特斯拉动态引力理论原文

1JournalofTheoreticsRedshiftCalculationsintheDynamicTheoryofGravityIoannisIraklisHaranasDepartmentofPhysicsandAstronomyYorkUniversity128PetrieScienceBuildingYorkUniversityToronto–OntarioCANADAEmail:ioannis@yorku.caAbstract:InanewtheorycalledDynamicTheoryofGravity,thecosmologicaldistancetoanobjectandalsoitsgravitationalpotentialcanbecalculated.WefirstmeasureitsredshiftonthesurfaceoftheEarth.ThetheorycanbeappliedaswelltoanobjectinorbitabovetheEarth,e.g.,asatellitesuchastheHubbletelescope.Inthispaper,wegivevariousexpressionsfortheredshiftscalculatedonthesurfaceoftheEarthaswellasonanobjectinorbit,beingtheHubbletelescope.OurcalculationswillassumethattheemittingbodyisastarofmassM=MX-ray(source)=1.6×108MsolarmassesandacoreradiusR=80pc,atacosmologicaldistanceawayfromtheEarth.WetaketheorbitalheighthoftheHubbletelescopetobe450Km.Introduction:ThereisanewtheoryofgravitycalledDynamicTheoryofGravity[DTG].BasedonclassicalthermodynamicsRef:[1][2][3][9]ithasbeenshownthatthefundamentallawsofClassicalThermodynamicsalsorequireEinstein’s2postulateofaconstantspeedoflight.DTGdescribesphysicalphenomenaintermsoffivedimensions:space,time,andmass.Ref[4]Thetheorymakesitspredictionsforredshiftsbyworkinginthefivedimensionalgeometryofspace,time,andmass,anddeterminestheunitofactionintheatomicstatesinawaythatcanbecalculatedwiththehelpofquantumPoissonbracketswhencovariantdifferentiationisused:[][]{}ΦΓ+=Φ,,qsqsqxgipxµµννµδ=.(1)In(1)thevectorcurvatureiscontainedintheChrisoffelsymbolsofthesecondkindandthegaugefunctionΦisamultiplicativefactorinthemetrictensorgνq,wheretheindicestakethevaluesν,q=0,1,2,3,4.Inthecommutator,xµandpνarethespaceandmomentumvariablesrespectively,andfinallyδµqistheCroneckerdelta.InDTGthemomentumascribedasavariablecanonicallyconjugatedtothemassistherateatwhichmassmaybeconvertedintoenergy.Thecanonicalmomentumisdefinedasfollowsbelow:,(1a)44mvp=wherethevelocityinthefifthdimensionisgivenby:Dαγ•=4v,(1b)andisatimederivativewheregammaitselfhasunitsofmassdensityorkg/m•γ3,andαoisadensitygradientwithunitsofkg/m4.Intheabsenceofcurvature,(1)becomes:[]Φ=Φ,qννµδ=ipx.(2)3From(2)weseethattheunitofactionistheproductofamultipleofCronecker’sδµqfunctionandthegaugefunctionΦ.ItcanbealsoshownthatifweusegaugefieldequationsRef:[6]thenthegaugefunctionΦisoftheform:()−+=ΦRRBtAkλexpexp.(3)Assumingconservationofphotonenergyandexpandingtheexponentialsandthencomparingthisexpressionwith(11),weneedthentoevaluatetheconstantsA,B,andk.Recallingthattheemissiontimete=0andthereceivedtimetr=L/c,theexpressionfortheredshiftreducestothefollowing:Ref[5]1exp2e−+−−=∆=−⊕⊕−−rrememobobRobobemReobRreRMRMcHLReMReMcGzλλλλλ,(4)where⊕⊕RMisthegravitationalpotentialoftheearth,obobRMisthereducedgravitationalpotentialatthedetectionpoint,andememRMisattheemissionpointoftheradiation.Sinceλ<<R,expression(4)canbesimplifiedfortheearth’ssurface(Es):Ref[5].4[]+−−=+cHLRMRMcGzememobobEs21ln,(5)andfororbitingHubbletelescope(ht)ofaheighththefollowingexpression:[]()++−+−=+⊕⊕⊕⊕hRRcHLRMhRMcGzememht21ln.(6)AsaresultoftheanalysisinRef[5],wesolvetwoequationswithtwounknowns,thegravitationalpotentialGM/RandthecosmologicaldistanceLoftheemittingobject.Thesecanbefoundfrom:[][++−++=⊕⊕⊕EshtzhRRzhRcRGM1ln1ln12](7)and[]()+++−+=⊕⊕⊕RcGMhRzzHcLhtEs21]1ln[1ln.