3for many QCD calculations and some variations require the full Planck energy density of~10113J/m3.Spacetime: The General Relativity Model: We will be viewing the general relativitydescriptionofspacetimeasdescribingonlythemacroscopicpropertiesofspacetime.Generalrelativity visualizes spacetime as a smooth, well behaved medium consisting of 3 spatialdimensionsplustime.Spacetimecanbecurvedbyenergyinanyformbutitisnotsubjecttotherandomfluctuationsofthequantummechanicalmodel.GeneralrelativityisaclassicaltheorythatdoesnotrecognizePlanck’sconstant,PlancklengthorPlancktime.Thedistancebetweentwocloselyspacedpointsisnotconsideredtofluctuatebutthereisalimitastotheprecisionofthemeasurement.Thisprecisionlimitissetbythepossibilityofformingablackholeiftoomuchenergyisrequiredtomakethemeasurement.However,eventhislimitisamixtureofquantummechanicsandgeneralrelativity.Ingeneralrelativitytherearenoquantizedoperations.
4 Puthoff, H.E. Phys. Rev. A Volume 40, p.4857, 1989 Errata in Phys. Rev A volume 44, p. 3385, 1991 See also New Scientist, volume 124, p.36, Dec. 2, 1989
Generalrelativity GR teachesthatenergyinanyformgeneratesgravity.Accordingtogeneralrelativity theuniversewould collapse into ablackhole if the energydensity of theuniverseexceedsthe“critical”energydensity.Accordingtocosmologicalobservation,spacetimeis“flat”on the largescaleexceedingabout½billion lightyears. Theobservedenergydensityof theuniverse about10‐9J/m3 appearstobewithinthemarginoferror within1% ofequalingthecriticalenergydensityoftheuniverse.Therefore,accordingtogeneralrelativitythequantummechanicalmodelofvacuummustbewrongbecausethequantummechanicalmodelrequiresenergydensityvastlyexceeding the criticaldensityofabout10‐9 J/m3. According togeneralrelativity,anenergydensityof10113J/m3isridiculous.ThisenergydensitywouldformablackholeevenforaspherethatisPlancklengthinradius.General relativitydoeshave its shareofpredictionsnot sharedbyquantummechanics. Forexample,therateoftimedependsongravityinGRwhilequantummechanicsconsiderstherateoftimetobeconstant.Also,GRpredictsthatpropervolumealsoisaffectedbygravity.Quantummechanicsdoesnotrecognizeagravitationaleffectonvolume.Reconciling the QM and GR Models: Thediscrepancy between the quantummechanicalenergydensityofvacuum ~10113J/m3 andthecosmologicallyobservedenergydensityoftheuniverse ~10‐9J/m3 isthelargestnumericaldiscrepancyinallofphysics.Thedifferenceisafactorofabout10122butthisisusuallyroundedoffto“merely”afactorof10120.Thestandardinterpretation is that theremustbe someother effect that cancelsoutwhat appears tobearidiculouslylargequantummechanicalenergydensity.However,thereisgoodevidencethatthevacuum fluctuations exist. They are required formany currentquantummechanical effects.Theycannotsimplybecanceledbyanothereffectthatsomehoweliminatesalltheeffectsofthesefluctuations.Furthermore,cancelingout10113J/m3wouldrequireanequallylargeeffectintheoppositedirection.Noeffectthatcancels10113J/m3hasbeenproposed.Oncloseexaminationwereallydonotneedatruecancelationofenergy.Wemerelyneedoneormoremechanismsthatallowthequantummechanicalvacuumenergytoexistbutnotinteractwith us or our observable universe except through the quantum mechanical interactionsmentioned.ItwillbeproposedlaterthatthequantummechanicalmodelofspacetimeiscorrectregardingtheenergydensityofspacetimeatthequantumscaleofPlancklengthandPlancktime.Also, thegeneralrelativitymodel iscorrectregardingtheenergydensityofspacetimeonthemacroscopicscalethatdoesnotrecognizefluctuationsatthescaleofPlancklengthandPlancktime. Since theGRpredictionsarevirtuallyuniversallyaccepted,wewill concentrateon theenergy density predictions of quantum mechanics which are generally presumed to beeliminatedbysomeunknownoffsettingpropertyofspacetime.Thisseemsobvioussincewedonotmacroscopicallyinteractwiththistremendousenergydensitynorhasitcausedtheuniversetocollapseasimpliedbygeneralrelativity.
It is proposed here that spacetime is a composite of the quantum mechanical model and the general relativity model. The quantum mechanical model of spacetime has quantum fluctuations and tremendous energy density. It is describing undetectable waves in spacetime that lack quantized angular momentum and are as homogeneous as quantum mechanics allows. Usually we ignore this by renormalization because it is a uniform background energy density of the vacuum. The general relativity model only recognizes the small portion of the energy in the universe that possesses quantized angular momentum (fermions and bosons). This portion is capable of forming energy concentrations such as massive bodies which distort the macroscopic homogeneity of the quantum mechanical model to form curved spacetime.Therestofthisbookisdevotedtoexplainingvariousaspectsoftheabovestatement.Thefactorof10120discrepancybetweenthetwomodelsisthedifferencebetweentheminutefractionofenergy particles,photons,etc. thatpossessesquantizedangularmomentumandthevastlylargervacuumenergydensitythatdoesnotpossessquantizedangularmomentum.Thisvacuumenergywilllaterbeshowntobeahomogeneoussuperfluidandhaveotherpropertiesthatpreventgravitationalcollapse.Thesestatementsareonlymadetoalertthereaderthattheobviousobjectionswillbeaddressedlater.Anotherobjection addressed later is the contention that the largeenergydensity of vacuumfluctuations is impossible because the volume of the universe is expanding yet the vacuumenergydensityisperceivedtoremainconstant.Thisseemstoimplythatavastamountofnewenergyisbeingaddedtotheuniverseeachsecondtoaccompanythenewvolumebeingcreated.Thisanswerrequirestwochapters 13&14 foracompleteexplanation,butakeypointinthisexplanationisthatspacetimeisundergoingatransformationthatstartedattheBigBangandcontinues today. The expansion of the proper volume of the universe is one result of thistransformation.Anotherresultisthatourstandardofaunitofenergyisshrinking.Adecreasingstandardwillmakeaconstantamountofenergyonanabsolutescaletoappeartogrowonourshrinkingscale.Newenergyisnotbeingaddedtotheuniversebutthepropertiesofthevacuumfluctuationsarechanging.Thiswillbeexplainedinmoredetailinchapters13and14.Vacuum Fluctuations and Vacuum Energy: Intheremainderofthisbooktheterms“vacuumenergy”and“vacuumfluctuations”willbeusedinterchangeably.Inbothcasestheyrefertothequantummechanicalmodelofspacetimewithenergydensityofabout10113J/m3.Forexample,“vacuumfluctuations”impliesquantummechanicalfluctuationsofthevacuum fluctuationsofspacetime whichwillbedescribedinthenextsectionofthisbook.Suchfluctuationsalsocanbedescribedas“vacuumenergy”.Thereasonforusingtwodifferenttermsisbecausesometimesitisdesirabletoemphasizetheenergycharacteristicsandsometimesitisdesirabletoemphasizethefluctuationcharacteristic.
Inthisbooktheterms“vacuumenergy”and“vacuumfluctuations”willneverimplydarkenergyor thecosmologicalconstant. Theseareconcepts fromcosmology that implyavastly lowerenergydensityandadifferentexplanation.Darkenergywillbediscussedinchapters13and14.A model of the universe will be presented that is based on spacetime undergoing atransformationthatproducestheobservedincreaseinpropervolumeandotherobservationswithouttheneedofdarkenergy.
DipoleWavesinSpacetimeThusfarwehavetalkedaboutvacuumfluctuationsandinferredthatthesecanbeconsideredwavesinspacetime.Nowitistimetobemorespecificaboutthepropertiesofthesewavesinspacetime.Sincethestartingassumptionofthisbookisthattheuniverseisonlyspacetime,thegoal is tosee if it ispossible toprove thatallparticles, fieldsand forcesare formedoutof4dimensionalspacetime.Acriticalstepisto“invent”amodelofwavesinspacetimethatcouldpossibly be the universal building block of all particles and forces. Once such a model ispostulated,itmustbetestedtoseeifitactuallycorrespondstoreality.Iffundamentalparticlesareultimatelyconfinedwavesinspacetime,itisnecessarytolookforanexplanationthatincorporateswavesinspacetimewithcharacteristicsthatcanbethebasicbuilding block for all matter and forces. Gravitational waves do not have the necessarypropertiestobebothvacuumfluctuationsandthebasicbuildingblockofallparticlesandforces.Weare looking forawave inspacetimethatchangesboththerateof time distorts the timedimension andchangesthedistancebetweenpointsinawaythatchangespropervolume.Weknowfromgeneralrelativitythatmassaffectsboththerateoftimeandpropervolume masscurvesspacetime .Therefore, if we are trying to build matter out of waves in spacetime, we must use waves in spacetime that possess the ability to affect both the rate of time and the distance between two points. Wemustusewavesthathavetheabilitytodynamicallycurvespacetime.Theonlywaveinspacetimethatcanaffecttherateoftimeandpropervolumeisahypotheticaldipolewaveinspacetime.The immediateproblem is thatdipolewaves in spacetimeare forbiddenon themacroscopicscaleaddressedbygeneralrelativity.Instandardtextsongeneralrelativitythesubjectofdipolewaveswarrants just a briefmention because they are considered impossible. For example,perhaps the most authoritative text on general relativity is the 1300 page tome titled“Gravitation”byCharlesMisner,KipThorneandJohnArchibaldWheeler.Onpage975ofthe24thprinting,dipolewavesinspacetimereceiveathreelinementiontotheeffectthattherecanbenomassdipoleradiationbecausethesecondtimederivativeofthemassdipoleiszero d p 0 .Thisconclusionultimatelyfollowsfromtheconservationofmomentum.Thegenerationofdipolewavesinspacetimewouldrequirethecenterofmassofaclosedsystemtoacceleratein violation of the conservation ofmomentum. Furthermore, if a dipolewave in spacetimesomehowexisted,thepassageofthiswavepastanelectricallyneutral,isolatedmasswouldcause
