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1、MathematicalTheoryOfSpace-TimeChun-Xuan.JiangChinaAerospaceScienceAndTechnologyCorporationP.O.Box142-206,Beijing100854,P.R.Chinajl36211668701AbstractUsingspace-timeringweestablishthemathematicaltheoryofspace-time.Usingtwomethodswededucethenewgravitationalformula.Tardyonicrotatingmotionproducesthecen
2、trifugalforce,buttachyonicrotatingmotionproducesthecentripetalforce,thatisgravity.Usingitweestablishtheexpansiontheoryoftheuniverseandsuggestthenewuniversemodel.Weprovethatintheuniversetherearenodarkmatterandnodarkenergy.Newgravitationalformulachangesallthat.Multiverseandgravitationalwavesdonotexist
3、.Theoryofeverythinghasthetwoforces:(1)thesubluminalforce(electromagnetismandweakforce)and(2)Superluminalfbrce(gravityandstrongfbrce).Bellconjectureiswrong.Thequantumentanglementsandnon-localityareunobservable,onlythegravitonicandtachyonicentanglements,butnoelectronicandphotonicentanglements.Keywords
4、:newgravitationalformula,expansiontheoryofuniverse,newuniversemodel.PACS:04.90.+e,98.80.-k.1.MathematicalTheoryofSpace-TimeThroughouthistory,thenotionofspaceandtimehasundergoneanumberofdramatictransformation,thankstofiguresrangingfromAristotle,LeibnizandNewtontoGauss,PoincareandEinstein.Inthepresent
5、understandingofnature,spaceandtimeformasingleentitycalledspace-time.In1975Jianghasestablishedthemathematicaltheoryofspace-timewithSASC.Thistheoryplaysakeyrolefortheentirefieldofphysicstounlockthedeepestmysteriesoftheuniverse.IntheUniversetherearetwomatters:(I)observablesubluminalmattercalledIardyon(
6、Iocality)and(2)unobservablesuperluminalmattercalledtachyon(non-Iocality)whichcoexistinmotion.Tachyoncanbeconvertedintotardyon,andviceversa.Tardyonicrotatingmotionproducesthecentrifugalforce,buttachyonicrotatingmotionproducesthecentripetalforce,thatisgravity.Usingtardyonicandtachyoniccoexistenceprinc
7、iplewededucethenewgravitationalformula,Forestablishingthemathematicaltheoryofspace-time.wefirstdefinespace-timeringl,l(ctxZ=Lctrct+jxwherexandtarethetardyonicspaceandtimecoordinates,Cislightvelocityinvacuum,(O1(1)canbewrittenasEuIerformZ=CTo/=CTo(Ch。+/She),(2)whereCt0isthetardyonicinvariance,tardyon
8、ichyperbolicalangle.From(1)and(2)wehaveCf=%ChaX=Ct0sh(3)Ct0=y(ct)2-x2.(4)From(3)wehave=th1=th1(5)ctcwherecuisthetardyonicvelocity.Usingthemorphismj:ZTjz,wehavejz=元+jetX(iej=x0(chsh6),(6)whereXandiarethetachyonicspaceandtimecoordinates,X0istachyonicinvariance,tachyonichyperbolicalangle.From(6)wehaveJ
9、=x0ch,Cf=MoShe.(7)元O=Ji，一(Cf)2(8)From(7)wehave=th-1=th1-(9)xuwhereucisthetachyonicvelocity.Figure1showstheformulas(1)-(9).j：ZfjZisthattardyoncanbeconvertedintotachyon,butJ:jzzisthattachyoncanbeconvertedintotardyon.w=0M=cisthepositiveacceleration,but万=8f瓦=cisthenegativeacceleration,whichcoexist.Atthe
10、ct-axisu=0andx=0wedefinethetardyonicresttimet.AtthexaxiswedefinethetachyonicrestspaceX0=11mwr=constant(10)ur0Sinceatrestthetachyonicresttimef=0andi7=oo,weprovethattachyonisunobservable.Fig.land(10)aremathematicaltheoryofspace-time,whicharethefoundationsofphysicsandcosmology.Usingitweprovethatdarkmai
11、ler,darkenergy,gravitationalwaves，blackholesdonotexist,quantumentanglementandquantumcomputersareunobservable,onlythegravitonicandtachyonicentanglements,butnoelectronicandphotonicentanglements.FromFig.lwededucenewgravitationalformula.AnC22.NewGravitationalFormula:F=nodarkmatterRAssume=、from(5)and(9)w