(8)Inthistheory,thepredictedredshiftsaresignificantlydifferentwhenmeasuredonthesurfaceoftheEarth,orataheightof450kmforexampleabovethesurface.InEinstein’stheoryofrelativity,theredshiftofanobjectmaybewrittenasfollows:−−=ememobobRMRMcGz2,(95wherethesubscriptsspecifytheemitterandobservergravitationalpotentialsrespectively.SincetheredshiftofanobjectatcosmologicaldistanceLisgivenby:LcHz=,(10)thenthetotalredshiftwillbegivenfrom:Ref[4]LcHRMRMcGzememobob+−−=2,(11)whereHisHubble’sconstant,cisthespeedoflight,andLthecosmologicaldistancetotheobject.Anydifferenceintheredshiftwillcomefromthedifferencebetweenthegravitationalpotentialatthesurfaceoftheearthandatsomeheightabovethesurface.However,thisdifferencewillbesmallduetothesmallsizeoftheearthcomparedwithcosmologicalobjects.ComparedwiththeSun,thiseffectwouldbeoftheorderof10-5.InthecasezEs≈zht(7)and(8)simplifyasfollows:[1ln2EsememzcRGM+=],(11a)=⊕⊕2RGMcHcL.(11b)6LetusnowproceedbywritingthetwofudamentalrelationspredictedbytheDTGintermsofemittedλemandobservedλob.Since1−=emobzλλweobtain:+−+=⊕⊕⊕meobEsemobhtememhRRhRcRGMλλλλ)()(2lnln1,(12)and++=⊕⊕⊕2)()(1lncRGMhRHcLobhtobEsλλ.(13)Solving(13)forthewavelengthoftheradiationasobservedbytheHubbletelescopewehave:−+−=⊕⊕⊕2)()(expcRGMcLHhRhobEsobhtλλ.(14)Attheearth’ssurfacethewavelengthoftheobservedradiationhasthevalueof:−+=⊕⊕⊕2)()(xpecRGMcLHhRhobhtobEsλλ.(15)7Similarly,wecanfindidenticalexpressionsasdescribedaboveforthequantitiesintermsofanorbitalheighth,cosmologicalredshiftz,andEarth’sgravitationalpotentialatheighth.Thusfrom(12)wehave:[][]−=⊕−+⊕⊕RhcRGMeeRhemRhobhtobEs21)()(expλλλ(16)and+++=⊕⊕⊕emobEsemememobhthRRcRGMRhhλλλλ)(2)(lnexp.(17)CalculatingtheRedshiftExpressions:Foralltheexpressionsabove,wenowuse:massoftheearthM=5.97×10⊕24kg,h=450km,R=6.378×10ob6m,andztot=4.4.ThisperticularredshiftisassociatedwiththeX-raysource4U0241+61whichhasamassMsource=1.6×108Msolar.Anobjectofsuchredshiftwillbeatadistance:Ref[7]()[]yearslight10203.9z1-11095.110×=+=−objectd(17a)From(13)and(12)weobtainthefollowingrelationshipsforthewavelengthsattheearth’ssurfaceandattheHubbletelescope:Es(ob))(0.750λλ≅obht(18)8)()(336.1obhtobEsλλ≅.(19)Next,wecalculatethesamewavelengthswithamaincontributionduetothequasar’sgravitationalpotentialaswellastheemittedandobservedwavelengths,radiusoftheearth,andheightaboveoftheearth’ssurface.[][]0705.00705.1ht(obs))(999.0−≅emobEsλλλ(20)em)(832.4λλ≅obht.(21)Weseethat(20)and(21)alsocontaintheemittedwavelengthsinceitappearsintheanalyticalsolutionforλhtandλEs.LetusnowchoosethecommonlyoccuringLyman(Lα)lineinquasarspectra,havinganemittedwavelengthλem=1216DA.Ifthequasar’sredshiftztot=4.4,thenstandardtheorypredictsthatthislinewouldberedshiftedbyafactor(1+ztot)λgiving6566DA:Ref[8]Nextwefindthefollowingresults:(23)%0.19ofe%differencA6579A4924A6566Es)()()(Re====λλλλDDDobsDynaEsobshtlEsobsNext,using(22)weobtain:9(24)%01.0difference%A6565A5875A6566Es)()()(Re−====λλλλDDDobsobsDynaEsobshtlEsCalculationoftheDynamicalRedshiftsGiventhetotalredshiftofthequasarztot=4.4wecanobtainandsolvethesystemofequationswhichDTGclaimsforthedynamicalredshiftsontheearthandattheheightoftheHubbletelescope.Usingthedistancetothequasarasgivenin(17a)andtakingitsmasstobeMX—RayQuasar=1.6×108MSolar-Masses=3.04×1038kg,weneedtosolvethesystemofthefollowingequations:()()[]()()[][]010937.61ln1ln173.15491.001ln934