the center of mass to undergo an oscillating displacement which is also a violation of theconservationofmomentum.Clearly,dipolewavesinspacetimecannotexistonthemacroscopicscalegovernedbygeneralrelativity.However, if we are exploring the possibility of constructing the entire universe out of 4dimensionalspacetime,dipolewavesinspacetimehavealotofappealanddeserveacloserlook.Matteraffectsboththerateoftimeandpropervolume mattercurvesspacetime .Therefore,dipole waves in spacetime need to be considered as the spacetimewave building block formatter.Arethereanyconditionswheredipolewavesinspacetimewouldbepermitted?Theanswerisyesprovidedthatthedipolewavesconformtoaseverelimitation.Thefollowingisthesecondkeyassumptionofthisbook:SecondAssumption: Dipole waves in spacetime are permitted by the uncertainty principle provided that the displacement of spacetime caused by the dipole wave does not exceed Planck length or Planck time. This restriction will be called the “Planck length/time limitation”.The spacetime basedmodel proposes that dipolewaves in spacetime can exist on the scalegovernedbyquantummechanics.Thisistosaythattherearedisplacementsofspacetimethataresosmallthatthedisplacementsarebelowthequantummechanicaldetectablelimitsetbytheuncertaintyprinciple.Thisisanalogoustothereasoningthatpermitsvirtualparticlepairstotemporarilyexistprovidedthattheyarepermittedbytheuncertaintyprinciple.ItisproposedthatdipolewavesinspacetimecanexistindefinitelyprovidedthatthespatialdisplacementofspacetimedoesnotexceedPlancklengthandthetemporaldisplacementofspacetimedoesnotexceedPlancktime.Thesesmalldisplacementswouldbeundetectableevenwithaninfinitelylongobservationtime. Thesedipolewavesare thebackground“noise”of thevacuum. Theyactuallyarethecauseoftheuncertaintyprinciple.Asuperficialanalysisoftheminimumdetectablechangeinlengthmeasuredoveralongtimewould use the uncertainty principle equation: ΔxΔp ½ħ and substitute for Δp the largestpossible value of momentum uncertainty for a single quantized unit. This would be PlanckmomentumwhichisthemomentumofahypotheticalphotonwithPlanckenergy. Usingthismaximummomentumforasinglequantizedunit,theminimumvalueofΔxis:Δx Lp Plancklength .However,thisquestionoftheminimumlengthmeasurementhasbeengivenamorerigorousexaminationthatincludesbothquantummechanicsandgeneralrelativity.Theconclusionofall
thesearticles5,6,7,8,9,10 is that that there isa fundamental limit to lengthmeasurement deviceindependent ontheorderofPlancklength Lp 1.6 10‐35m .Asimilaranalysisoftime2,3hasconcluded that there is a fundamentalminimumdetectableunit of time differencebetweenclocks whichisontheorderofPlancktime Tp 5.4 10‐44s .LikeallPlanckunitdefinitions,thePlancklength/timelimitationignoresnumericalfactorsnear1.Therefore,amoreprecisestatementofthislimitationmightincludeanumericalfactornear1thatisbeingignoredhere.Since we cannot be sure if there is a numerical factor near 1 that is being ignored in anydiscussionofPlancklengthorPlancktime,thisoffersjustificationforignoringnumericalfactorsnear 1 in the plausibility calculations made in the remainder of the book. Presumably,subsequentanalysisbyotherscaninserttheignoredfactorsnear1iftheyareneeded.However,itwillbeshownthroughouttheremainderofthebookthattheplausibilitycalculationsgivethecorrectanswersbyignoringnumericalfactorsnear1.Onlyinthecosmologychapters 13and14 willweneedtouseawell‐knownnumericalfactornear1.Wewill accept thePlanck length/time limitationandproceedassuming thatdipolewaves inspacetime can have this displacement and yet have the wave properties fundamentallyundetectable.Thislimitationisconceptuallyunderstandableifitisviewedasasignaltonoiselimitation.IftheverynatureofspacetimeisthattherearequantumfluctuationsofPlancklengthandPlancktime,thenitisquitereasonablethatitisimpossibletomakephysicalmeasurementsbelowthisnoiselimit. Therefore,quantummechanicspermitsadipolewaveinspacetimetodisplace a particle’s center of mass by Planck length without violating the conservation ofmomentum. Similarly, a dipolewave candisplace time thedifferencebetween clocks at aspecific location by Planck time compared to the surrounding volumewithout violating anyconservation requirement. Even though thewave properties of spacetime dipole waves areundetectable,thisdoesnotimplythatspacetimedipolewavesareinconsequential. Itwillbeshown that any dipole wave that possesses quantized angular momentum any fermion ofboson willproducedetectableinteractionswithoutpermittinganexperimentalmeasurementofthePlancklengthandPlancktimedisplacementsofspacetimewhichconstitutesomeofitswaveproperties.Another characteristic of dipolewaves in spacetime is that they arenot strictly longitudinalwavesortransversewavesbecausetheyarereally4dimensionalwaves.Awavethatmodulatestherateoftimesuchthatperfectclockscandifferby Tpispresentinall3spacialdimensionsofaphysicalvolume.Thereforeithasbothatransverseandlongitudinalquality.Similarly,a
5 Padmanabhan, T.: Limitations on the operational definition of spacetime events and quantum gravity. Class. Quantum Grav. 4 L107 (1987) 6 Garay, L. J.: Quantum gravity and minimum length. Int. J. Mod. Phys. A 10, 145-166 (1995), arXiv:gr-qc/9403008 7 Baez, J. C., Olson, S. J.: Uncertainty in measurements of distance. Class. Quantum Grav. 19:14, L121-L125 (2002) 8 Calmet, X., Graesser, M,. Hsu, S. D.: Minimum length from quantum mechanics and general relativity. Phys. Rev. Lett. 93, 211101 (2004) [arXiv:hep-th/0405033v2] 9 Calmet, X.: Planck length and cosmology. Mod. Phys. Lett. A 22, 2027-2034 (2007), [arXiv:0704.1360v1] 10 Calmet, X.: On the precision of length measurement. Eur. Phys. J. C 54: 501-505, (2008) [arXiv:hep-th/0701073v1]
wavethatmodulatesthe3spatialdimensionsby Lpisproducingavolumechangewhichisbothtransverse and longitudinal. Again all 4 dimensions are being modulated simultaneouslybecausethereisalsoacoordinatedmodulationoftherateoftime.Whentherateoftimeslows,thevolumeincreasesandviceversa.Itisproposedthatvacuumfluctuations,quantumfoam,zeropointenergy,vacuumenergy,theuncertaintyprincipleetc.arealljustdifferentwaysofdescribingdipolewavesinspacetimewitha spatial displacement amplitude in the range of Planck length ΔL Lp and a temporaldisplacementamplitudeofPlancktime ΔT Tp .Thissaysthatthedimensionlessstrainwaveamplitude As forareducedwavelengthofλexpressedusingspatialpropertiesandtemporalpropertieswouldbe:As ΔL/L Lp/λstrainamplitudeexpressedusingPlancklengthandλAs ΔT/T TpωstrainamplitudeexpressedusingPlancktimeandωFigures5‐3and5‐4 in chapter5 aredrawn for adifferentpurpose,but they canbeused toillustratestrainamplitude.Figure5‐3hasadisplacementamplitudeof Lp.TheXaxisonthisgraph is designated in units of reducedwavelengths λ. The strain amplitude at any instantcorresponds to the slope of the graph. For example, themaximum slope maximum strainamplitude isLp/λwhichoccurswhenthewavecrossesthe“X”axis y 0 .Similarly,figure5‐4relatestothetemporalpropertiesofadipolewaveinspacetimewithamaximumandminimumtemporaldisplacementof Tp.Therefore,maximumtemporalstrainamplitudecorrespondstoTpω.ThePlancklength/timelimitationimpliesthefollowingcorollary:
CorollaryAssumption:The maximum strain amplitude (Amax) permitted for a dipole wave in spacetime is Lp/λ in the spatial domain and Tpω in the temporal domain. Amax = Lp/λ. = Tpω Static versus Dynamic Units:Wearegoingtointerruptthediscussionofdipolewavestoinsertanoteaboutunits.Manytimesinthisbook,Plancklengthwillberepresentingawaveamplitudedimension dynamicdimension ratherthanastaticdistanceasmightbeequatedtorulerlength.Iwillattempttoclearlyspecifywhenlengthrepresentsawaveamplitudeorastraininspacetimewithunitsoflengthbutnottobeconfusedwithstaticlength distance .Itisalsopossibletohaveawave amplitude associatedwith Planck time. For example if awave in spacetime causedprefectclockstospeedupandslowdownbyPlancktime,thenPlancktimewouldbeexpressingawaveamplitude adynamicunit ratherthantheconventionalideaofatimeintervalsuchas1second.What Are Dipole Waves In Spacetime? Wewill start theexaminationofdipolewaves inspacetimebymakingananalogytoelectromagneticdipoles.Forexample,acarbonmonoxidemoleculehasthecarbonatomnegativelychargedandtheoxygenatompositivelycharged.The
bond between these two atoms has similarities to a mechanical spring. When the carbonmonoxidemoleculeisgivenenergy,itwillvibrateandrapidlyrotatearoundatransverseaxis.This isa rotatingelectromagneticdipolewhichemitsaphoton intoacharacteristicemissionpatternassociatedwithdipoles.TheCOmoleculeoscillatingdipoleemissionisalwayscombinedwithachangeofoneunitofangularmomentumassociatedwithachangeinrotationalenergylevel.Theemissionofaphotonalwaysremovesħofangularmomentum.Next,supposethatwehadadiatomicmoleculewherebothoftheatomswerepositivelycharged.Oscillatingorrotatingthismoleculewouldalsoproduceelectromagneticradiation,butatamuchlowerefficiencybecausebothatomshavethesamecharge.Thisproducesadifferentemissionpattern known as a “quadrupole emission pattern”. Even though quadrupole emission isdifferent thandipoleemission, thephotonsproducedbyquadrupoleemissionhavethesamefundamental properties as photons produced by dipole emission. Both are electromagneticradiationwithtransversewaveproperties.Thisiswheretheelectromagneticanalogytodipolewaves inspacetimebreaksdownbecausewaves inspacetimehavea fundamentaldifferencebetweendipolewavescomparedtoquadrupolewaves gravitationalwaves .Masshasonlyonepolarity.Therefore,itisimpossibletogeneratedipolewavesinspacetimebyoscillating or rotating two connected masses. The lowest order wave obtainable byunsymmetrical acceleration of mass such as an oscillating ellipsoid or a rotating rod isquadrupolegravitationalwaves.Gravitationalwavesaretransversewaveswhichpropagateatthe speedof light in themediumof spacetime. For example, a gravitationalwavepassing aspherical volume would convert the spherical volume into an oscillating ellipsoid. Onedimensiontransversetothepropagationdirectionelongateswhiletheorthogonal transversedimension contracts. These offset each other so that the oscillating ellipsoid has the samevolumeasthesphericalvolume.Also,agravitationalwavedoesnotchangetherateoftimeasitpassesatestvolume.Toobtaindipolewavesinspacetimebyacceleratingmass, itwouldbenecessarytohavethecenter ofmass of a closed system accelerate in violation of the conservation ofmomentum.Anotherimpossiblealternativewouldrequireonemassofordinarymatterandanothermassthatexhibitednegativeenergy.This“anti‐gravitymatter”wouldproduceaninversecurvatureofspacetimecomparedtoordinarymatter.Asdistancetotheanti‐gravitymatterdecreased,therate of time would increase and proper volume would decrease the opposite of ordinarymatter .Amasswithanti‐gravitywouldbetheequivalentofanegativegravitationalchargeanditwouldalsohavetobehypotheticalnegativeenergy.Ifaparticleofordinarymatterwasattachedtoahypotheticalantigravityparticleandthecombinationrotated,thewaveemittedwouldcausetherateoftimeatanypointintheequatorialplanetospeedupandslowdown.Alsopropervolumewouldexpandandcontractattheselocations.Thehypotheticalwaveinspacetimethatwouldbe
