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AGeometricModelBasedonFrequencyThatRevealstheNatureofTimeTheodoreJ.St.John,MS,MA,Ph.D.
Abstract
Thepurposeofthispaperistopresentahypothesis:thatfrequencyisthe
keytounderstandingthefundamentalnatureoftime.Timeandspacearemirror
imagesofeachotherandtheyaretwodifferentwaysofexpressinginverse
frequency.Thereasonthisisimportantisbecause,bystartingwithfrequencythe
relationshipsofphysicscanbeexpressedbylinearequations.Itisknownthat
frequencyisdirectlyproportionaltoandthusequivalenttoquantumenergy.By
expressingtherelationshipofspatialfrequencyvs.temporalfrequencyasasimple
geometricmodel,severalwell-knownrelationshipsfallintoplacewithouthavingto
stretchthemodelintowarpedexpressionsofspacetimethatrequirecomplicated
hyperbolicfunctionsorfieldequations.Theresultisasensibleinterpretationofthe
meaningoftime,spacetime,quantumparticlesandquantumwavefunctions.The
modelalsolendsitselfdirectlytoanunderstandingofhowspaceandtimebecome
dissociatedandtransformintoquantumbitsofinformation,whichautomatically
modelsrealityasaquantumcomputer.Theimplicationsoftheseinterpretations
provideabridgebetweenphysics,asaphysicalscience,andlifesciencesthattakein
informationfromtheirsurroundings,convolveitwithitselfasparticlesandthereby
shapeandreshapematter,allowinglivingorganismstochangewithtimeandadapt
totheirenvironment.
Introduction
Therehavebeenmanybooksandarticlesaboutthenatureoftime,especially
sinceStephenHawking,broughtittotheforefrontinhisbookABriefHistoryoftime.
(Hawking1990)PhysicistLeeSmolinsaidthatunderstandingthenatureoftime
mightbethemostimportantquestionforthisgenerationofphysiciststoanswer
becausetimeholdsthesecrettounderstandingtheuniverse.(Smolin,TimeReborn:
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FromtheCrisisinPhysicstotheFutureoftheUniverse2013)Heconcludedthat
timeisrealinthesensethat:“Whateverisrealinouruniverseisrealinamomentof
time,whichisoneofasuccessionofmoments.”Anotherphysicist,RichardMuller,
explainedthattheBigBangasa4-dimensionalexplosion“continuouslycreatesnot
onlynewspacebutalsonewtime.”(Muller2016)Butmanyothersstillthinkthat
timeisanillusion(Barbour1999).Andthereareafewwhoconsidertimetobe
somethingthatcanbeviewedasanintrinsicgeometricpropertyofthree-
dimensionalspace.Chappell,et.al.presentedthisusingCliffordgeometricalgebra.
(Chappell,etal.2016)However,they“absorbedtimeintoanexpressionofan
invariantspacetimedistance”.Soratherthanexplainingthenatureoftime,theyhide
itinthesquareofaquaternion,whichagreeswithwhatmostCosmologistsbelieve:
thattimeissomehowmixedwithandthushiddeninspacetocreatespacetime.
However,thenatureofspacetimeisevenmoremysteriousthantime.
Generalrelativitytheoryisthemainframeworkthathasbeenusedtoapproachthe
problemofunderstandingspacetime,andithasservedtoexplainalargebodyof
observationalinformation,includingtheredshiftinlightfromfar-awaystarsand
galaxies,nuleosynthesis,(whichpredictstheamountofhydrogenthatshouldhave
fusedintohelium)andthemicrowavebackgroundradiation,believedtobethe
“echo”oftheBigBang.(Kaku1993,pg.643)Butthishasgeneratedevenmore
questionsandcomplextheories,likeStringTheory,M-Theory,CausalSetTheory,
theAmplituhedronTheoryandLoopTheory.
AccordingtoGeorgeMusser,contributingeditoratScientificAmericanand
authorofSpookyActionataDistance(Farrar,StrausandGiroux,2015)andThe
CompleteIdiot’sGuidetoStringTheory(Alpha,2008),“Ifphysicistshavelearned
anythingfromthelongslogtounifytheirtheories,itisthatspaceandtimeforma
systemofsuchstaggeringcomplexitythatitmaydefyourmostardenteffortsto
understand.”(Musser2018)“Thebottom-linelessonofquantumgravity”said
Musser,“isthatnotallphenomenaneatlyfitwithinspacetime.Physicistswillneed
tofindsomenewfoundationalstructure,andwhentheydo,theywillhavecompleted
therevolutionthatbeganjustmorethanacenturyagowithEinstein.”
