CofounderofsemiinvasivesemiconductortestingApparentlyrespectableProfessorFRSFREngFInstPWarningTodaysmaterialishereticalDonotuseinTripos RossAndersonandRobertBrady Heresy CambridgeFebruar ID: 289634
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RossPuremaths!cryptography!hardwarereverseengineering Cofounderofsemi-invasivesemiconductortestingApparentlyrespectable(Professor,FRS,FREng,FInstP...)Warning!Today'smaterialisheretical.DonotuseinTripos! RossAndersonandRobertBrady Heresy Cambridge,February20153/48 Beginnings 2011:Neutrinostravelfasterthanlight!(sinceretracted,but...)SowhereonearthdoestheLorentzcontractioncomefrom?Coulditbesomekindofuid?Buthowcouldyougetanegativedielectriccoefcient? RossAndersonandRobertBrady Heresy Cambridge,February20156/48 Breakthrough? Robert:asolutiontoEuler'sequationthat'salsoasolutiontoDirac's!Recall:ForalosslesscompressibleuidF=�rP=Du Dt=(@u @t+(u:r)u)ThisisEuler'sequation,whichdescribesasuperuidlike4He... RossAndersonandRobertBrady Heresy Cambridge,February20157/48 Dirac'sequationRecall:Foranelectroni~@ (x;t) @t=(mc2+c( 1p1+ 2p2+ 3p3)) (x;t)where 2i=2+I4; i j+ j k=0; i+ i=0Fluxringswithasingletwistobeythis,sobehavelikeelectronsandpositrons!(Brady,`Theirrotationalmotionofacompressibleinvisciduid',arxiv1301.7450)Isthisobservable? RossAndersonandRobertBrady Heresy Cambridge,February20158/48 Heresy 1 Whoweare 2 Superuidquantumgravity? 3 Bouncingdropletexperiments 4 Threedimensions 5 UpdatingMaxwell'smagneticlineofforce/molecularvortex 6 ConsequencesforFaraday'smodeloflight 7 Conclusion–amathematicalheresy RossAndersonandRobertBrady Heresy Cambridge,February201512/48 DeectionfromboundaryofdishWeblewupastroboscopicphoto(Protière2006)andmeasuredit Forceisinversesquareneartheboundary,1 2mv2=1 2mv2o�K=rAngleofincidence6=angleofreection RossAndersonandRobertBrady Heresy Cambridge,February201515/48 Application:degassingoilsThesecondaryBjerknesforceisusedtodegasoilsviaultrasonicvibration Bubblespulsateinphase,attractoneanotherandmerge RossAndersonandRobertBrady Heresy Cambridge,February201518/48 MagnitudeofthesecondaryBjerknesforceOurcalculationfortheresonantcasewheremaximumspeedc SecondaryBjerknesforceF= bc r2 1b=mc2 ! CompareforcebetweenelectronsF= ~c r2 1 137:036~=mc2 ! ThenestructureconstantofthesecondaryBjerknesforceistwoordersofmagnitudelargerthanforanelectronbisananalogueofPlanck'sreducedconstant RossAndersonandRobertBrady Heresy Cambridge,February201519/48 TwowaystocalculatetheeldofawalkerConventionalapproach EachbounceexcitesastandingBesselfunctionsolutiontothewaveequation,whichdecaysslowlyduetoabsorptionattheboundaryandbandgapeffects.Simulateinacomputer. Symmetryapproach Besselfunctionf(x;y;t)obeyswaveequation.ThewaveequationissymmetricunderLorentztransformation,sothatf(x0;y0;t0)isanothersolution,wherex0= (x�vt)t0= t�vx c2 =1 r 1�v2 c2 Asecond-orderscalesymmetryisalsoinvolved.Decayisslowbecauseofparametriceffects. RossAndersonandRobertBrady Heresy Cambridge,February201522/48 PredictionforarotatingdropletpairRotatingdropletpair Interactionwithimageintheboundary Staticforcescancel(dropletsareantiphase) Magnetic-likeattractionremains Predictnestructureconstant1/20 Couderobserveddropletpair`hopscotch' Visualisingthemechanism Floweld–BesselfunctionJ1 Rotatesaroundthecentre Attractedtoimageinboundary,liketwovortices RossAndersonandRobertBrady Heresy Cambridge,February201527/48 Furtherexperimentalresults YCouder,EFort`Single-ParticleDiffractionandInterferenceataMacroscopicScale'PRL97154101(2006)AEddi,EFort,FMoisi,YCouder`Unpredictabletunnelingofaclassicalwave-particleassociation'PRL102,240401(2009)EFortetal`Path-memoryinducedquantizationofclassicalorbits'PNAS1074117515-17520(2010) RossAndersonandRobertBrady Heresy Cambridge,February201528/48 Wheredothequantumphenomenacomefrom?Factorisetheeldofadroplet Stationarydroplet h= =Rcos(�!ot) =J0�!or c Lorentztransformwhere =Rcos(�!ot0)=Rcos(kx�!t)k= !o c2vx!