generatedwouldbeadipolewaveinspacetime.Theeffectonspacetimewouldbetheequivalentofamodulatedgravitationalfield.Electricallyneutralparticles,nomatterhowmassive,wouldundergoanoscillatingaccelerationtowardsandawayfromthehypotheticalrotatingobject.Thisdipole wave in spacetime is the simplest type of hypothetical wave, but it would also be aviolationoftheconservationofmomentumif itoccursonthemacroscopicscale largerthanPlancklength .Thereisnowayofgeneratingadipolewaveinspacetimewithordinarymatter.Envisioning a Dipole Wave in Flat Spacetime: Chapter 5will give some figures to helpquantifyadipoleinspacetimeincludingfigures.Thereisnowayofgeneratingtotallynewdipolewaves newenergy inspacetime.Planckamplitudedipolewavesinspacetimeandquantizedangularmomentumareallpartof thepropertiesof spacetimeand these fluctuationsexistedsincetheBigBang.Imagineanemptyvoidwithnovacuumfluctuationsatanyscale.Thisvoidwouldhavenophysicalproperties–nospeedoflight,noimpedance,nogravitationconstant,nopermittivity εo ,nofieldofanykind.Thisquietvoidgoestoofar,soinsteadwewillimagineperfectlyflatspacetimewithaperfectlyuniformrateoftimeandperfectlyuniformEuclidiangeometryevenatthesmallestscale.Next,wewillimaginethisvolumefilledwithmultiplesmallamplitudedipolewavesinspacetime.Thetemporalpartofadipolewavecausestherateoftimetospeedupandslowdownslightly.If therewereperfectpointclocksdistributedthroughout thisvolume,someclocks located involumesof“fasttime”wouldberunningslightlyfasterthanclocks locatedinthe“slowtime”volumes of spacetime. The dipolewaves are oscillations, therefore a clock that is runningslightly fast one instant would run slightly slow at a later time. There is also chaoticrearrangements of the dipole waves, so the distribution also changes. If it was possible tomomentarily freeze thedipolewaves inspacetime,wewould find that thevolume isnot flatspacetimeeither.Thelocationsthathaveslowrateoftime,haveaslightlylargervolumethanexpectedfromEuclidiangeometry.ThelocationsthathavefastrateoftimehaveslightlylesspropervolumethanexpectedfromEuclidiangeometry.Thisconnectionbetweentherateoftimeandvolumealsooccursonthemacroscopicscale.Aswasdiscussedinchapter2,avolumethatexhibitsafastrateoftimealsoexhibitsanon‐Euclidiandecreaseinpropervolumecomparedtothesurroundingspace.Similarly,avolumethatexhibitsaslowrateoftimealsoexhibitsnon‐Euclidianenlargedpropervolume.Likeallwaves,dipolewavesinspacetimealwayshaveequalamountsofwavemaximumsandwaveminimums.Forexample,afastrateoftimecanbeconsideredawavemaximumandaslowrateoftimecanbeconsideredawaveminimum. Thepoint is thateventhoughthere isarandomqualitytothedipolewaves,thereisalwaysapairingofmaximumandminimumspacetimedistortionsoveradistanceofonewavelength.Ifwewereflippingcoinstodeterminethedistributionoffastandslowvolumesofspacetime, itwouldbepossible to finda few locations thatbychancehadagroupingofalmostall fastorslowtimedistortionsandthiswouldbedetectable.However, ifthereneedstobeapairingoffastandslowtimecomponentsonthescaleofperhapstwotimes
Plancklength,thenthisdictatesadifferentrangeofpossibilities.Allthatispossibleisaslightvariation in the orientation of fast and slow locations. This is a plausible mechanism thatenforces the Planck length/time limitation over a time period long enough to make ameasurementatthespeedoflightacrossatestvolumeofspacetime.Dipolewaves in spacetime represent the simplest type of wave distortion of spacetime. Incontrast,avolumefilledwithchaoticgravitationalwaves quadrupolewaves wouldhavenooscillationoftherateoftimeandnooscillationinpropervolume.Therewouldbeaneffectonthedistancebetweenpoints,butanincreaseindistanceinonedimensionisoffsetbyadecreaseindistanceinanorthogonaldimensionsothatthereisnonetchangeinvolume.Thewaythatgravitationalwavesaffectspacetimemeansthattheycanproduceameasurableoscillationinthedistancebetweentwopoints.Inotherwords,gravitationalwavescanproducechangesinthedistancebetween twopoints that ismuch greater thanPlanck length. This is a fundamentaldifferencebetweendipolewavesinspacetimeandgravitationalwaves.Thewavepropertiesofgravitationalwavesaredetectable, thewavepropertiesofdipolewaves inspacetimearenotdetectableasdiscretewaves.However,itwillbeshownthattherearemanyobservableeffectsofthesePlanckamplitudewavesinspacetime. “Spacetime Field”: What is a field? John Gribbin11 describes a field as a physical quantity that has a value for each point in space and time. John Archibald Wheeler says a field “occupies space‐Itcontainsenergy.Itspresenceeliminatesatruevacuum.”12RichardFeynmansaid,"Afieldhassuchfamiliarpropertiesasenergycontentandmomentum,justasparticlescanhave".13AlbertEinsteinequated“field”to“physicalspace”.Thestandardmodelisafieldtheory. Fundamentalparticlesaredescribedas“excitations”oftheirassociated“fields”. Therefore,eventhestandardmodelhasthevacuumfilledwithfieldenergy.Sinceparticlesareexcitationsoffields,andfieldsexertforces,itmightbesaidthatallparticlesandforcesarederivedfromfields.Inotherwords,thestandardmodelimpliesthat“theuniverseisonlyfields.”Itisashortjumpfromthisto“theuniverseisonlyspacetime”.Thestandardmodelcurrentlyhas17namedfundamentalparticlesbutthisnumbercouldbeincreased if the “color” difference is counted as separate particles. This implies theunappealingprospectthatthevacuumcontainsatleast17overlappingfields.Thestandardmodel describes these particles, but it does not give a physical description of the fieldsthemselves. Lacking this base, physics currently contains manymysteries which can bedescribedmathematicallybutarenotunderstoodconceptually.
11 John Gribbin (1998). Q is for Quantum: Particle Physics from A to Z. London: Weidenfeld & Nicolson. p. 138. ISBN 0-297-81752-3 12 John Archibald Wheeler (1998). Geons, Black Holes, and Quantum Foam: A Life in Physics. London: Norton. p. 163. 13 Richard P. Feynman (1963). Feynman's Lectures on Physics, Volume 1. Caltech. pp. 2–4
Theproposalpresentedinthisbookisthatthereisonlyonetrulyfundamentalfieldwhichwillbenamedthe“spacetimefield”.Thisistheseaofdipolewavesinspacetimepreviouslydescribed Planckfrequency,displacementamplitudeof Lp,TpandPlanckenergydensity .Besides wave properties, the spacetime field will be shown to possess impedance, bulkmodulus, pressure and superfluid characteristics which will be described. All thefundamentalparticleswillbeshowntobeafewcombinationsoffrequency,amplitudeandspinwhichachievearesonancewithinthespacetimefield.Thereisonlyoneuniversalfieldthespacetimefield whichhasmultipleresonances stabilityconditions correspondingtothe fundamental particles. Rather than 17 separate fields which lack conceptuallyunderstandablephysicsandunification,asinglefieldwillbedescribedinenoughdetailtoeventuallypermitcomputermodelingofthequantummechanicaloperationsofphysics.Predominant Frequency of Dipole Waves in Spacetime: Zeropointenergy isdescribedasharmonicoscillators,eachwithenergyofE ½ħω.TheusualdescriptionisthateachharmonicoscillatoroccupiesavolumeofV kλ3 k c/ω 3wherekisanumericalfactornear1. Thisleads to theconceptof thespectralenergydensitydiscussedpreviously in thischapter. TheusualassumptionisthatallfrequenciesarecontinuouslypresentuptoamaximumfrequencyequaltoPlanckfrequency.The“spectralenergydensity”ofthesewavesscalewithω3,thereforethehigherfrequenciesdominatetheenergydensity.I previously used thiswave frequency and density description in earlier drafts of this book.However,Ialwaysknewthattherewasanotheralternativemodelofthefrequencydistributionwhichisslightlydifferent.Icannotchoosebetweenthesetwoalternatives,soIwillmentionthealternativealso.InthisalternativethespacetimefieldisdipolewavesatPlanckfrequencywhenviewed from the rest frameof referenceof the cosmicmicrowavebackground CMB .Otherfrequencies canexist in spacetimeas spatial and temporalmodulationsof this seaofPlanckfrequency dipole waves in spacetime. Therefore, the presence of these other frequenciesbroadensthespectrumaroundPlanckfrequency.Inthisalternativemodel,theBigBangonlyinitiallygeneratedPlanckfrequency ∿1043s‐1 dipolewaves.Thesemonochromaticwavesthenbecamethefoundationofthespacetimefield.Allthelowerfrequencydipolewavesthatwillbeshown to be required to make particles and forces are wave distortions on this energeticbackgroundofPlanckfrequencywaves.BothalternativeshavelowfrequencywavesontopofpredominantlyPlanckfrequencywaves.It should be mentioned that the spacetime field is a completely different concept than thegranularity or pixelationproposedby “loopquantumgravity”. In loopquantumgravity, thepredictedgranularityofspacetimehasdimensionsontheorderofPlancklength.ThereisalsoaminimumunitoftimeequaltooneunitofPlancktime. Therefore, the loopquantumgravitymodel has spacetime broken into static pixels of volume and time. These pixels are not
oscillatingdipolewaves inspacetimeand thereforedonotrepresent the tremendousenergydensityofspacetimerequiredtoexplainzeropointenergy.Planck Scale:ThementionofPlancklengthandPlancktimedoesnotnecessarilyimply“Planckscale”.Theterm“Planckscale”hascometoimplytheconditionsthatwouldexistifparticlesorphotons had Planck energy Ep 1.22 1019 GeV or 1.96 109 Joule . For example, ahypothetical particle with Planck energy Planck mass would have the force of gravity becomparable to the strong force or the electromagnetic force. Such a particle would have aComptonfrequencyequaltoPlanckangularfrequencywhichistheinverseofPlancktime.ThenaturalunitoflengthofsuchahypotheticalparticleisPlancklength.AllofthesepropertiesarehypotheticalbecauseaPlanckmassfundamentalparticledoesnotexist.Itwouldbethesmallestpossibleblackhole.Fermionswillbeshowntobeawaveinthespacetimefieldthatpossessesquantizedangularmomentumwhichisconfinedtoaspecificvolume.Thisisarotatingdistortionofthespacetimefieldatfrequenciesintherangeof1020Hzto1026Hz.TherotatingdistortionofthespacetimefieldhasadisplacementamplitudeofPlancklengthandPlancktimebutthefrequencyismanyordersofmagnitudelessthanPlanckfrequency.ThereforetheenergyismuchlessthanPlanckenergyanddoesnotfitthedefinitionof“Planckscale”.Properties of Dipole Waves in Spacetime: Itisimportanttoalsounderstandthatdipolewavesinthespacetimefieldtravelatthespeedoflightbuttheydonotfreelypropagatelikephotonsorgravitationalwaves. Sincedipolewaves affect the rateof timeand theproper volume, theyinteractwitheachother.Herearesomeotherproposedpropertiesofdipolewavesinspacetimethatarepresentedhereinsummaryformandexplainedlater.