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Ratherthanproposinganewfoundationalstructure,thispaperreflectson
andreconsidershowtheoldfoundationswereinterpreted.AccordingtoE.A.Burtt
inTheMetaphysicalFoundationsofModernScience,beforethedaysofNewton,the
treatmentoftimeasanindependententitywasconsideredbymanytobea
philosophicalblunder.(Burtt2003,pg.158)
“Clearly, justaswemeasurespace, firstbysomemagnitude,and
learn
howmuchit is, later
judgingothercongruentmagnitudesbyspace;so
we first reckon time from some motion and afterwards judge
other
motions by it; which is plainly nothing else than to compare
some
motionswithothersbythemediationoftime;justasbythemediationof
spaceweinvestigatetherelationsofmagnitudeswitheachother.”
Inotherwords,aunitoftimeisjustaunitofmotionthatiscapturedor
“clocked”byacyclicalmotiondeviceasaunitmeasuredinthepast,tobeusedasa
commondenominatorforothermotion.Spacetimethenissimplyaspatiotemporal
processthatimplicitlyflowsandweexperienceitasmotion.Butitmustbeexpressed
asapairofexplicitmeasurablequantitiesthatappearto“dancewitheachother”
andmoveindependentlywithaninverserelationship.Thisinverserelationshipwill
beexplainedandillustratedbelowinasimplegeometricmodel.
TheHypothesis
Thehypothesispresentedhereisthatfrequency,whichisdefinedasinverse
time,e.g.incyclespersecond,shouldbeconsideredthemostfundamental
spatiotemporalprocess-unitinnature.Thentime,astheinverseoffrequency,is
simplyamirrorimageofaquantumunitofenergy,bothofwhicharebyproductsof
relativemotion.Wemaythinkthatwesensetime,butmotion,whichisubiquitous,
iswhatweactuallysense.Aquantumunitofenergyisjustenergyinmotionand
thereisnosuchthingasanobjectatrest.Anobjectonlyappearstobeatrestinits
ownreferenceframe.Itisalwaysinmotionrelativetoeverythingelseinthe
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universethatismovingwithrespecttoit.Thereasonthattimeisa“problem”inthe
firstplaceisbecausewearetaughttothinkofitasaprimaryfundamentalunit.And
thatisbecausedoingsoallowedearlyphysiciststopredicttheoutcomeofrelative
motion.Thatiswherethemoneyis,sotospeak,becausemeteringmotionand
predictingtimeandlocationofarrivalisextremelypracticalanduseful.Butthat
modelseparatesandhidesthefundamentalnatureofrealityandfoolsusinto
thinkingthatthephysicalaspectiswhatisreal.Eventuallythatmodelreachedits
limitandbegantocreateproblems,liketheonesdescribedaboveandother
“singularityproblems”.(Smolin,TheTroubleWithPhysics2006)
ThesolutionIsubmitistorecognizefrequency–theinverseoftime–as
primary.Westartwiththeconceptofenergy.Theword“energy”referstoan
implicitconceptthatjustis.Tosaythatitisimplicitmeansitcannotbeexpressed,
onlyimplied.Ifwetrytoexpressit,wemakeitexplicitviatheexpression.Asimplicit
totheuniverse,energyisubiquitous;itcanneitherbecreatednordestroyed.But
onceexplicated,(seeDavidBohm’sWholenessandtheImplicateOrder(Bohm1980))
itcanbechangedinform.Andtheword“form”impliesashapethatcanbe
representedbyaquantity.Themostfundamentalunitofenergyisaquantumunit,
andweknowfromquantummechanicsthatitcanbeexpressedasafunctionof
frequency:𝐸 =
ℎ𝑓,whereℎisPlanck’sconstant.Infact,thesameequationholds
whetherfreferstotemporalfrequency,whichisinversetime𝑓!
=!!,orspatial
frequency,whichisinversespace,𝑓!
=!!,wherecisthespeedoflight.Thesis
usuallywrittenaswavelength(𝜆)asintheequation𝐸 =
!!!.Andsince!