.01ln173.1510841.5104=×++−+−=+−+−×−−htEsEshtzzzz(25)fromwhichweobtainthepercentchangeofredshift:(26)%,089.1%052.0%635.0%583.0htEsEshtzzzzz==∆==IfwetakethevalueofzES=4.4wefindthat:10(27)%359.0%040.4%400.4=∆==zzzhtEsDynamicalRedshiftEquationsIfwenowallowthepotentialduetotheemittingbodytochangeingeneralbyafactorA,inthesystemofequationsin(25)thenwecanwritetwosolutionsforzinthefollowingform:Eshtzand[][1e583.11e635.15--5101.769101.769−=−=××AhtAEszz](28)orin-termsoftheemittedwavelengthwehave:(29).583.1635.15510769.110769.1emEsAemhtAee−−××==λλλλSimirarly,wecanobtainthedynamicalredshiftsatthesurfaceoftheearthandattheheightoftheHubbletelescopeifweallowforthecosmologicalredshifttochange(smallerorlarger)byafactorB.Thusweobtain:(30)1e000.11000.10.491824B459407.0−=−=EsBhtzez11whichin-termsoftheemittedwavelengthbecomes:(31).000.1000.1491824.0emEs459407.0emBBhteeλλλλ==ToobtainadynamicalredshiftsordynamicalwavelengthsatthesurfaceoftheearthorattheHubbletelescopeourconstantsAandBshouldingeneralhavethefollowingvalues:()()[]()()[]()()==+=+=emEshtemEsEs631.0ln56529611.0ln565291631.0ln5652914.0611.0ln56529λλλλλλAAzzAzzAhthtEsEs(31a)also()()[]()()[]()()==+=+=emhthtemEsEs999.0ln176.2999.0ln033.21999.0ln033.21999.0ln033.2λλλλλλBBzzBzzBhthtEsEs(31b)12PlottingtheEquationsToplotequations(28)and(29)weletAtakesomevaluesbelowandaboverelativeto2)(cRGMquasarzeenalgravitatio=andweobtainthefollowinggraphsinFigure1and2zEs,zht05000100001500020000200022002400260028009DynamicalRedshiftsHZESZHTLvsAHGMe€€€€€€€€€€€€Rec2L=A(GMe/Rec2)Figure:1PlotsofDynamicalRedshiftsattheEarth’sSurfaceandatHubbleTelescopeversusQuasars’sGravitationalRedshiftFactor.λEs,λht1302000040000600008000010000002000400060008000100009DynamicalWavelengthsHlESlHTLvsAHGMe€€€€€€€€€€€€Rec2L=A(GMe/Rec2)Figure:2PlotsofDynamicalWavelengthsattheEarth’sSurfaceandatHubbleTelescopeversusQuasars’sGravitationalRedshiftFactor.Similarlyfortheequations(30)and(31)containingBweobtaintwographsinfigures3and4:zEs,zht1400.020.040.060.080.11220123012401250126012709DynamicalRedshiftsHZESZHTLvsBHHL€€€€€€€cLB(LH/c)Fig:3PlotofDynamicalRedshiftsatEarthsSurfaceandHubbleversusCosmologicalRedshiftFactor.λEs,λht0123456050001000015000200009DynamicalWavelengthsHlESlHTLvsBHHL€€€€€€€cLB(LH/c)15Fig:4PlotsofDynamicalWavelengthsattheEarth’sSurfaceandatHubbleTelescopeversusQuasars’sGravitationalRedshiftFactor.Conclusions:Inthispaper,wehavehighlightedafewaspectsofthedynamictheoryofgravity.Analyticalexpressionswereobtainedfortheobservedwavelengthsontheearth’ssurfaceandforanorbitalheighthgiventhegravitationalpotential,thecosmologicaldistance,andtheredshiftfactor.Finally,alltheseexpressionsforthewavelengthsontheearth’ssurface,aswellasattheheightoftheHubbletelescope,werecalculatedforaparticularquasistellarobjectofmassMX-ray(source)=1.6×108MsolarmassesandradiusR=80pc.Weseethat,inthedynamictheoryofgravitythoseequationswhichdescribethevaluesofthewavelength-changeattheearth’ssurface,andattheheightoftheHubbletelescope,producechangesrelativetotheoriginalwavelength.Fortheobserver,thelightemittedfromthequasarontheearthwillbeslightlyredderinthistheorythanintherelativisticone.Thesamewavelengthswillalsoberedderw.r.ttheHubbletelescopeobservedwavelength.Thereisa0.19%percentagedifferencebetweentheDTGandthetotalrelativisticpredictionatheighthabovethesurfaceoftheearth,whenthetotalredshiftisthesumofrelativisticandcosmological.ItseemsthatattheHubbleheightthewavelengthobservedwillbe1.336timeslessthanthatfromDTGontheearth’ssurface.WhentheobservedwavelengthatthesurfaceoftheearthandatHubblearegivenintermsofthegravitationalpotentialofthequasar,andataheighthabovetheearth,aswellastherelativisticallyobservedwavelengthontheearth’ssurfaceandtheemittedwavelengths,thenthereisa–0.01%percentagedifferencebetweenthetotalrelativisticredshiftandthatwhichDTGpredicts.TheobservedwavelengthatHubblewavelengthisalso1.117timeslessthanthatobservedatthesurfaceoftheearth.16Next,solvingthesystemoftwoequationsintwounknownsforthesamequasar,thepercentchangesoftheredshiftsattheearth’ssurfaceandatHubblewerecalculated,andfromtheretheactualzvalues.Apercentagedifferenceof–8.18%wasfound,andalsoa∆z=0.359betweenthetwovaluesofzESandzHT.Finally,generalsolutionsofz’sandλ’swereobtainedin-termsofAandBbeingsomemultipleorsubmultiplevaluesofgravitationalandcosmologicalredshift,andthenplotted.ForverylargevaluesofAandB,theDTGredshiftsandwavelengthsseemtodiverge,whereasatsmallvaluesofAandB,theybothfollowalinearbehaviourthatseemstoconvergetoeach-otheratA=0andB=0.ThiscouldmeanthatthereisnodistinctionbetweenDTGandrelativisticgravitationaleffectswhenAandBareverysmall.TheeffectsbecomedistinctatlargervaluesofAandBasshownbythegraphs.HereitmayberesonabletoassumethatobjectsoflargeredshiftandpotentialmightbecanditatesindetectingDTGeffects.References[1]P.E.Williams,“OnaPossibleFormulationofParticleDynamicsinTermsofThermodynamicConceptualizationsandtheRoleofEntropyinit.”ThesisU.S.NavalPostgraduateSchool,1976.[2]P.E.Williams,“ThePrinciplesoftheDynamicTheory”ResearchReportEW-77-4,U.S.NavalAcademy,1977.[3]P.E.Williams,“TheDynamicTheory:ANewViewofSpace,Time,andMatter”,LosAlamosScientificLaboratoryreportLA-8370-MS,Feb1980.[4]P.E.Williams,“QuantumMeasurement,Gravitation,andLocalityintheDynamicTheory”,SymposiumonCausalityandLocalityinModernPhysics17andAstronomy:OpenQuestionsandPossibleSolutions,YorkUniversity,NorthYork,Canada,August25-29,1997.[5]P.E.Williams,UsingtheHubbleTelescopetoDeterminetheSplitofaCosmologicalObject’sRedshiftintoitsGravitationalandDistanceParts,Apeiron,Vol.8,No.2,April2001.[6]P.E.Williams,TheDynamicTheory:ANewViewofSpace-Time–Matter,1993,http://www.nmt.edu/~pharis/[7]ScienceJournal,Summer2000,Vol:17,No.1,p:3http://www.science.psu.edu/journal/sum2000/DistObj.html[8]P.J.E.Peebles,PrinciplesofPhysicalCosmology,PrincetonUniversityPress,1993,p:548[9]P.E.Williams,MechanicalEntropyandItsImplications,Entropy,2001,3,76-115/www.mdpi.org/entropy/JournalHomePage RedshiftCalculationsinthe DynamicTheoryofGravity IoannisIraklisHaranas 128PetrieScienceBuilding YorkUniversity Toronto–Ontario Abstract: InanewtheorycalledDynamicTheoryofGravity,thecosmologicaldistancetoanobjectandalsoitsgravitationalpotentialcanbecalculated.WefirstmeasureitsredshiftonthesurfaceoftheEarth.Thetheorycanbeappliedaswelltoanobjecti Figure:1PlotsofDynamicalRedshiftsattheEart andatHubbleTelescopeversusQuasars’sGravitat Factor. Figure:2PlotsofDynamicalWavelengthsattheEa andatHubbleTelescopeversusQuasars’sGravitat Factor. Fig:4PlotsofDynamicalWavelengthsattheEart andatHubbleTelescopeversusQuasars’sGravitat Factor. References