1 Everypartofadipolewave in thespacetime fieldbecomesthesourceofanewwavecalledawavelet .
ThirdAssumption:There is only one fundamental force: Fr = Pr/c. This is a repulsive force
that occurs when waves in the spacetime field, traveling at the speed of light, are deflected.Thissinglefundamentalforceexertedbythedeflectionofwavesinspacetimepropagatingatthespeedof lightwill be called the “relativistic forceFr.”Also,Pr represents “relativisticpower”whichispowerpropagatingatthespeedoflight.Forexample,lightandgravitationalwavesarebothpowerpropagatingatthespeedoflight.Dipolewavesinspacetimewillalsobeshowntobeanotherformofenergypropagatingatthespeedoflight.Therelativisticforceistheonlyforcedeliveredbydipolewavesinspacetime.Thisenergyalwayspropagatesatthespeedoflight,evenwhenitseemstobeconfinedtoalimitedvolume. Thelimitedvolumeistheresultofspeedoflightpropagationinaclosedloopandinteractingwiththesurroundingvacuumenergy explainedlater .Iproposethattherelativisticforceistheonlytruly fundamental force in the universe. All other forces of nature are just differentmanifestationsof this truly fundamental force.Therelativistic force isderived fromtheonlyfundamentalformofenergyintheuniverse,dipolewavesinthespacetimefield.ItisacommonassumptionamongphysiciststhattheforcesofnaturewereallunitedatthehighenergyconditionsthatexistedshortlyaftertheBigBang.ItistruethatahypotheticalparticlewithPlanckmasswouldhaveagravitationalforceroughlycomparabletotheelectromagneticforceorevencomparabletothestrongforceatshortdistances.Accordingtothecommonlyheldview, the forces of nature separated when the universe expanded and the energy densitydecreased.Theimplicationisthattodaytheforcesofnaturearefundamentallydifferent.Thefundamentalforcesareusuallythoughttobetransferredby“messengerparticles”suchasvirtualphotons, virtual gluons and gravitons. Furthermore, gravity is not included in the standardmodel.Apopularphysicalinterpretationofgeneralrelativityconsidersgravitytobeageometriceffectandnotatrueforce.Therefore, the above assumption is a radical departure from conventional thought. It isproposed thatall forces, thestrong force, theelectromagnetic force, theweak forceand thegravitationalforce ,aretheresultofthedeflectionofwavesinthespacetimefieldtravelingatthespeedoflight. Thecasewillbemadethateventodaythefourforcesofnature includinggravity arestillcloselyrelatedbecausetheyareallderivedfromtherelativisticforce.
TheforceF Pr/ciswellknownastheforceassociatedwithphotonpressurewherePristhepowerof abeamof light. Forexample, theemissionorabsorptionof3 108wattsof lightproducesaforceof1Newton.Theword“deflection”isusedtocoveranychangeinpropagation.Forexample,eventheabsorptionofaphotonbyanelectroninanatomischaracterizedhereasaninteractionbetweenwavesinthespacetimefieldthatinvolvesa“deflection”.Inlaterchaptersit will be shown that the electromagnetic force, the strong nuclear force and even thegravitationalforcearealltheresultofdipolewavesinthespacetimefieldinteractingandbeingdeflected.Energy Density Equals Pressure: Photon pressure is always repulsive. In fact, pressure in any form is always repulsive. EnergydensityUisfundamentallyequivalenttopressureℙwhenwearedealingwithenergypropagatingatthespeedoflight.EventhoughtheunitslookdifferentJ/m3versusN/m2 ,indimensionalanalysisnotationthedimensionsofbothenergydensityandpressurearethesame:M/LT2 mass/lengthtime2 .Forexample,blackbodyradiationinsideauniformtemperatureclosedcontainerhasradiationpressurebeingexertedonthewallsandhasaradiationenergydensityfillingthecontainer. Therelationshipbetweenenergydensityandpressureforblackbodyradiation electromagneticradiation isU 3ℙ. Thefactorof3 inacontainer filledwith blackbody radiation is traceable to 3 spatial dimensions. A laser withcollimatedelectromagneticradiationreflectingbetween2mirrorswouldeliminatethefactorof3andhaveU ℙwhereℙisthepressureexertedonthe2mirrors.Weareignoringnumericalfactorsnear1intheseconceptualequationsthereforewewillequateU ℙ.Therelationshipbetween energy density andpressure is important in cosmology because radiation pressureinsideastarpreventsthestarfromundergoingagravitationalcollapse.Forexample,thecenterof thesun isata temperatureofroughly15milliondegreesKelvin. At this temperature, thephotonenergydensityisabout3 1013J/m3andthephotonpressureisabout1013N/m2.Thisinternalpressurestabilizesthesun’soutputandmakeslifeonearthpossible.Therelationshipbetweenpressureandenergydensityinagasorliquidismorecomplex.Thesimplestexampleoftheenergystorageofthepressurecomponentinafluidcanbeillustratedby the followingexample. Imagine twoheliumatomscolliding inavacuum. Thiscollision isviewedfromtheframeofreferencewheretheatomsareinitiallypropagatingatequalspeedinopposite directions. The kinetic energy of each atom can be associated with a typicaltemperatureusing theBoltzmannconstant. When theatomscollide, the speedmomentarilydrops to zero in this frame of reference and the absolute temperature of each atom alsomomentarily drops to zero. The kinetic energy temperature is temporarily converted tointernalenergyineachatomresultinginadistortionoftheelectroncloudofeachheliumatom.Inahighpressuregastherearemanysuchcollisionspersecond.Theenergyassociatedwiththepressureofthegascanbetracedtothefactthatatomsinthegasspendpartofthetimewithadistortedelectroncloudthathashigherenergythananisolatedatomwithnodistortion.Ahighpressuremonatomicgashas3energycontributionstoitstotalenergydensity;1 theinternal
energy E mc2 oftheindividualatoms,2 thekineticenergyofthetemperatureand3 thepressurecomponentresultinginadistortedelectroncloud.Nowwewilllookatthemuchsimplercaseofconfinedlight.EachphotonhasenergyofE ħω,andthetotalenergydensityoftheconfinedlightisU 3ℙforchaotic3dimensionalpropagationsuch as confined black body radiation. It is proposed that the equivalence between energydensityandpressureappliesinallcasesbecausetheunitsarethesame M/LT2 andthephysicalinterpretationoftheseunitsisthesame.Thereareafewcasesinphysicswheretwodissimilardefinitionscanhave the sameunitswhenexpressedas length, timeandmass. Forexample,torqueandenergybothhaveunitsofML2/T2.However,itisclearthattorqueisforceappliedthrougharadiallengthrwithoutmotion nowork .EnergyisforceappliedthroughadistanceML/T2 L .Theunitsofenergyhavetobeinterpretedasrequiringmotionthroughadistancework .Thereisneveranexamplewhereaunitoftorqueisequaltoaunitofenergybecausethephysicalinterpretationoftheunitsisfundamentallydifferent.Inthecaseofenergydensityandpressure,thephysicalinterpretationisthesame.Itisproposedthatatthemostfundamentallevel,energydensityALWAYSimpliespressure.Itisproposedthateventheenergydensityofaprotonorelectronimpliespressure. Itisnotpossible to casually ignore theenergydensityof aprotonandassume that since there isnoobviouscontainerrestrainingtheimpliedpressurethattheequivalencebetweenenergydensityand pressure has somehow been broken. The standard model assumes that fundamentalparticleshavenointernalstructureandnovolume pointparticles .Evenstringtheoryhasonedimensional stringswithnovolume.Therefore,bothof these require infinite energydensitywhichimpliesinfinitepressure.Thelawsofphysics“breakdown”–endofstory!Thealternativeoffered by the spacetime based model of particles and forces is that everything isunderstandable.Thelawsofphysicsneverbreakdown.Distortionsofspacetimecanappeartobepointparticlesiftheexpectationisaclassicalobjectwithahardsurface.However,wewillshowhowitispossibleforfundamentalparticlestobeareasonablefinitevolumedistortionofspacetimewhichappearstobeapointparticleinexperiments.Attractive Forces: Thepreviousassumptionissurprisingbecauseitclaimsthatthereisonlyonefundamentalforceandbecauseitclaimsthatthissinglefundamentalforceisonlyrepulsive.The obvious question is: How can attractive forces such as gravity, the strong force or theelectromagneticforcebetheresultofasingleforcethatisonlyrepulsive?Thedetailedanswertothisquestionrequiresadditionalinformationcoveredinsubsequentchapters.However,itispossibletogiveabriefintroductoryexplanationhere.ItwaspreviouslyexplainedthatvacuumfluctuationshaveenergydensityequaltoPlanckenergydensity. From the equivalence of energy density and pressure, it follows that vacuumfluctuationsarecapableofexertingamaximumpressureequaltoPlanckpressure 10113N/m2.Lateritwillbeshownthattheproposedspacetimebasedmodeloffundamentalparticleshasa
specific energy density and this requires that vacuum energy/pressure exert an offsettingpressuretoachievestability.Forexample,aprotonhasaknownradiusofabout10‐15m.Thisvolumecombinedwiththeproton’senergyimpliesthataprotonhasenergydensityofabout1034 J/m3. Thisenergydensity impliesthat thewaves formingaprotongeneratean internalpressure of about 1034 N/m2. Stated another way, an isolated proton is stabilized by thespacetime field exerting a repulsive force on all sides of the proton. An electric field is adistortionofthespacetimefieldthatwillbediscussedinchapter9.Iftheprotoncomesnearanelectron,theprotonexperienceswhatweconsidertobeaforceofelectrostaticattraction.Itwillbeshownthatthisisactuallyanunbalancedrepulsiveforce.Thevacuumpressurerequiredtostabilizeaprotonisunbalancedbythedistortionofthespacetimefieldcausedbytheelectron’selectricfield.Thisresultsinwhatappearstobeaforceofattraction.Inthismodeltherearenoexchangeparticlesthatsomehowachieveattraction.Allactionatadistanceisultimatelytraceabletoalocalizedimbalanceinvacuumpressure.Therearealsonoattractiveforces.Thereisonlyanunbalancedrepulsiveforce unbalancedpressure exertedonfundamentalparticlesby thedipolewaves thatare thevacuumfluctuationsof thespacetimefield.Thisintroductoryexplanationlacksmanyessentialdetailsthatwillbeprovidedlater.