12、egetthetardyonicandtachyoniccoexistenceprinciplel-4J0uu=c2.(11)Usingtheanalyticalmethodwededucethenewgravitationalformula.Differentiating(11)bythetime,wegetdu(cdu=dtWdfandcancoexistinmotion,buttheirdirectionsareopposite.dtdtWestudythetardyonicandtachyonicrotatingmotions.In1673Huygensdiscoveredthatth
13、etardyonicrotationproducescentripetalacceleration(13)(14)dudtwhereRisrotatingradius.Substituting(13)into(12)wehavethetachyoniccentrifugalaccelerationdudt(13)and(14)havethesameform.From(13)wegetthetardyoniccentrifugalforceF=(15)RwhereMistheinertialmass.From(14)wegetthetachyoniccentripetalforce,thatis
14、gravity2F=-,(16)RwheremisthegravitationalmassconvertedintobytachyonicmassIn.(15)and(16)havethesameform.(16)isthenewgravitationalformula.Usingthegeometricalmethodwededucethenewgravitationalformula.Figure2showsthattherotationcoofbodyAemitstachyonmassin,whichformsthetachyonandgravitationfieldandgivesth
15、ebodyBrevolutionsuandu.WVAFig.2.OnbodyBtheanddtdFromFig.2.itfollowsUAt_mRuFrom(17)itfollowsthetardyoncentripetalaccelerationontdu.w=Iim=dtFromFig.2.itfollowsut_i-F-TFrom(19)and(11)itfollowsthetachyoncentrifugalaccelerdu1.min=Iim=dtzOnbodyBtheandcoexistence.dtdtFrom(18)itfollowsthetardyoncentrifugalf
16、orceonbodyM/F-丁，whereMBisbodyBmass.UU7coexistencet.(17)hebodyB2-4J,Y.(18)R-.(19)ationonthebodyB2-4,一9/Lz-=.(20)?R3L2-4,(21)From(20)itfollowsthetachyoncentripetalforceonbodyB,thatisgravity2-4,10,=,(22)Rwheremisthegravitationmassconvertedintobytachyonmass而whichisunobservable,butmisobservable.(22) isth
17、enewgravitationalformula.In19762thissimplethoughtmadeadeepimpressiononme.Itimpelledmetoestablishthenewgravitationaltheory.OnbodyBtheFandFcoexistence.FromFig.3,itfollows(23)F+F=0.From(21),(22)and(23)itfollows(24)m=u2瓦TBodyBincreasesmassmandcentrifugalforceisgreaterthangravitationforce,thenbodyBexpand
18、soutward.Darkmatterwhichcausescosmicattractioniswrong.From(22)itfollowsNewtoniangravitationformula.ThemisproportionaltobodyAmassMa,in(24)inisproportionaltoM,isinverselyproportionaltothedistanceRbetweenbodyAandbodyB.Itfollowsm=k-,(25)RwherekisconstantSubstituting(25)into(22)itfollowstheNewtoniangravi
19、tationformula2-4,10R2whereG=kc2=6.673108cm3/gsec2isgravitationconstant.Nowwestudythefreelyfallingbody.Tachyonicmass而canbeconvertedintotardyonicmassm,whichactsonthefreelyfallingbodyandproducesthegravitationalforce(27)mc2RwhereRistheEarthradius.Wehavetheequationofmotion(28)wheregisgravitationalacceler
20、ation,Mismassoffreelyfallingbody.From(28)itfollowsthegravitationalcoefficient(29)Q=券=6.9x1OToMc2Eotvosexperiment510-9andDickeexperiment10.Sincethegravitationalmassmcanbetransformedintotherestmassinfreelyfallingbody,weprovethatthefreelyfallingbodiesfallwiththesameacceleration.Theequivalenceprinciplei
21、smistakel1.3. TheexpansiontheoryoftheuniversenodarkenergyUsingnewgravitationalformulawestudytheexpansiontheoryoftheUniverseIO.Figure4showsaexpansionmodeloftheUniverse.Therotation(DofbodyAemitstachyonicflow,whichformsthetachyonicfield.TachyonicmassnactsonbodyB,whichproducesitsrotationco2,revolutionua
22、ndgravitationalforce(30)mc2whereRdenotesthedistancebetweenbodyAandbodyB,misgravitationalmassconvertedintobyUchyonicmassinwhichisunobservablebutinisobservable.TherotationofthebodyBaroundbodyAproducesthecentrifugalforce(31)Fig. 4. A expansion model of the UniversewhereMBistheinertialmassofbodyB,uisthe
23、orbitalvelocityofbodyB.AttheQ)pointweassumeFl+Fi=0.(32)From(32)itfollowsthatthecoexistenceofthegravitationalforceandcentrifugalforce.From(30)-(32)itfollowsthegravitationalcoefficient77=f-).(33)MBc)AttheO3pointthetachyonicmassmcanbeconvertedintotherestmasstninbodyB,itfollows1.MRU2mu2/、F,=-.(34)RRSinc