!definesthe
momentumofaphotonandmomentumimpliestheparticulateformofenergy(a
quantumparticle),spatialfrequencyisgenerallyignored.Perhapsthatisbecause
focusingon“objects”isofmoreinteresttothosewhowanttobeobjective.However,
timeisnotanobjectandsoitcannotbeunderstoodbyfocusingonobjectivereality.
Method
Theapproachusedhereistopresentamodelwithoneunitofenergyandits
equivalent–oneunitoffrequency–onarectangularcoordinatesystem,asshownin
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Figure1(withenergyrepresentedbyavectorarrowwithmagnitudeofone),and
frequenciesrepresentedasthefirstunittoscaletheaxes.Sothefrequencyofone
unitofenergywouldbeonecycleperwhateverunityouchoose.Andthevalueofc
woulddependonthatchoiceofunits.Wewillnotchoosecommonphysicalunits.
Instead,“naturalunits”areexpressed(i.e.madeexplicit)sothateachoneis“one
unitofenergy”.
BecausethetipofeacharrowinFigure1representsthe“particleboundary”
(thismeanstheenergyboundaryofaquantumparticle,notthephysicalboundary),
theregionoutsideofoneunitrepresentsthepartoftheuniversethatisnotthe
particle.Logically,“nottheparticle”meanstheinverseoftheparticle;therefore,
outsideoftheboundaryonthespatialaxisrepresents3-Dspace(s)andonthe
temporalaxis,itrepresentstime(t).
Figure1
Thismayseemlikeanunconventionalwayofusingarectangularcoordinate
systembecausetheunitsforenergyaredifferentfromtheunitsofspaceandtime.
Butwedothesamethingwithvectorsthatrepresentmotionthathasmagnitude
anddirection.Itisasuperpositionofrelationships.Regardlessofwhatunitsof
measurementsareassigned,therelationshipsremainthesame.The“outside”
domaincorrespondstorelativisticrelationshipsandthe“inside”domain
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correspondstoquantumrelationships.Thesetwodomainsareoftenmixed
mathematically,forexampleaunitofpowerisaunitofenergyperunittimeor
𝑃 =
!!.InFigure1,thisusestheinsideunitofenergyasthenumeratorandthe
outsideunitasthedenominatorandtheresultistheslopeofthediagonalline.Orif
yourotatetheaxeswithtemporalunitsastheverticalandspatialunitsasthe
horizontal,theslopewouldrepresentaunitofforce,sinceforceisaunitofenergy
perunitdistanceor𝐹 =
!!,whereswouldrepresentaunitofmeasureinone
dimension–thedirectionoftheforce.(Halliday,ResnickandWalker1993)
AsitisinFigure1,theslopeofthediagonallineis!!=
𝑐ontheoutsideand
! !!!= !
!ontheinside.InHartreenaturalunits,𝑐 =
1isthespeedoflightand!
!= 𝛼is
thefinestructureconstant,whichisconsideredbymosttobeafundamental
constantinnature(Nair,etal.2008).Inthegeneralrelativityframework,itisa
fundamentalphysicalconstantcharacterizingthestrengthoftheelectromagnetic
interactionbetweenelementarychargedparticles.Butithasmultiplephysical
interpretations(seehttps://en.wikipedia.org/wiki/Fine-structure_constant)and
someevensuggestthatitmaynotbestrictlyconstant(Webb,etal.1998).According
tothemodelpresentedhere,itissimplyacluethattheexpressionofthequantum
domainisthemirrorimageoftherelativisticdomain.
Presentingspaceandtimeinthiswayallowsseveralotherrelationshipsto
fallinplaceaswell,asshowninFigure2,wherethesubscriptin𝐸!
standsfor
deBroglie,todistinguishitfrom𝐸! ,whichisrestenergyand𝐸!
,whichistotal
energy.(ReproducedfromFigure6of(StJohn,TheHolomorphicProcess-
UnderstandingtheHolographicNatureofRealityasaMetamorphicProcess2018))
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Figure2
Noticethatthekineticenergytermisrepresentedbythepartofthetotal
energyvectorthatliesoutsideofthe“particle”boundary.Itisareflectionofthefact
thataquantumparticleisaunitofenergy,geographicallyexpressedintheenergy
domain,whichissuperimposedovertherelativisticdomain(sandt,notlabeledin
thisfigure).Inotherwords,aparticle,oranyphysicalobject,canbeperceivedasan
independentobject–or–asanobjectthatisinmotionrelativetoanythingelseinthe
universethatismovingrelativetoit.Andthetworepresentationscanbe
superimposedbyapplyingtheappropriatescalingfactororcoordinate
transformation.TheLorentzfactor,𝛾servesthispurposehere.
