Propagation-Based General Relativity

arXiv:gr-qc/9601051v29Sep1996Propagation-BasedGeneralRelativityEdwardM.Schaefer∗PlanningSystemsInc.,7923JonesBranchDr.,McLean,VA22102(September6,1996)AbstractItisassumedthattheradialpropagationoflightwithrespecttothenaiveco-ordinatesystemoftheobserverisuniformandisotropicandthatthephysicalrateofpropagationoflightisthesameforallobservers.Inacceleratedframesofreference,theseassumptionsleadtothefindingsthatthemeasuredvalueofcisafunctionofthegravitationalenergyperunitmass(GEPUM)oftheobserver,andthatthisisduetothephysicalcharacteristicsofthestandardmeasuring-devicesbeingafunctionoftheirGEPUM.Theconsequencesofthesefindingsincludeobserverswhoatrestwithrespecttoeachotherassign-ingdifferentvaluestothesamephysicalseparation,themixedmetrictensorgμνdescribinghowgravitationaffectsmeasuring-devices,andtheDe-Brogliewavelengthbeingafunctionofanobject’sGEPUM.Howthemeasuredvaluesofvarioustypesofphysicalquantitiesareaffectedisdescribed.Thegravita-tionalDopplershiftingoflightisvieweddifferently.ThecorrectvalueforthedeflectionoflightisobtainedwithouttheuseofHuyghen’sPrinciple.TheSchwarzschildsolutionisre-examined:Thephysicalsizeofradialcoordinate2mis0,atravelermustperceivehimselftogoaninfinitedistancetoreachtheradialcoordinateof2m,andgravitationalself-potentialenergyreachesaminimalvalueattheradialcoordinate3m.Therefore,blackholesdonotex-istinthistheory;Gravitationalcollapseformshyper-massivestar-likeobjectsinstead.04.20.Cv,04.40.Dg,04.70.-s,98.62.Ai,98.63.JsTypesetusingREVTEX∗E-mail:[e-mail]1INTRODUCTIONThecornerstoneofthetheoriesofRelativityisthestatementthatthepropagationoflightisuniformandisotropicforallobservers.Theterm“uniform”usuallyreferstoEinstein’sassumptionthatallobserversmeasurethesamevalueforthespeedoflight(c)[1,2].Thisassertionisbasedontwoadditionalassumptions:•cisphysicallythesameforallobservers,whichwillbereferredtoasAbsoluteUnifor-mity.AbsoluteUniformityistheheartandsoulofRelativity,andisretainedinthetheoryproposedinthisarticle.•Allmeasuringdevicesofidenticalconstructionarephysicallyidentical.ThiswillbereferredtoasConstructionUniformity.InSpecialRelativity(SR),anotherformofuniformityinvolvingthepropagationoflightexists:Theradial1propagationoflightwithrespecttothenaivecoordinatesystemofeveryobserverisinstantaneouslythesamethroughouttheuniverse,wherethenaivecoordinatesystemisthatcreatedbytheobserverwhenitisassumedthatlighttravelsinstraightlines.ThiswillbereferredtoasExtendedUniformity.AlthoughExtendedUniformityandConstructionUniformitypeacefullyco-existinSR,thesamedoesnotapplytoGeneralRelativity(GR).Thisisbecausethecoordinatesizeofastandardmeasuring-rodandtherateatwhichastandardclockticksbothdecreaseastheirgravitationalenergyperunitmass(GEPUM)decreases.WhenAbsoluteUniformityandConstructionUniformityareassumed,itispredictedthattherateofpropagationoflightwithrespecttoanaivecoordinatesystemwillbediminishedasitdescendsintoagravitationalfield[2],therebyviolatingExtendedUniformity.Theresultingtheory,whichiscurrentlyaccepted,isreferredtointhisarticleasMeasurement-BasedGR(MGR).Ontheotherhand,whenExtendedUniformityisusedinsteadofConstructionUnifor-mity,theGReffectsonthecoordinatefeaturesofclocksandmeasuring-rodsproducethepredictionthatcincreasesasone’sGEPUMdecreases.IfAbsoluteUniformityisalsoas-sumed,thenitcannotbeachangeinthephysicalquantitywhichistherateofpropagationoflight(∗c)whichcausesthechangeinc.Instead,thephysicalattributesofthestandardsoflengthandtimemustnowbeafunctionoftheirGEPUMandnotsolelyafunctionoftheirconstruction.Inthisarticle,itisassumedthatAbsoluteUniformityandExtendedUniformityaretheunderlyingprinciplesonwhichtheuniverseoperates.ThetheoryconstructedonthesepostulatesisreferredtoasPropagation-basedGR(PGR).Inthistheory,physicalspace,time,mass,andchargeareasmeasuredwithrespecttothenaivecoordinatesystemofanobserverwithagivenGEPUM.Theresultingmodeloftheuniversemakesanumberofsur-prisingpredictions,includingafindingthatblackholescannotexist,andthatgravitationalcollapsehaltsitselfbeforeasingularitycanbeformed.1Thisqualifierisnotneededinflatspace-times.However,thedistortingeffectsofcurvedspace-timescanmaketherateoflateralpropagationoflightappeartobedifferentthanthatofitsradialpropagation.Theresultinglossofisotropywouldinvalidatetheresultingtheoryiftheselateraleffectsweretreatedasbeingphysicallyasperceived.2FUNDAMENTALSA.Quantities,Values,andEffectsGiventhelossofConstructionUniformity,howshouldstandardsofmeasurementbecreatedand/orreconciled?InPGR,thephysicalstandardscontinuetobedescribedbytheirconstructionbecause:•Wearephysicalbeingsandwhatweexperienceisaphysicalworld.Thephysicalstandardsthereforeshouldhelpaphysicalbeingtodescribethevariousphenomenaoftheuniverseasperceivedbyitself.•TheexistingtensorsofGRalreadyassumetheuseofmeasuring-deviceswhichareofidenticalconstruction,andpermitthemeasurementsmadewiththemindifferentframesofreferencetobereconciled.Togowithanothertypeofstandardwouldrequirethedevelopmentofanewmathematicalframeworktosupportit.Thephysicalsizeofthestandardmeasuring-devicesbeingafunctionoftheirGEPUMmeansthat