24、eF2+Fx0,centrifugalforceF2isgreaterthangravitationalforceF1,thenthebodyBexpandsoutwardsanditsmassincreases.ThisisaexpansionmechanismoftheUniverse.From(31,32,34)wehave21.-mu-*(35)(36)(37)F2+F=-=MBeKFrom(35)weobtaintheexpansionaccelerationa_mu2/g。一mbrSubstituting(33)in(36)weobtainIfbodyAistheEarth,the
25、nbodyBistheMoon;ifbodyAistheSun,thenbodyBistheEarth;.Itcanexplainouracceleratinguniverse.Intheuniversetherearenodarkmatterandnodarkenergy.Thissimplethoughtmadeadeepimpressiononme.Itimpelledmetoestablishaexpansiontheoryoftheuniverse.Darkenergyresponsiblecosmicrepulsioniswrong.IfthebodyAistheSunandbod
26、yBistheplanet.Wecalculatethegravitationalcoefficientsasshownintable1.Table1:ValuesofthegravitationalcoefficientsPlanetU(kmsec)7(101)Mercury47.89255.2Venus35.03136.5Earth29.7998.7Mars24.1364.8Jupiter13.0619.0Saturn9.6410.3Uranus6.815.2Neptune5.433.3Pluto4.742.5Thegravitationalfieldofthesolarsystemist
27、heoriginoftheplanetmass.Fromittheplanetacquiremass.4. ThenewuniversemodelFromthetachyonictheorywesuggestthenewuniversemodel.Theuniversehasnobeginningandnoend.Theuniverseisinfinite,butithasacenterconsistingofthetachyonicmatterwhichisstronggravitationalfield(SGF),whichgovernsmotionofthewholeuniverse.T
28、hereforethewholeuniverseisstableandharmonious.InthesunthereisacenterconsistingofthetachyonicmatterwithSGF,whichgovernsmotionofthesolarsystem.Itisstableandharmonious.IntheearththereisacenterconsistingofthetachyonicmatterwithSGF,whichgovernsmotionoftheearthandthemoon.Itisstableandharmonious.Inthemnthe
29、reisacenterconsistingofthetachyonicmatterwithSGF,whichgovernsmotionofthemoon.Itisstableandharmonious.InatomicnucleusthereisacenterconsistingofthetachyonicmatterwithSGF,whichgovernsmotionofthenucleus.Thereforeatomicnucleiarestableandharmonious.Thetachyonictheorygovernstheamazingharmonyofthewholeunive
30、rsefromthesmallesttothelargestscales.Newgravitationalformulachangesallthat.IntheUniversetherearenodarkmatter,nodarkenergyandnogravitationalwaves.Multiverse,inflationandprimordialgravitationalwavesdonotexist5-7.Theoryofeverythingisaquesttounderstandandunifywhatarecurrentlyconsideredtobethetwoseparate
31、fundamentalforcesofnature:(l)thesubluminalforce(electromagnetismandweakforce)and(2)superluminalforce(gravityandstrongforce).Itisasimple,elegant,unifyingtheory.Note.Thesuperluminalforceexistsandinteractswithordinarymatterforexamplegravityandstrongforce.FromFig1weprovethatthesuperluminalforcehasneverb
32、eenobservedforexamplegravitons,gravitationalwavesandquantumentanglements.Bellconjectureiswrong.Quantumentanglementandnon-localityareunobservable.Onlythegravitonicandtachyonicentanglements,butnoelectronicandphotonicentanglements.5. ConclusionInsummary.WededuceCardyonicandtachyoniccoexistenceprinciple
33、.UsingitWededucethecentrifugalformulaandnewgravitationalformulaWeestablishtheexpansiontheoryoftheuniversewithoutdarkenergyandsuggestthenewuniversemodelwhichisamazingharmony.Thenewgravitationalformulaisfoundationsofparticlephysicsandcosmology.Weprovethatintheuniversenodarkmatter,nodarkenergy,nogravit
34、ationalwavesandnoquantumgravity.Wheredidwecomefrom?Wherearewegoing?Whatmakesuptheuniverse?Thesequestionshaveoccupiedmankindforthousandsofyears.Overthecourseofhistory,ourviewoftheworldhasbeenchanged.Theologiansandphilosophers,physicistsandastronomershavegivenusverydifferentanswers.Wheredidwecomefrom?