Figure1andFigure2werepresentedtovalidatethismodeloffrequency
withitsinverses(spaceandtime).Inordertouseittounderstandthenatureof
time,theouter(relativistic)rectangulardomainwillbescaledasusual,seeFigure3,
withlinearincrementsoftime,andtheinner(frequency)domainwillbescaledwith
incrementsofinversetime.ThusFigure3isatwodimensionalrepresentationofa
torus,withthequantumdomainastheregioninsidethecircle–theeventreference
or“eventhorizon”inblackholelingo–andtherelativisticdomainontheoutside.
Theverticalaxisstillrepresents3-Dspace,butwe’refocusingontimeinthisfigure,
sothelabelsareleftoffinthefigure.Allfourquadrantsareshownbecausetheinner
domainwillbeidentifiedasapolardomaininthenextsection.
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Figure3
Historically,physicistshavetaken𝑡 =
0tobealegitimatestartingpointfor
measurement.ButaccordingtoFigure3,𝑡 = 0correspondsto!!=
∞oraninfinite
frequency.Obviouslythereisnosuchthingasinfinitefrequency,sousing𝑡 =
0asa
referencepointforlinearlyscaledmotioncreatesaproblem.Theproblemisthat
regardlessofwhatunitsofmeasureyouchoose,oneunitisoneunit.Andifthe
fundamentalunitofmotionisaunitoffrequency,thenunitsofspaceandtimemust
berepresentedasinversesbetween0and1.Inotherwords,ameasurementofone
unitisatruemeasurementsousing𝑡 =
1asaneventreferencemakesthemodelfit
reality.Theproblemwithback-projectingthatmeasurementtozeroisthatit
stretchesthetruth,andtryingtoforcerealitytofitthemodelcreatesawarped
interpretationofreality.Withoutageometricmodel,mathdoesn’trevealthis
problem.DifferentialCalculusforexample,handlesthisstretchingoperationby
shrinkingthepolardomainintermsoftimedowntoapoint:thelim!→!∆!∆!,andthen
definesthatusinglinearunitsofmeasureasinstantaneousspeedinonedirection.
Formostpracticalpurposesthisisfineandveryusefulbecauseitisaccuratewithin
theprecisionlimitsofmeasurement.
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Butquantumphysicsisallaboutthepartinsidethelimitas∆𝑡 → 0and
∆𝑠 →
0.Whenitwasbeingdeveloped,NielsBohrformulatedthe“correspondence
principle”,whichrequiresthatthebehaviorofsystemsdescribedinthenew
quantummodelmustreducetothesameprovenresultsastheclassicalmodel.But
thentheyhadtoprovideinterpretationsthatdidnotcorrespondtorealityaswe
knowitinthe“realworld”.Theyacceptedthatthequantumworldwasjustweird.
Andphysicistsworkingwithspecialandgeneralrelativityhaveacceptedthesame
“copout”:thatthecosmosisjustwarpedandweird.
Toanengineer,theproblemisthatphysicistsarenotconcernedwiththereal
worldandtherefore,mistakethemapfortheterritory.Engineersrecognizethe
warpingeffectasanartifactthatiscausedbymapping,whichisarequiredpartof
anengineer’scurriculumbecauseitisastandardmethodusedforsolvingboundary
valueproblems.Conformalmapspreserverelationshipsintheformofsizeand
attitude(senseofangles)fromonedomaintoanother.(Kreyszig1979,pg.599)In
thiscase,theslopeofthediagonallineinthefigureisaconformalprojectionofa
unitinthedimensionperpendiculartothespace-timeplane,i.e.themotion
dimension.Therefore,themodelpresentedhereiscalledtheSpace-Time-Motionor
STMmodel.(StJohn2018)
Sothequantumpoint,lim∆!→!∆!→!isjustthecircleyoumightdrawonaplaneto
representthethirdaxiscomingoutofthepage.Incontrolsystemdesign,engineers
makegreateffortstoensurethatcontrolsystemsavoidapproachingsingularpoints,
like𝑡 =
0called“poles”becausetheyrepresentconditionsofmaximuminstability
inthesystem.(Ogata1970,pg.23)That,Isubmit,istheproblemwithmodern
theoreticalphysics.Themodelsthatheldtimeasaprimaryfundamentalunit
becameunstableandtheback-projection“blewup”ina“cataclysmicexplosion10-
20billionyearsago”,asMichioKakuputit(Kaku1993)becausetheyassumethat
therewasabeginningtotheuniverse.Butifthereisnosuchthingaszerotimeor
zerospace,i.e.nobeginningtotheuniverse,theneventhoughrealeventscanbefit
intothemodel,themodelstilldoesn’tfitreality.