= !o Wavelength(deBroglie!) =2 k=b pb=2mc2 ! bisthesameanalogueofthePlanckconstantwhichwesawintheinversesquareforce RossAndersonandRobertBrady Heresy Cambridge,February201529/48 Klein-GordonandSchödingerequations =Rcos(!ot)obeys@2 @t2=�!2o ButthemotionhasLorentzsymmetrysoweneedaLorentzcovariantequation,whichis@2 @t2�c2r2 =!2o theKlein-GordonequationtheSchrödingerequationisalow-velocityapproximationtothisSofarsogood.Butcanthisworkinthreedimensions? RossAndersonandRobertBrady Heresy Cambridge,February201531/48 Faraday'smodeloflight1846-Faraday Lightiswavesinlinesofforce Polarisedandabsorbeddiscretely Doesnotexplainrefraction,diffraction,interference RossAndersonandRobertBrady Heresy Cambridge,February201534/48 Maxwell'scalculation(modernnotation,unitcharge) pmomentumperunitvolume B=r pMagneticeld(denition)r:B=0Gauss'slawformagnetismsincer:(r p)=0 =RB:dsMagneticux(denition) =H p:d`6=0MolecularvortexhasuxStokes'stheorem E=�d p dtForceperunitvolumeNewton'ssecondlawrE=�dB dtFaraday'slawofinductionrd p dt=d dt(r p) RossAndersonandRobertBrady Heresy Cambridge,February201536/48 Maxwell'scalculation(modernnotation,unitcharge) pmomentumperunitvolume B=r pMagneticeld(denition)r:B=0Gauss'slawformagnetismsincer:(r p)=0 =RB:dsMagneticux(denition) =H p:d`6=0MolecularvortexhasuxStokes'stheorem E=�d p dtForceperunitvolumeNewton'ssecondlawrE=�dB dtFaraday'slawofinductionrd p dt=d dt(r p) RossAndersonandRobertBrady Heresy Cambridge,February201536/48 ContraintsAmolecularvortexcanbeanyaxiswithmassowingaroundit(H p:d`6=0) Anordinaryvortexisnotagoodexample Pinnedtotheuid,notsymmetricunderLorentztransformation ButMaxwell'sequationsaresymmetricunderLorentztransformationButwenowknowanordinaryvortexisnottheonlypossibility... RossAndersonandRobertBrady Heresy Cambridge,February201538/48 Berry'sphasevortexexperiment1980-Berry,Chambers,Large,Upstill,Walmsley Waterwavespastasteadyvortex Phaseofwaveadvancesby2naroundthecentre HrS:d`=2n–denesa`phasevortex' Measuredananalogueofmagnetic(Aharonov-Bohm)effect RossAndersonandRobertBrady Heresy Cambridge,February201540/48 Heresy 1 Whoweare 2 Superuidquantumgravity? 3 Bouncingdropletexperiments 4 Threedimensions 5 UpdatingMaxwell'smagneticlineofforce/molecularvortex 6 ConsequencesforFaraday'smodeloflight 7 Conclusion–amathematicalheresy RossAndersonandRobertBrady Heresy Cambridge,February201542/48 Linearlypolarisedlight1+�1/J1(krr)cos(!t�kzz)cos(�o) Oscillatingdipoleparallelto=o Linearlypolarisedlightisamplitudemodulation Fouriercomponentshavevariousvaluesofkz RossAndersonandRobertBrady Heresy Cambridge,February201544/48 Belltests Belltestexperiment 100%correlationwhenpolarisersareparallel cos(2 )correlationwhenpolarisersareatangle Clauser,Horne,ShimonyandHolt(1969) assumedpolarisation`carriedbyandlocalisedwithin'aphoton NottrueonFaraday'smodel CHSHconcludedthatcos(2 )isimpossible RossAndersonandRobertBrady Heresy Cambridge,February201545/48 Heresy 1 Whoweare 2 Superuidquantumgravity? 3 Bouncingdropletexperiments 4 Threedimensions 5 UpdatingMaxwell'smagneticlineofforce/molecularvortex 6 ConsequencesforFaraday'smodeloflight 7 Conclusion–amathematicalheresy RossAndersonandRobertBrady Heresy Cambridge,February201546/48 Conclusion-amathematicalheresyEuler(1746)mayberight Lightiswavesinafrictionlesscompressibleuid GuidedbyFaraday/Maxwelllinesofforce WavesobeyMaxwell'sfullequationstorstorder Polarised,Absorbeddiscretely,ConsistentwiththeBelltests Analoguegravity–Euler'suidhassymmetryofgeneralrelativity Emergentquantummechanics–bouncingdroplets Ourhereticalprogramme DeriveallofphysicsfromEuler'sequationforacompressibleuid OrproveEulerwrongbyfailinginanyareayouchoose RossAndersonandRobertBrady Heresy Cambridge,February201547/48 Conclusion-amathematicalheresyEuler(1746)mayberight Lightiswavesinafrictionlesscompressibleuid GuidedbyFaraday/Maxwelllinesofforce WavesobeyMaxwell'sfullequationstorstorder Polarised,Absorbeddiscretely,ConsistentwiththeBelltests Analoguegravity–Euler'suidhassymmetryofgeneralrelativity Emergentquantummechanics–bouncingdroplets Ourhereticalprogramme DeriveallofphysicsfromEuler'sequationforacompressibleuid OrproveEulerwrongbyfailinginanyareayouchoose RossAndersonandRobertBrady Heresy Cambridge,February201547/48 Conclusion-amathematicalheresyEuler(1746)mayberight Lightiswavesinafrictionlesscompressibleuid GuidedbyFaraday/Maxwelllinesofforce WavesobeyMaxwell'sfullequationstorstorder Polarised,Absorbeddiscretely,ConsistentwiththeBelltests Analoguegravity–Euler'suidhassymmetryofgeneralrelativity Emergentquantummechanics–bouncingdroplets Ourhereticalprogramme DeriveallofphysicsfromEuler'sequationforacompressibleuid OrproveEulerwrongbyfailinginanyareayouchoose RossAndersonandRobertBrady Heresy Cambridge,February201547/48