35、Weanswerthisquestionsthiswayrnm1tachyons-Iardyonsf11,thatistachyonscanbeconvertedintotheelectronsandpositronswhicharethebasicbuilding-blocksoftheelementaryparticles8-9.Thetachyonsaretheoriginofmass.Wherearewegoing?Weanswerthisquestionthiswaym-mthatisthetardyonsproducetachyonsl.Thetardyonsandtachyons
36、makeuptheUniverse.p-inc1/_Nt.In1976Jiangfoundagravitationalformula2:/R,wheremisthetachyonicmass.In2004JiangstudiedtheUniverseexpansionandfoundanewgravitationalF=-mcVpformula/,wheremisgravitationalmassconvertedintobytachyonicmass%10.Newtoniangravityformulaisbasedonempiricalevidence.Hedidnotexplainwha
37、tisgravity?howitworks?Ingeneraltheoryofrelativitythereisnogravitationalformulall1.InmodifiedgravityandmodifiedEinsteingravitytherearenogravitationalformula12.Therecannotbereallygravitationaltheorywithoutgravityformula.Atachyonisinstabilityappearsasafieldwithanegativemasssquaredwhichiswrong12.Thetach
38、yonsarestable.Ithasnoresttimeandnorestmassl.ReferencesChun-XuanJiang,Atheoryofmorphismsbetweenthetardyonandtachyon,physics(Chinese),4.(1975)119-125.2 Chun-XuanJiang,Onnatureforgravitation,J.Beijingobservatory(Chinese),7(1976)32-38.3 Chun-XuanJiang,Anapproachonthenatureofattractiveforce,Potentialscie
39、nce(Chinese),4(1982)19-20.4 Chun-XuanJiang,Aunifiedtheoryofthegravitationalandstronginteractions,HadronicJ.,24(2001)629-638.5 RA.R.Adeetal.(BICEP2Collaboration),DetectionofB-modepolarizationatdegreeangularscalesbyBlCEP2,Phys.Rev.Lett112,241101(2014).6S.Dodelson,Howmuchcanwelearnaboutthephysicsofinfl
40、ation?PhyS.RevJLettJ12,191301(2014).7 J.CaligiuriandA.Kosowsky,InflationarytensorperturbationsafterB1CEP2.Phys.Rev.Lett,l12,191302(2014).8 Chun-XuanJiang,AsimpleapproachtothecomputationthetotalnumberofhadronicconstituentsinSantillimodel,HadronicJ.,3(1979)256-292.9 Chun-XuanJiang,Amathematicalmodelfo
41、rparticleclassification,ActaMath.Scien,8(1988)133-144.10JChun-XuanJiang,Newgravitationalformulaandexpansiontheoryoftheuniverse.In:newstudiesofspace-timetheory(Chinese),Dizipress,pp.254-259,2005.11 A.Einstein,Themeaningofrelativity,5,hedn,(Princetonuniversitypress,Princeton,1956).12 AustinJoyce,Bhuve
42、neshJainJustinKhoury,MarkTrodden.Beyondthecosmologicalstandardmodel.PhysicsReports568(2015)1-98.AcknowledgmentsTheauthorthanksprofessorWalterLewinforhismails.(I)FromWalterH.GLeWinyeWinsDace.mit.eduDateiSunJOJun201222:22:21-0400(EDT)SubjectzRe:Fwd.To:123jiangchunxuan;IeWinmit.eduCc:lucvanocken.bePubl
43、ishthisinarefereedjournalandonceitisacceptedbuyyourselfafirstclasstickettoStockholmtopickupNobelprizeforphysics.(2)FromWalterH.GLeWinyewinsDace.miteduDate:Sun,17Jun201206:19:37-0400(EDT)SubjectzReTo:123jiangchunxuanCc:lucvanocken.beDearJiangThankforyouremail.Isuggestyousubmityourtheorytoarefereedjournal.Ifitisaccepted,thenbuyyourselfaplanetickettoStockholmtopickupaNobelprize.Greetings.Prof.WalterLewinexplains5NewtonslawofgravitationinMfTcourse8.01