ImpedanceofSpacetimeThefirststepinunravelingthe10120discrepancybetweenthequantummechanicalmodelandthe general relativity model is to see if there is anything in general relativity that actuallysupports the idea of a large vacuum energy density. It is proposed that an analysis ofgravitationalwaves indeedgivessupport to thequantummechanicalmodelof thespacetimefield.GravitationalwavesareaformofenergythatpropagatesatthespeedoflightastransversewavesINspacetime.Theyproduceadynamicdistortionof2ofthe4dimensionsofthespacetimefield.Thedistortionconvertsthesphericalvolumeintoanoscillatingellipsoid.Onetransverseaxisoftheellipsoidelongateswhiletheorthogonaltransverseaxiscontracts.Thisoscillationoftheellipsoidproducesnonetchangeinvolumefromtheoriginalsphericalvolumeandthereisnochangeintherateoftime.Sincegravitationalwaves quadrupolewaves donotmodulatevolume or the rate of time, gravitationalwaves can have a displacement of spacetimemuchgreaterthanthePlancklength/timelimitationthatappliestodipolewavesinspacetime.Gravitational waves transfer energy and angularmomentum. In 1993 the Nobel Prize wasawardedtoRussellHulseandJosephTaylorfortheproofthatabinaryneutronstarsystemwasslowingdownitsrotationbecauseitwasemittingabout1025wattsofgravitationalwaves.Theamountofslowingwaswithin0.2%oftheamountpredictedbygeneralrelativity.Theemissionofgravitationalwavesproducesaretardingforceontherotatingbinarystars,thusproducingan
observableslowingoftherotation lossofenergyandangularmomentum .Ifitwaspossibleto reverse the direction of these gravitational waves, the gravitational waves would returnenergyandangularmomentumtothebinaryneutronstarsystem.Thereasonthatgravitationalwavesareintroducedintoadiscussionabouttheenergydensityofspacetimeisthatgravitationalwavesarepropagatinginthespacetimefield.Theyareanalogoustosoundwavespropagatinginanacousticmedium.Thesamewaythattheequationsforsoundpropagation give information about the acoustic medium, so also the gravitational waveequationscangiveinformationaboutthepropertiesofthespacetimefield.Zs – The Impedance of Spacetime:Inacoustics,allmaterialsofferoppositiontoacousticflowwhenanoscillatingacousticpressureisapplied.Forexample,tungstenhasthehighestacousticimpedance which is about 2.5x106 times greater than the acoustic impedance of air.Electromagneticradiationalsoexperiencesacharacteristicimpedanceasitpropagatesthroughspace.Theelectricfield andmagneticfield arerelatedbythe“impedanceoffreespaceZo”.Therelationshipis:
Zo≡ / = 376.7Ωimpedanceoffreespace
Gravitational waves also experience impedance as they propagate through spacetime. IidentifiedtheimpedanceexperiencedbygravitationalwaveswhenIfirststartedworkingonthisproject.IwassurprisedthatIinitiallycouldnotfindanyotherreferencetothis.Afterabout5years, Idiscoveredthattheimpedanceofspacetimehadbeenpreviously identifiedbyBlair14fromananalysisofgravitationalwaveequationsandreportedinthe1991bookTheDetectionofGravitationalWaves.However,eveninthatbooktheimpedanceofspacetimeisonlycasuallymentionedandisnotusedinanycalculations.Sincethen,theimpedanceofspacetimeappearstobeignoredbythescientificcommunity.Aswillbeseen,theimpedanceofspacetimeisthekeytoquantifyingthepropertiesofthespacetimefield.MostofthecalculationsintheremainderofthisbookdependonthisimpedancewhichisidentifiedbyBlairas:
Zs c3/G 4.038 1035kg/sZs impedanceofspacetime
The reasoning that ledme to independentlydiscover the impedanceof spacetimestartedbycomparinggravitationalwavestoacousticwaves.Allpropagatingwavesinvolvethemovementofenergy.Inotherwords,propagatingwavesofanykindareaformofpower.Thereisageneralequation thatapplies towavesofanykind. Themostcommon formof thisequationrelatesintensity“ ”,thewaveamplitudeA,thewaveangularfrequencyω,theimpedanceofthemediumZandadimensionlessconstantk.Theintensity canbeexpressedinunitsofw/m2.
14 Blair, D. G. (ed.): The Detection of Gravitational Waves. p 45. Cambridge University Press, Cambridge New York Port Chester (1991)
kA2ω2ZWe will first illustrate the use of this general equation using acoustic waves. The acousticimpedanceis:Za ρcawhereρisdensityandcaisthespeedofsoundinthemedium acousticspeed .Acousticimpedancehasunitsofkg/m2susingSI dimensionalanalysisunitsofM/L2T .Theamplitudeofanacousticwaveisdefinedbythedisplacementofparticlesoscillatinginanacousticwave.Theamplitudeterminacousticequationshasunitsoflengthsuchasmeters.When the equation k A2ω2Z is used for gravitational waves, the amplitude term is adimensionlessratiowhichinitssimplestformcanbeexpressedasstrainamplitudeA ΔL/L.Thisratioisexpressingastraininspacetimewhichcanalsobethoughtofasthemaximumslopeof a graph that plots displacement versus wavelength. When the amplitude term isdimensionlessstrainamplitude,thenforcompatibilitytheimpedanceofspacetimeZsmusthavedimensionsofmass/time M/T .Eventhough kA2ω2Zisauniversalwave‐amplitudeequation,itcanonlybeusedifamplitudeAandimpedanceZareexpressedinunitscompatiblewithintensity watts/m2 inthisequation.Forexample,electromagneticradiationisusuallyexpressedwithamplitudeinunitsofelectricfieldstrengthandthe impedanceof freespaceZo inunitsofohms. Thiswayofstatingwaveamplitudeandimpedancedoesnothavethecorrectunitsrequiredforcompatibilitywiththeaboveintensityequation.Asdiscussedinchapter9,thereareotherwaysofexpressingthesetermsthatmakeelectromagneticradiationcompatiblewiththisuniversalequation.The intensity of gravitationalwaves can be complex because of nonlinearities and radiationpatterns. However,thisintensitycanbeexpressedsimplyifweassumeplanewavesandtheweak gravity limit.15 Using these assumptions, the gravitational wave intensity is oftenexpressedas:
υ2A2where: intensityofagravitationalplanewaveandυ frequency
However,thiscanberearrangedtoyieldthefollowingequation: kA2ω2 c3/G k adimensionlessconstant;ω angularfrequencyAs ΔL/L strainamplitudewhereLismeasurementlengthandΔListhechangeinlength
15 D. G. Blair, The Detection of Gravitational Waves, Cambridge University Press, 1991, p. 34
Itisobviouscomparingthisequationtothegeneralequation kA2ω2Zthatthetwoequationshavethesameformandthattheimpedancetermmustbe:Z Zs c3/G5 Wave-Amplitude Equations:Nowthatwearearmedwiththeimpedanceofspacetime,theequation for intensity can be converted into equations that express energy density U ,energy E andpower P .Ifwearerestrictedtowavespropagatingatthespeedoflight,thenwecanalsoconvert the intensityequation intoanexpressionof the force F exertedbythepropagating wave. This conversion incorporates the equation F P/c where P is powerpropagatingatthespeedoflight.Thesewillbecalledthe“5wave‐amplitudeequations”.Theseequationsalsousethesymbolsof: area m2 ,V volume m3 andk dimensionlessconstantnear1
kA2ω2Z intensity w/m2 U kA2ω2Z/cU energydensity J/m3 U /c andU ℙ pressureE kA2ω2ZV/cE energy J E V/c P kA2ω2Z P power J/s P F kA2ω2Z /cF force N F /c These5equationswillbeusednumeroustimesintheremainderofthebook.Itisproposedthatallenergy,forceandmatterisderivedfromwavesinthespacetimefieldandthese5equationswillbeusedtosupportthiscontention.TheamplitudetermAneedsfurtherexplanation.Weare presuming waves propagating at the speed of light and we are temporarily excludingelectromagneticwavesuntilchapter9.Thisleavesgravitationalwavesanddipolewavesinthespacetimefield.Weneedtostandardizehowwedesignatetheamplitudeofthesewaves.Forgravitationalwaveexperimentswherethewavelengthismuchlongerthanthemeasurementpathlength λ L ,itisacceptabletodesignatethestrainamplitudeasAs ΔL/L.However,whenwearedealingwithanarbitrarywavelengthwhichmightbesmall,itisnecessarytospecifystrain as the maximum slope of a graph that plots displacement versus wavelength. Thismaximumslopeoccurswhenthedisplacementiszeroandthestrainismaximum seefigures5‐3and5‐4inchapter5 .IfwedesignatethemaximumdisplacementasΔL,andthewavelengthasλ,thenthemaximumstrain maximumslope isAs ΔL/λ.whereλ λ/2π.Thisexamplepresumesthatweareworkingwithadisplacementof length. Gravitationalwavesproducealength modulation with offsetting effects in orthogonal dimensions such that there is nomodulationofvolumeandnomodulationoftherateoftime.Therefore,gravitationalwavesarenot subject to thePlanck length/time limitation that applies todipolewaves. As previouslyexplained, dipole waves have amaximum spatial displacement amplitude of ΔL Lp and amaximumtemporalamplitudeofΔT Tp.Therefore,themaximumstrainamplitude Amax ofadipolewaveis:
Impedance of Spacetime from the Quantum Mechanical Model:Nowthatweareequippedwiththe5wave‐amplitudeequations,thedipolewavehypothesisandAmax Lp/λ,itispossibletoanalyzezeropointenergyfromanewperspective.Ifzeropointenergyisreallydipolewavefluctuations inthemediumofspacetime, then itshouldbepossibletodoacalculationwhichsupports this idea. For review, the quantum mechanical model of the spacetime field hasspacetimefilledwithzeropointenergy quantumoscillators withenergyofE ½ħω.Ifweareignoring numerical factors near 1, therefore we can consider each quantum oscillator asoccupyingavolumeV λ3.Thismeansthattheenergydensityofthequantummechanicalmodelofzeropointenergy isU ħω/λ3 ħω4/c3.Nowwearereadytocalculatetheimpedanceofspacetimeobtainedfromacombinationof1 zeropointenergywithenergydensityU ħω4/c3;2 dipolewavesinspacetimewithmaximumamplitudeofAmax Lp/λ,and3 thepreviouslyobtainedequationforenergydensityU A2ω2Z/c.Rearrangingtermswehave:Z Uc/A2ω2
Set:U ħω4/c3andA Amax ħ ⁄
Zħ
ħ ZsSuccess!
