Modified Newtonian dynamics as a prediction of gen

arXiv:physics/0607102v2[physics.gen-ph]7Sep2006MODIFIEDNEWTONIANDYNAMICSASAPREDICTIONOFGENERALRELATIVITYSABBIRA.RAHMANE-mail:[e-mail]sicalvacuumasafeaturelessrelativisticcontinuuminmotion,andexploreitsconsequences.ByproposingthatthecentralsingularityofaSchwarzschildblackholeactslikeaspacetime-reflectingmirror,weareabletoshowthattheequationsofclassicalelectrodynamicsfollowfromthemotionofaspace-fillingfluidofneutralspinorswhichweidentifywithneutrinos.Themodelpredictsthatantimatterhasnegativemass,andthatneutrinosarematter-antimatterdipoles.TogetherthesesufficetoexplainthepresenceofmodifiedNewtoniandynamicsasagravitationalpolarisationeffect.Theexistenceofantigravitycouldresolveothermajoroutstandingissuesincosmology,includingtherateofexpansionoftheuniverseanditsflatness,theoriginofgammaraybursts,andthesmallnessofthecosmologicalconstant.Ifourmodeliscorrectthenalloftheseobservationsarenon-trivialpredictionsofEinstein’sgeneraltheoryofrelativity.1.IntroductionAlthoughtherehasbeenplentyofspeculationonthematterbothintheacademicliteratureandinthepopularpress,no-onereallyknowswhathappenstoaninfallingparticlewhenithitsthecentralsingularityofaSchwarzschildblackhole.Thesingu-larityissomethingofanuisanceasitcorrespondstoapointwheretheclassicallawsofgeneralrelativitybreakdown,andmanyphysicistsexpectthatsuchsingularitieswillnotariseinacompletequantumtheoryofgravity1.Inthispaper,werestrictourselvestotheclassicalrealmandproposethatuponhittingthesingularitythein-fallingparticleisreflectedbackoutbothspatiallyandtemporallytore-emergefromtheeventhorizontravellingbackwardsintime.Toanexternalobserverthiswilllooklikeapairannihilationeventtakingplaceattheeventhorizon.Thissimpleproposalhasanumberofinterestingconsequenceswhichweconsiderhereinsomedetailinthelightofknownphysicalobservations.Inarecentpaper2,Blanchetshowedthatifthereweretoexistaspace-filling‘aether’consistingofdarkmatterparticleswhichtaketheformofmatter-antimatterdipoles,thenthiswouldsatisfactorilyexplaintheexistenceofmodifiedNewtoniandynamics(MOND)asasimplegravitationalpolarisationeffect,incompleteanalogywiththepolarisationofdielectricsinclassicalelectrodynamics.Bytreatingthephysicalvacuumasafeaturelessrelativisticcontinuum,notonlyareweabletoderiveclassicalelectrodynamicsfromfirstprinciples,butwearealsoabletoshowthatgeneralrelativitygivesrisetopreciselythescenariodescribedbyBlanchet,andthereforethatMONDisanon-trivialpredictionofgeneralrelativity.Inparticular,ourmodelpredictsthatantimatterhasnegativemassandthatneutrinostakepreciselytheformofmatter-antimatterdipoles.Takentogethertheseproper-tiesalsohavethepotentialtoresolveanumberofthemostimportantoutstandingproblemsincosmology,includingtheapparentmassoftheneutrino,thepresenceofdarkmatter,theexistenceofdarkenergy,theapparentflatnessoftheuniverse,theoriginofgammaraybursts,andthesmallnessofthecosmologicalconstant.Thestructureofourpaperisasfollows.Webeginin§2withtwobasicpremises,namely(i)thatthetheoryofrelativityholds,and(ii)thatthephysicalvacuumisafeaturelessrelativisticcontinuuminmotion.In§3weshowthatitispossibletodescribethewholeofclassicalelectrodynamicsintermsofthemotionofatwo-componentrelativisticfluidwhereeachcomponentisatime-reversedversionoftheother.In§4weshowthatthepresenceofthistwocomponentfluidisapredictionofgeneralrelativityifourproposalregardingtheSchwarzschildsingularityiscorrect,andthatthefluidparticlesarechargelessneutralspinorswhichcanbeidentifiedwithneutrinos.WethenshowthattheseneutrinoshavepreciselythepropertiesrequiredtoexplaintheoccurrenceofmodifiedNewtoniandynamics,andhencethatMONDisaconsequenceofEinstein’sgeneraltheoryofrelativity.In§5weoutlinebrieflyhowthepredictionofantigravitymightpotentiallyresolvesomeoftheothermajoroutstandingissuesincosmology.Weendin§6withasummaryanddiscussionofourresults.Weassumeametricwithsignature(+,−,−,−),andfollowtheconventionsofJackson3throughout.2.SpacetimeandthePhysicalVacuumInthissectionweestablishthereferencesystemandthecoordinatesthatwillbeusedtodescribethedynamicsofthevacuum,andweshowhowMaxwell-likeequa-tionsappearasidentitiessimplyasaconsequenceofassumingthattheunderlyingspacetimeisLorentzianratherthanGalilean.2.1.CoordinatesandReferenceFramesWebeginourinvestigationwiththeassumptionthatthephysicalvacuumisnoth-ingbutafeatureless,space-filling,continuousrelativisticfluid(i.e.arelativisticcontinuum),whosepropertiesaredescribedcompletelybyitsmotionthroughout(Minkowski)spacetime.Inparticular,wemakenopriorassumptionsaboutpossiblesubstructureorthemassdensityofthevacuum,sothattheonlyphysicaldimensionsenteringourdiscussionarethoseoflengthandtime.LetusconsideranarbitraryrelativisticinertialframeofreferenceinM3,1with4-coordinatesxμ=(ct,x,y,z),sothatthespacetimepartialderivativesaregivenby∂μ=(1c∂∂t,−∇)and∂μ=(1c∂∂t,∇)respectively.Itisimportanttonotethattheforthcominganalysiswillbecompletelyindependentoftheparticularframeofreferenceused.Letτbethepropertimeinthisinertialframe,andletrdenotethe3-position(x,y,z)ofapointinthecontinuum.Consideringtheinstantaneousmotionatpropert