A Short Introduction to Bit-String Physics

arXiv:hep-th/9707020v11Jul1997SLAC–PUB-7205June1997AShortIntroductiontoBIT-STRINGPHYSICS∗†H.PierreNoyesStanfordLinearAcceleratorCenterStanfordUniversity,Stanford,CA94309AbstractThispaperstartswithapersonalmemoirofhowsomesignificantideasaroseandeventstookplaceduringtheperiodfrom1972,whenIfirstencounteredTedBastin,to1979,whenIproposedthefoundationofANPA.Ithendiscussprogramuniverse,thefinestructurepaperanditsrejection,thequantitativeresultsuptoANPA17andtakeanewlookatthehandy-dandyformula.Followingthishistoricalmaterialisafirstpassatestablishingnewfoundationsforbit-stringphysics.Anabstractmodelforalaboratorynotebookandanhistoricalrecordaredeveloped,culminatinginthebit-stringrepresentation.Isetupatic-toclaboratorywithtwosynchronizedclocksandshowhowthiscanbeusedtoanalyzearbitraryincomingdata.Thisallowsmetodiscuss(briefly)finiteanddiscreteLorentztransformations,commutationrelations,andscatteringtheory.Earlierworkonconservationlawsin3-and4-eventsandthefreespaceDiracandMaxwellequationsiscited.Thepaperconcludeswithadiscussionofthequantumgravityproblemfromourpointofviewandspeculationsabouthowabit-stringtheoryofstrong,electromagnetic,weakandgravitationalunificationcouldtakeshape.Revisedandconsiderablyextendedversionoftwoinvitedlecturespresentedatthe18thannualinternationalmeetingoftheALTRNATIVENATURALPHILOSOPHYASSOCIATIONWesleyHouse,Cambridge,England,September4-7,1996∗WorksupportedbyDepartmentofEnergycontractDE–AC03–76SF00515.†ConferenceProceedings,entitledMerologies,willbeavailablefromANPAc/oProf.C.W.Kilmister,RedTilesCottage,HightStreet,Bascombe,Lewes,BN85DH,UnitedKingdom.1Pre-ANPAIDEAS:Apersonalmemoir1.1FirstEncountersWhenIfirstmetTedBastinin1972andheardoftheCombinatorialHierarchy(hereinafterCH),myimmediatereactionwasthatitmustbedangerousnonsense.Nonsense,becausethetwonumberscomputedtoreasonableaccuracy—137≈¯hc/e2and2127+136≈¯hc/Gm2p—areempiricallydetermined,accordingtoconventionalwisdom.Dangerous,becausetheideathatonecangaininsightintothephysicalworldby“purethought”withoutempiricalinputstruckmethen(andstillstrikesme)assubversiveofthefundamentalEnlightenmentrationalitywhichwassohardwon,andwhichisprovingtobealltoofragileinthe“newage”environmentthattheapproachtotheendofthemillenniumseemstoencourage[84,86].ConsequentlywhenTedcamebacktoStanfordthenextyear(1973)[8],ImadesuretobeathisseminarsoastoraisethepointaboutempiricalinputwithasmuchforceasIcould.Despitemybias,Iwasstruckfromthestartofhistalkbyhisobvioussanity,andbyaremarkhemadeearlyon(buthassinceforgotten)totheeffectthatthebasicquantizationisthequantizationofmass.Whenhispresentationcamearoundtothetwo“empirical”numbers,IwasstruckbythethoughtthatsometimeagoDyson[19]hadprovedthatifonecalculatesperturbativeQEDuptotheapproximationinwhich137electron-positronpairscanbepresent,theperturbationseriesinpowersofα=e2/¯hc≈1/137isnolongeruniformlyconvergent.Hence,thenumber137asacountingnumberalreadyhadarespectableplaceintheparadigmforrelativisticquantumfieldtheoryknownasrenormalizedquantumelectrodynamics(QED).TheproblemformebecamewhyshouldtheargumentsleadingtoCHproduceanumberwhichalsosupportsthisparticularphysicalinterpretation.AstotheCHitself,IreferyoutoCliveKilmister’sintroductorytalkintheseproceedings[39],wherehediscussesanearlyversionofthebit-stringconstructionofthesequenceofdiscriminatelyclosedsubsetswithcardinals22−1=3→23−1=7→27−1=127→2127−1≈1.7×1038basedonbit-stringsoflength2,4,16,256respectively..Thefirstthreetermscanbemappedbysquarematricesofdimension22=4→42=16→162=256.The2562discriminatelyindependentmatricesmadeavailablebysquaringthedimensionneededtomapthethirdlevelaremanytwofewtomapthe2127−1discriminatelyclosedsubsetsinthefourthlevel,terminatingtheconstruction.Inthehistoricalspiritofthismemoir,IaddthatthankstosomearcheologicalworkJohnAmsonandIdidinJohn’satticinSt.Andrews,theoriginalpaperonthehierarchybyFredrickParker-Rhodes,draftedlatein1961,isnowavailable[79].InowaskyoutojoinwithmehereinmycontinuinginvestigationofhowtheCHcanbeconnected2toconventionalphysics.Asyouwillseeinduecourse,thisresearchobjectivediffersconsiderablyfromtheaimsofTedBastinandCliveKilmister.They,inmyview,areunnecessarilydismissiveoftheresultsobtainedinparticlephysicsandphysicalcosmologyusingtheconventional(ifmath-ematicallyinconsistent)relativisticquantumfieldtheory,inparticularquantumelectrodynamics(QED),quantumchromodynamics(QCD)andweak-electromagneticunification(WEU).Beforeweembarkonthatjourney,Ithinkitusefultounderstandsomeofthephysicsback-ground.Dyson’sargumentitselfrestsononeofthemostprofoundandimportantpapersintwen-tiethcenturyphysics.In1937CarlAndersondiscoveredinthecosmicradiationachargedparticlehecouldshowtobeintermediateinmassbetweentheprotonandelectron.Thiswasthefirsttobediscoveredofthehostofparticlesnowcalledcollectively“mesons”.OnesuchparticlehadalreadybeenpostulatedbyYukawa,asortof“heavyphoton”whichheshowed,usinga“massiveQED”,gaverisetoanexponentiallyboundedforceoffiniterange.IfthemassoftheYukawaparticlewastakentobeafewhundredelectronmasses,thiscouldbethe“nuclearforcequantum”.Anderson’sdiscoveryprompted