Link between QM and GR Models of Spacetime:Thisisafantasticoutcome!Wetooktheenergydensityofzeropointenergyandcombinedthatwiththestrainamplitudeofadipolewavein the spacetime field and an equation from acoustics. Whenwe solved for impedanceweobtainedc3/G.Thisisthesameimpedanceofspacetimethatgravitationalwavesexperienceastheypropagate through spacetime. Tome, this implies that the characteristics of spacetimeobtainedfromgeneralrelativityagreewiththequantummechanicalmodelofthespacetimefieldfilledwithzeropointenergyandexhibitingenergydensityof10113J/m3.Howcanthisbe?Thegeneralrelativitymodelincorporatescosmologicalobservationandsetstheenergydensityoftheuniverseatabout10‐9J/m3.Actuallythisisanerroneouscomparison.Thequantummechanicalmodelofthespacetimefieldisgivingthehomogeneousinternalenergydensityofspacetimeitself.Whengravitationalwavespropagatethroughthespacetimefield,theyareinteractingwiththisinternalstructureofthespacetime field and thegravitationalwavesexperience impedanceofZs c3/G. Theenergydensityof10‐9J/m3obtainedbycosmologicalobservationisnotseeingtheinternalstructureofspacetime with its tremendous energy density of dipole waves. Instead, the cosmologicalobservationsarejustlookingattheenergydensityofthefermions,bosonsand“darkenergy”discussed later . This isnot thesame thingas the internal structureof thespacetime field.Gravitationalwaves can propagate through the spacetime field that contains no fermions orbosonsandstillexperienceZs c3/G.Assumingthatthetotalenergydensityoftheuniverseis
10‐9J/m3islikelookingonlyatthefoamonthesurfaceoftheoceanandignoringallthewaterthatmakesuptheocean.The first part of reconciling the difference between the general relativity and quantummechanicalmodelsof spacetime is toview thequantummechanicalmodelasdescribing theinternalstructure themicroscopicstructure of thespacetimefield. Meanwhile, thegeneralrelativitymodelisdescribingthemacroscopiccharacteristicsofspacetimeandtheinteractionswithmatter.If the spacetime field canpropagatewaves such as gravitationalwaves ordipolewaves , itimpliesthatthespacetimefieldmusthaveelasticity.Thiselasticityrequirestheabilitytostoreandreturnenergyasthewavepropagates.Themediumitselfmusthaveenergydensity.Thequantummechanicalmodelofspaceisfilledwithaseaofenergeticfluctuations dipolewaves .If these are visualized as energetic waves in the spacetime field, then a new wave can bevisualizedascompressingandexpandingthesepreexistingwaves.Ifthisnewwavecausesthepreexistingwavestoslightlychangetheirfrequencyanddimensions wavelength astheyarebeingcompressedandexpanded,thenthispictureprovidesthenecessaryelasticityandenergystoragetothespacetimefield.Thismightsoundlikeacircularargumentsinceeachwavecontributestotheelasticityrequiredbyallotherwaves.Whataboutthe“first”wave?Thissubjectwillbediscussedfurtherinthetwocosmologychapters13and14.However,itwillbeproposedthattherewasnofirstwave.Thespacetimefieldcameintoexistencealreadyfilledwiththesevacuumfluctuations.Energeticwavesaresimplyafundamentalpropertyofthespacetimefieldthatgivethevacuumpropertiessuchasεo,µo,c,G,Zs,etc..Infact,thespacetimefielddoesnothavewaves;thespacetimefieldIStheseaofvacuumfluctuations waves describedbythequantummechanicalmodel.Spacetimeneverwasthequietandsmoothmediumassumedbygeneralrelativity.Thereforethereneverwasatimewhenafirstwavewasintroducedintoaquietspacetime.ThiswavestructurewithitsPlancklength/timelimitationcanbeignoredonthemacroscopicscalebutspacetimehasaquantummechanicalbasis.Thetaskisnottofindamechanismthatcausescancelationofthistremendousenergydensity.Thisenergydensityisreallypresentinthespacetimefieldandisnecessarytogivethespacetimefieldthepropertiesdescribedbygeneralrelativity.Insteadthefocusneedstoturntofindingthereason that thishighenergydensity isnotmoreobviousandwhy itdoesnot itselfgenerategravity.Istheresomethingabouttheenergyinvacuumfluctuationsthatmakesitdifferentthantheenergyinmatterandphotons?Thisquestionwillbeansweredlater.Energy Density of Spacetime Calculated from General Relativity: Previouslyweshowedthatit was possible to deduce the impedance of spacetime Zs c3/G from quantummechanicalconsiderations,zeropointenergyandanequationfromacoustics.However,nowwewillshow
thatitispossibletocalculatetheenergydensityofthespacetimefieldusingjustequationsfromgeneral relativity and acoustics. Since general relativity and quantum mechanics are oftenconsideredtobeincompatible,itmightseemunlikelythatwewouldturntogeneralrelativitytoanalyzethequantummechanicalenergydensityofspacetime.Thereasonforsuspectingthatthismightbeafruitfulapproachisthatgravitationalwavesarelikesoundwavespropagatinginthemediumofspacetime.Itiswellknownthatanalyzingtheacousticpropertiesofamaterialcanreveal someof itsphysicalpropertiesof themedium including itsdensity. Gravitationalwaves are like sheer acoustic waves propagating in the medium of the spacetime field.Therefore,wewillmakeanalogiestoacousticsandattempttocalculatetheenergydensityofthespacetimefield.Thefollowingequationfromacousticsrelatesthedensityofthemediumρtointensity ,particledisplacementΔx,acousticspeedofsoundca,andangularfrequencyω. kρω2caΔx2. Thespacetimefielddoesnothaverestmasslikefermions,butgravitationalwavesdopossessmomentum.Aspreviouslyexplained,ifwecouldconfinegravitationalwavesinahypothetical100%reflectingbox,thenthegravitationalwaveswouldexhibitrestmess.Theboxismerelyturningtravelingwavesintostandingwaves.Thewavesthemselvespossesscharacteristicsthatcan be associated with not only energy density but also mass density under specializedconditions.Ifwecancalculatetheenergydensityofthespacetimefieldusingequationsfromacoustics and gravitational waves, then this will be important not only for establishing thequantummechanicalpropertiesofspacetime,butalsoformakingaconnectionbetweengeneralrelativityandquantummechanics.Earlierinthischapter,anequationwasreferencedwhichconnectstheintensity ofgravitationalwaveswiththefrequencyυandthestrainamplitudeAofthegravitationalwaves.Thisequationassumestheweakfieldlimitwherenonlinearitiesareeliminatedandalsoassumesplanewaves.That equation is repeatedbelow. The amplitudeA of the gravitationalwave is given as thedimensionless strain amplitude maximum slope of A ΔL/λ where ΔL is the maximumdisplacementofspacetimeandthereducedwavelengthis:λ λ/2π c/ω.
υ2A2 kA2ω2 k
Wewillsettheintensityoftheaboveequationequaltotheintensityoftheacousticequation kρω2caΔx2andsolvefordensityρ.ToachievethiswewillsettheacousticdisplacementΔxequaltothegravitationalwavespatialdisplacementΔLandsetacousticspeedca c.
ωp ħ⁄ 1.85 1043s‐1 PlanckangularfrequencyThe terms “interactive density” and “interactive energy density” are necessary because thespacetimefielddoesnothavedensityandenergydensityintheconventionaluseoftheterms.Whenwethinkofthedensityofanacousticmediumsuchaswater,thishasthesamedensityeveniftheacousticfrequencyisequaltozero.Thespacetimefieldonlyexhibitsan“interactivedensity”whenthereisawaveinspacetimewithafinitefrequency.Ifthefrequencyis0,thenρi 0andUi 0.Iwanttobrieflypointoutthattheaboveequationsderivetheenergydensityofspacetimethatmustbethereinorderforgravitationalwavestopropagate.Thepresenceofthisenergydensityandthefrequencydependencewasobtainedfromagravitationalwaveequationandanacousticequationwithnoassumptionsfromquantummechanics.Proceedingwiththespacetimefieldinterpretationoftheseequations,agravitationalwaveisoscillatingapartoftheseaofdipolewavesthatformsthespacetimefield.Thesedipolewavesareslightlycompressedandexpandedbythegravitationalwave,sotheyrevealtheenergydensitythatisactuallyinteractingwiththegravitationalwave.ThedipolewavesinthespacetimefieldareprimarilyatPlanckfrequencyωp 2 1043s‐1.IftherewassuchathingasaPlanckfrequencygravitationalwavefillingaspecificvolume,thenthisPlanckfrequencygravitationalwavecouldefficientlyinteractwithalltheenergydensityinthatspecificvolumeofthespacetime.Noknownparticlescouldgeneratethisfrequency,butthisrepresents the theoretical limits of the properties of spacetime. For example, suppose weimaginetwohypotheticalPlanckmassparticlesformingarotatingbinarysystem.TheywouldbothbeblackholeswithradiusequaltoPlancklengthLp.Astheyrotatedaroundtheircommoncenterofmass,theywouldgenerategravitationalwaves.Iftheywereclosetomerging,thenthefrequencywouldbeclosetoPlanckfrequency.Toexplorethislimitingcondition,wewillassume
a gravitationalwavewith Planck angular frequency and substituteω ωp ħ⁄ intoUi c2ω2/G.ThisgivesPlanckenergydensityUp c7/ħG2 4.63 10113J/m3.Beforeproceeding,weshouldpauseamomentandrealizethatthissimplecalculationhasjustproven that general relativity requires that spacetimemust have Planck energy density forspacetimetobeabletopropagategravitationalwavesatPlanckfrequency. Generalrelativityalso specifies howwaves less thanPlanck frequency interactwith the energy density of the
spacetime field.Wenormally thinkofgeneral relativityasbeing incompatiblewithquantummechanics. However,generalrelativityactuallysupportsandhelpstoquantifytheproposedquantummechanicalmodelofthespacetimefield.InteractiveEnergyDensity fromWave‐AmplitudeEquation: It is possible to gain a differentperspectiveontheinteractiveenergydensityofspacetimebyfindingthesubstitutionintotheequationU kA2ω2Z/crequiredtoyieldUi c2ω2/G.
A 1Therefore,theinteractiveenergydensityisgeneratedwhenwesettheamplitudetermAequalto the largest possible value which is A 1. Planck energy density is obtained when wesubstituteboththelargestamplitudeA 1andthehighestpossiblefrequencyω ωp.AtanyfrequencyωlessthanPlanckfrequency,theinteractiveenergydensityUirepresentsthelargestpossible energy density at frequency ω assuming the medium has impedance equal to theimpedanceofspacetime:Zs c3/G.Togeneralizetheinteractiveenergydensitysothatitappliestomore than just gravitationalwaves,we have view the entire universe even particles asentirelywave‐based.Thiswillbeprovenintherestofthisbook.Thesignificancehereisthatwecanextrapolatefromtheinteractiveenergydensityencounteredbyagravitationalwaveoverdistanceλtotheinteractiveenergydensitythatexistsoverasphericalvolumeofspacetimewithradiusr.Tocalculatethis,wecansubstituteλ rsothatUi Fp/λ2becomesUi Fp/r2.AnalysisofWavesLessthanPlanckFrequency:AtfrequencieslowerthanPlanckfrequency,agravitationalwaveexperiencesamismatchwiththespacetimefieldthatprimarilyhaswavesatPlanckfrequency.Thereisonlyapartialcouplingtotheenergydensityofthespacetimefield.
