特斯拉动态引力理论原文

1JournalofTheoreticsRedshiftCalculationsintheDynamicTheoryofGravityIoannisIraklisHaranasDepartmentofPhysicsandAstronomyYorkUniversity128PetrieScienceBuildingYorkUniversityToronto–OntarioCANADAEmail:[e-mail]: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.SinceλR,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’sgravitationa