Thescalingofthelowerfrequenciesisgivenbytheequation .Anumericalexamplewillbegivenwhichassumesagravitationalwavewithanangularfrequencyof1s‐1andreduced wavelength of 3 108 m. For this wave, the frequency mismatch factor is
2.9 10‐87. Therefore, according to Ui Up the interactive energydensityencounteredbythisfrequencyis:Ui 1.35 1027J/m3orρi 1.5 1010kg/m3.Ifagravitationalwavewithangularfrequencyof1s‐1isassumedtohaveintensity 1w/m2,thenusing the previously stated gravitationalwave equation, the oscillating spatial displacementproducedoveradistanceequaltothereducedwavelengthis:ΔL 4.7 10‐10m.Iwillnotgothroughtheentirenumericalexample,butaλ3volumehasan interactivemassof4 1035kg.Ignoringnumericalconstants,theenergydepositedbythegravitationalwaveinthisvolumeisE λ2/ω 9x1016J.Ifyoucalculatethedistancethatthisenergywillmovea4x1035kgmassin
Thedipolewavesinspacetimecontainedinthegravitationalwavevolumecannotbephysicallymovedbecausetheyarealreadypropagatingatthespeedoflight.Instead,thegravitationalwaveiscausingaslightchangeinfrequencywhichproducesashiftinenergyequivalenttoimpartingkinetic energy to amass equal to the interactivemass discussed. Nowwe can conceptuallyunderstand why gravitational waves are so hard to detect. They are interacting with thetremendouslylargeenergydensityofthespacetimefield.Evenwithalargefrequencymismatch,thegravitationalwavesarestillchangingthefrequencyofaverylargeenergyofdipolewavesinspacetime.Connection to Black Holes: Sofar, thediscussionhascenteredofgravitationalwaveswithangular frequency ω and reduced wavelength λ interacting with the energy density of thespacetimefield. However,forgeneralusetheenergydensitycharacteristicsofthespacetimefieldshouldreallybeexpressedusingthesubstitutionλ r,whereristheradiusofasphericalvolumeofthespacetimefieldratherthanλorωpertainingtogravitationalwaves.Forexample,lateritwillbeproposedthatgravityandelectricfieldsbotharetheresultofadistortionofthespacetimefield.EventhoughthespacetimefieldhasPlanckenergydensity,thisimpliesaPlancklength interaction volume. A larger radius volume interacts in such a way that there is areductioninthecouplingefficiencysimilartotheeffectdescribedforgravitationalwaveswhenλ Lp.ThereforetheequationsforUiandρicanberewrittenusingradiusr.Therefore,wehave:
Therefore, it can be seen thatwe have the same equations. This is another case of generalrelativityconfirmingtheenergydensitycharacteristicsofthespacetimefield.Thepicturethatwillemergeisthatblackholesoccurwhentheenergywithinasphericalvolumeofradiusrfromfermionsandbosonsequalstheinteractiveenergyofdipolewaves whenUbh Ui Anotherinsightintoblackholescanbegainedbyimagingtworeflectinghemisphericalshellsconfining photons at energy density of about 3 J/m3. This photon energy density striking areflecting surface generates pressure of ℙ 2 newton/m2. To hold together the twohemisphericalshellswouldtaketwoopposingforcesof2newtontimesthecrosssectionalareaofthehemispheres.Nextwewillimagineincreasingthephotonenergydensitytothepointthat
itmeetstheenergydensityofablackholewitharadiusequaltotheradiusofthehemisphericalshells.Ignoringgravity,theforcerequiredtoholdtheblackholesizesphericalshellstogethercan be easily calculated. For energy propagating at the speed of light, as previouslydemonstrated,energydensityequalspressure U kℙ . TheequationUi Fp/r2 becomesℙ Fp/Rs2.Ignoringconstantsnear1,PlanckforcemustbesuppliedbythespacetimefieldoverareaRs2tocontaintheinternalpressureofanysizeblackhole.ThesmallestpossibleblackholeconsistingofphotonswouldbeasinglephotonwithPlanckenergyinavolumePlancklengthinradius.Aconfinedphotonof thisenergydensitywouldgeneratePlanckpressure Fp/Lp2 10113N/m2butsincetheareaisonlyLp2,thetotalforcerequiredtoholdthetwohemispherestogether isPlanck force 1044N.A supermassiveblackholesuchas foundat the centerofgalaxieshasmuchlargerradiusandthereforemuchlowerenergydensity.Howeverevenasupermassivebackholerequiresthesameamountofforce Planckforce toholdtheshellstogether.Normallyphysicistsmerelyacceptthatgravitycangenerate this forceandtheydonot try torationalize the physics that causes the various “laws” of physics. In the case of gravity, thespacetimefieldwillbeshowntoapplyarepulsiveforce pressure whichweinterpretastheforceofgravity. Themaximumforcewhich thespacetime fieldcangenerate isPlanck force,thereforeallblackholes,regardlessofsize,requirethisforcetoconfinetheinternalenergy.Why Does the Energy Density of the Spacetime Field Not Collapse into a Black Hole?Theenergy in thespacetime fielddoesnotcollapseandbecomeblackholesbecause this formofenergyistheessenceofspacetime vacuum itself.Thesewavesformthebackgroundenergetic“noise”oftheuniverse.Somequantummechanicalcalculationsrequire“renormalization”whichassumesthatonlydifferencesinenergycanbemeasured.Thereforethebackgroundenergeticfluctuationswhichonlymodulatedistanceby Lpandtherateoftimeby Tpcanusuallybeignored.However,whenweareworkingonthescalewhichcharacterizesvacuumenergy,thenthese small amplitudewavesmust be acknowledged andquantified. These small amplitudewavesarethebuildingblocksofeverythingintheuniverse.Theyareultimatelyresponsiblefortheuncertaintyprincipleandtheygivespacetimeitspropertiesofc,G,ħ,andεo.Thestandardmodelhas17namedparticleswithatotalof61particlevariations colorcharge,antimatter, etc. . Each of the fundamental particles is described as an “excitation” of itsassociatedfield.Therefore,accordingtothestandardmodelthereareatleast17overlappingfields,eachwithitsassociatedenergydensity.Forexample,theHiggsfieldhasbeenestimatedtohaveenergydensityof1046J/m3.Therefore,eventhestandardmodelhasenergetic“fields”whichdonot collapse into blackholes. The spacetime‐basedmodelmerely replaces the17 separatefieldswithunknownstructurewithone“spacetimefield”withquantifiablestructuralproperties.Gravitationalwaveequationshavebeenshowntoimplytheexistenceofthisvacuumenergy density. Zero point energy has long characterized the vacuum as being filled with“harmonic oscillators” with energy of E ½ ħω and energy density of U kħω/λ3. Thespacetime‐basedmodel of the universe characterizes the vacuumenergy as dipolewaves in
spacetimewhichlackangularmomentum.Thishomogeneousenergydensityisresponsibleforthepropertiesofthequantummechanicalvacuum.Curvatureofthespacetimefieldoccurswhenenergypossessingquantizedangularmomentumfermionsandbosons isaddedtothishomogeneousenergydensity.Blackholeswithradiusrareformedwhentheenergydensityoffermionsandbosons quantizedangularmomentum equalstheinteractiveenergydensityofasphericalvolumewithradiusr whenUi Ubh .Inthis case r Rs and we need to measure the radius by the circumferential radius methodpreviouslyexplained. Statedanotherway, theenergydensityof the spacetime fielddoesnotcauseblackholes,itformsthehomogeneousvacuumwithnocurvature.Introducingfermionsandbosonsintothishomogeneousfielddistortsthisuniformbackgroundenergydensity.Whenthisdistortingenergyequalstheinteractiveenergydensityofthespacetimefield,thenthisisthelimitingcondition.This“contamination”distortsthespacetimefieldtotheextentthatitformsablackhole.Interactive Bulk Modulus:InpreviousdraftsofthisbookIalsoincludedaderivationofthe“interactivebulkmodulusofspacetime”designatedwiththesymbolKs.Thebulkmodulusofa
Actuallyinacousticsitisknownthatthebulkmodulusisthesameastheenergydensityforidealgasses ignoringconstantsnear1 .Thiscanbeunderstoodbecauseaspreviouslyshown,energydensityisthesameaspressureforenergypropagatingatthespeedoflightorforidealgasses.Atthepointthat ⁄ 1,thiscorrespondstoΔℙ ΔUwhichinthiscontextisequivalenttotheinteractiveenergydensityofspacetime.Therefore,thisderivationisnotrepeatedhere.Insights into the Speed of Light: Thekeyconceptofspacialrelativityisthatthespeedoflightisconstantinallframesofreference.Inthe19thcenturyphysicistspostulatedthattherewasafluid‐likemediumthatpropagatedlightwavescalledthe“luminiferousaether”. ThisconceptwaslargelyabandonedaftertheMichelsonMorleyexperimentshowedthatthespeedoflightwas constant in all frames of reference and Einstein’s special relativity generated equationswhichdidnotrequiretheaether.However,Einsteinhimselfcontinuedtorefertotheaetheror“physical space” until his death.16 The description of the aether was merely changed tocorrespondtothephysicalpropertiesofspace.Isthereanyreasontobelievethatthespacetimefieldpossessesthepropertythatwouldallowwaves propagating in the spacetime field to propagate at the speed of light in all frames of 16 L. Kostro, Einstein and the Ether, (2,000) Apeiron, Montreal, Canada
reference? Gravitational waves propagate in the medium of the spacetime field and theypropagateatthespeedoflight.Inanyframeofreference,anobserverwouldseeagravitationalwavepropagatingatthespeedoflight.IfitwaspossibletodoaMichelsonMorleyexperimentusinggravitationalwaves,nomotioncouldbedetectedrelativetothemediumofthespacetimefield.Ifspacetimeisvisualizedasamediumconsistingofinteractingdipolewavespropagatingat the speed of light, then it is reasonable that itwould be impossible to detect anymotionrelativetothismedium.ItcanbeshownthatwavesofanykindthatpropagateinthemediumwithimpedanceZs c3/GandstrainamplitudeAs Lp/λwillpropagateatc,thespeedoflight.Vacuum Energy and the Einstein Field Equation:ThereisalsoasimilaritytotheEinsteinfieldequationwhichcanbeconsideredastatementthatenergydensityequalspressure.Ignoringthecosmologicalconstant,theEinsteinfieldequationcanbewrittenas:
Tμυ 8
Gμυset Fpand k
Tμυ kFpGμυThe left side of this equation has Tμυ which is the stress energy tensor with units ofenergy/length3whichisenergydensity.TherightsideofthisequationhasPlanckforceandGμυwhichistheEinsteintensorthatexpressescurvaturewithunitsof:1/length2.Therefore,theright side of this equation is force/area pressure. Therefore from the dimensions a validinterpretation of this equation is that the field equation is an expression of:energydensity kpressure.TheproportionalityfactorisequaltoPlanckforce c4/G timesanumericalfactornear1.Inthelimitofmaximumcurvature,Einstein’sfieldequationsaysthatPlanckforceisthemaximumpossibleforceintheuniverse17. Thoughts on the Impedance of Spacetime: It shouldbeemphasized that the impedanceofspacetimeisoneofthefewtrulyfundamentalpropertiesofspacetime.Forexample,lateritwillbeshownthatitispossibletomakeasystemofunitsthatuseonlythepropertiesofspacetime.OneofthethreepropertiesofspacetimeusedforthissystemofunitsisZs, theimpedanceofspacetime.InPlanckunits underlined ,theimpedanceofspacetimeisequalto1 Zs 1 .Also,theimpedanceofspacetimehasthefollowingconnectiontootherPlanckterms:Zs mp/Tp mpωp Fp/c pp/Lpwhere: mp Planck mass, Tp Planck time; ωp Planck frequency; Fp Planck force;pp Planckmomentum,TheimpedanceofspacetimeisintimatelyconnectedtoallthePlanckterms.ThesePlancktermsrepresentthelimitingvaluesofmass,force,length,momentum,etc.Theimpedanceofspacetime
17 Gibbons, G. W.: The Maximum Tension Principle in General Relativity Found. Phys. 32, 1891 (2002) http://arxiv.org/pdf/hep-th/0210109v1.pdf
isthemaximumpossiblevalueofimpedance.Inorderforgravitationalwavestopropagateatthe speed of light in the medium of the spacetime field, the required impedance is Zs. Theimpedance of spacetime also connects the mass of a black hole to its radius. For exampleZs 4.038 1035 kg/s, and a mass of 4.038 1035 kg has a defined Schwarzschild radiusRs≡Gm/c2equaltothedistancelighttravelsin1second about3x108meters .Ifamediumhasimpedance,theimplicationisthatthemediumhaselasticityandenergydensity.Inthecaseofwavesinspacetime,theimpedanceofspacetimeissolargeZs 4.038 1035kg/sthatevenasmallstrainamplitudeproducesaverylargeintensityforagivenfrequency.Thisenormous impedance of spacetime can only be achieved if spacetime has the large energydensity about 10113 J/m3 implied by zero point energy. The quantummechanical basis ofspacetimeisreal.Inchapter3wesawhowachangeinthegravitationalgammaΓaffectedtheunitsofphysics.ItshouldbenotedthattheimpedanceofspacetimeZsisoneofthefewtermsthatisunaffectedbya change in Γ. There is an analysis not presented here that concludes that Zs must beindependentofΓinorderforallthelawsofphysicstobecovariantwhenthereisachangeingravitationalpotential.Exchange Particles: Thestandardmodelusesexchangeparticlestotransferforce.Forexample,theelectromagneticforceissupposedlytheresultoftheexchangeofvirtualphotonsbetweenchargedpointparticles.Thesevirtualphotonstravelatthespeedoflight,sotheelectrostaticforceiscommonlyexplainedasresultingfromtheemissionorabsorptionofenergytravelingatthespeedoflight.Therefore,thepower P ofvirtualphotonsrequiredtogenerateagivenforceisalso:F Pr/c.Similarly,gravitonsarebelievedbymanyscientiststobetheexchangeparticlethatconveysthegravitationalforce.Whilethespacetimebasedmodeloftheuniversedoesnotrequireexchangeparticles,thepointisthatgravitonssupposedlyalsotravelatthespeedoflightandtheforcetheygeneratewouldalsobeF Pr/c. Forexample,apersonweighing70kgissupposedlybeingpulledtowardstheearthbyabout200billionwattsofgravitonsandthisisbeingresistedbyabout200billionwattsofvirtualphotonsstrikingthebottomofaperson’sshoestokeepthepersonfromsinking intotheEarth. It isproposedherethatgravitonsandvirtualphotonsarereplacedwithanequallylargepowerofinteractingwavesinspacetime.Gluonshavebeenignoredsofar,buttheyarealsoviewedashavinganexplanationassociatedwithwaves in spacetime discussed later .Theweak forcehasalreadybeenunitedwith theelectromagneticforcetoformtheelectroweakforce.Therefore,inthediscussiontofollow,Iwillconcentrateondeterminingtherelationshipbetweenthestrongforce,theelectromagneticforceandthegravitationalforce.However,abriefexaminationoftheweakforcewillbemadelater.NotethatIhaveusedtheterms“thestrongforce”and“thegravitationalforce”.Bothofthesetermsarecurrentlyoutoffavoramongphysicists.Atonetime“thestrongforce”wascommonly
usedtodescribetheforcethatboundprotonsandneutronstogetherinthenucleusofanatom.Sincethediscoveryofquarks,itwasnecessarytonametheforcethatbindsquarkstogetherandtheterm“thestronginteraction”isnowcommonlyused.Withthischangeinterminology,theforcethatbindsprotonsandneutronsisnow“theresidualstronginteraction”.Ineedasimplenameforthestrongestofallforces.Ichoosetoresurrecttheterm“thestrongforce”andredefinethisastheresultantforcefromaninteractionbetweenquarks wavemodel andvacuumenergywavemodel thatbindsquarkstogether.Newton considered gravity to be a force, but a popular physical interpretation of generalrelativity considers gravity to be the result of the geometry of spacetime. The equations ofgeneral relativity are commonly interpreted as describing curved spacetime. However, theconceptofcurvedspacetimedoesnotleadtoaconceptuallyunderstandableexplanationofhowaforceisgeneratedwhenamassisheldstationaryinagravitationalfield.Itwillbeshownthatgravity isareal force that iscloselyrelatedtoboththeelectromagnetic forceandthestrongforce.Therefore,theterm“thegravitationalforce”willbeusedevenpriortoofferingthisproof.
FieldsOnecommonconceptualmodeloftheuniverseamongphysicistsisamodelwhereparticlesareemphasized.Discreteparticlesareviewedaspointsofenergyaccompaniedbyawavefunction.TheCopenhageninterpretationofthiswavefunctionisawaveofprobabilitythatinfluencesthelocationofthepointparticlewhenthereisaninteraction measurement .Inotherwords,thisschoolofthoughtconsiderstheparticleportionthedominantconceptualportionofthewave‐particleduality.However, there is anopposingviewheldbymanyprominentquantum fieldtheorists.Theconceptisthattheuniverseismadeofmultiplefieldsratherthanprimarilybeingparticlebased.Particlesareviewedasquantizedexcitations quantizedwaves existingwithinthesefields.Thishasbeendocumentedinapaper18byArtHobsontitled“Therearenoparticles,there are only fields”. This paper gives numerous references supporting this position. Forexample,asFrankWilczekexplains19,“Inquantumfieldtheory,theprimaryelementsofrealityarenotindividualparticles,butunderlyingfields.Forexample,allelectronsarebutexcitationsofanunderlyingfield,….theelectronfield,whichfillsallspaceandtime.” Inthisconceptualmodel,eachfundamentalparticlehasitsownfield.Eventhestandardmodelisreallyaquantumfieldtheory.All17particlesofthestandardmodelareassociatedwith17differentoverlappingfields and this does not even include the gravitational field or other possible fields if morefundamental particles are discovered. This multitude of superimposed fields creates anunappealingcomplexpicture.
18 A. Hobson “There are no particles, there are only fields” Am. J. Phys. 81 (3), March 2013 19 F. Wilczek, “Mass Without Mass I: Most of Matter,” Phys. Today 52(11), 11-13 (1999)
Albert Einstein said the following in his 1923 Nobel lecture, “The intellect seeking after anintegratedtheorycannotrestcontentwiththeassumptionthatthereexiststwodistinctfields,totallyindependentofeachotherbytheirnature”.Hewasreferringtotheelectricfieldandthegravitational field appearing tobedistinctbuthebelieved that theymustbe closely related.Einsteinworked forabout30yearsattempting tounite these two fields. Today,Einstein’s2fieldshavegrownto17distinctfields–andcounting.Apparentlytheproliferationoffieldshasmadetheconceptofunitingtheseintoasinglefieldisadistantmemory.However,ifthebasicassumption of this book is that the universe is only spacetime, then the following corollaryfollowsfromthisstartingassumption:CorollaryAssumption: There is only one truly fundamental field. This single field is the quantum mechanical model of the spacetime field with its dipole wave vacuum fluctuations. All fundamental particles and all forces are manifestations of this single spacetime field. Another way of phrasing the starting assumption the universe is only spacetime is thefollowing: The universe is made entirely of a single field and its quantized components. Thissingle field is known to us as the spacetime field, but more specifically it is the quantummechanical spacetimewave descriptionofthespacetimefield.ThespacetimefieldmodelhaschaoticspatialfluctuationswithdisplacementamplitudeequaltoPlancklengthandtemporalfluctuations differencebetweenclocks withdisplacementamplitudeequaltoPlancktime.Thechaoticseaofdipolewavesinthespacetimefieldthatarethebasicconstituentofspacetimewillbeshowntohaveknowablepropertiessuchas:waveamplitude,impedance,frequencyrange,bulk modulus, energy density, propagation characteristics, angular momentum, etc. Laterchapterswillexplainhowthissinglefieldcanformallparticles,allforcesandwhatappeartobeotherfieldssuchasgravitationalfieldsandelectricfields.Summary – Properties of Spacetime: In upcoming chapters we are going to attempt toconstruct the universe particles, forces and photons using only the quantum mechanicalpropertiesof spacetime. Besides the standardproperties of spacetimedescribedby generalrelativity,itisusefultosummarizetheadditionalpropertiesofspacetimethatwehaveaddedtoourtoolbag.Theseadditionsare:
2 Thequantummechanicalmodelofspacetimehasaseaofhighfrequency,smallamplitudevacuum fluctuations at Planck energy density ~ 10113 J/m3. This model is adoptedbecauseeventheimpedanceofspacetimeobtainedfromgeneralrelativitysupportsthismodel.
3 Dipole waves are allowed to exist in spacetime but they are subject to the Plancklength/timelimitationpreviouslydiscussed.Vacuumfluctuationsandzeropointenergyare actually dipole waves in spacetime. The uncertainty principle and probability
5 Wepresume that theonly truly fundamental force is therelativistic force Fr Pr/c which is the repulsive force exerted when energy traveling at the speed of light isdeflected.Thedipolewavesinspacetimearealwaysmovingatthespeedoflightevenwhentheyareconfinedtoalimitedvolume.
6 Fromtheequivalenceofenergydensityandpressure, it followsthatthe largeenergydensity of vacuum fluctuations dipole waves is exerting an equally large vacuumpressure.