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Ontheotherhand,frequencyisequivalenttoarealunitofenergy.Spatial
frequencyandtemporalfrequencyareexplicitunits,justlikespaceandtime,but
neitheroneisseparatedintothreedimensions,sotheyworktogetheraslinear
relations,commonlyusedasFourierandLaplacetransforms.Spaceandtimestill
workasscalesthatcanbemanipulatedanywayyouwant,tobuildsymbolicmodels
thatareappropriateforspecificapplications.Butextendingthelinearscalesbackto
theoriginbrushesoverthemeaningofthequantumunitofmotion.Thatunitisa
unitofvibration–akernelinformation.Andthatinformationreflectsthemeaningof
time.
Soratherthanstretchingorbrushingoverit,wewilluseapolarcoordinate
systemandcorrelatethepolardomainwithquantumspaceandtherectangular
domainwithrelativisticspace.Thenwecorrelatevectorsinrelativisticspacewith
phasorsinquantumspace.Thebenefitofthisapproachisthatitprovides
interpretationsthatcorrespondtoprovenresultsinbothquantumandrelativistic
models,describedin(StJohn2018),aswellastherealworld,i.e.itwillbeshown
belowthattherelationshipsderivedfromthisapproachproducethegoldenratio,
whichisevidentinthestructureoflivingorganisms.
PhaseVectorsandPhasorDiagrams
Vectorsaredefinedbytheirmagnitudeanddirectionandarenormally
superimposedoverrectangularcoordinatesystems.“Phasors”asshowninFigure4
arephasevectors,i.e.theydefinetheirangleasmeasuredfromareference(usually
thehorizontalaxis)inapolarcoordinatesystem.Soratherthanscalingtheinside
partofthetaxisas!!,phasorsuseangularfrequency,𝜔.Theyarecommonlyusedin
electricalengineeringtorepresentwavesofalternatingcurrentfortransmissionof
powerorradiosignals.Intheseapplications,phasorsalwayshaveconstant
magnitude,like𝐸,theradiusofthecircleinFigure1,sotheyaremoreusefulfor
constantamplitudewaves.Here,theportionofthevectorinsidethecircleinFigure
2thatrepresentsaparticle“atrest”isrepresentedasthesolidphasorinFigure4.
Theendpointofthisdiscussionwillbetoillustratewhatthistypeofcoordinate
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systemrevealsastimepasses(thegoldenratio),butwashiddenwhenthequantum
domainwasignoredandthushidden.
Aphasordiagramonlyneedsoneaxistoscaleitsmagnitudeandprovidea
referencefortheangleofthephasor,butinthisapplicationweneedboththe
quantumandrelativisticsystemsbecausewhateverhappensinonedomainalso
happensintheotherandwewillbeabletojumpbackanforthasneeded.
Figure4
Eventhoughenergyappearstobecollapsedandlocalizedintoaparticle,a
particleisstillinmotionrelativetoeverythingelseintheuniverse,soitmustbe
expressedasaspatiotemporalunit.Thiscanbeaccomplishedbyseparatingthe
phasorinFigure4intoaspatialcomponent(atanangle𝑘𝑟totheleftdashed
phasor)andatemporalcomponent(atanangle𝜔𝑡totherightdashedphasor).The
differenceangle𝜃 = (𝑘𝑟 −
𝜔𝑡)representsthephasedifferencebetweenthetwo.As
timepasses,thesetwoexpressasseparatewaves,but𝜃 =
0representsthephasor
thatremainsconstanttorepresentthesolidphasor(nottheonesthataredashed
lines),collinearwiththerelativisticvector𝐸! inFigure2.
Thephaseangleisthesameexpressionusedastheargumentofatransverse
wave,suchas𝑦 𝑥, 𝑡 = 𝑦!sin(𝑘𝑥 −
𝜔𝑡),where𝑦!isthemaximumamplitudeofthe
wave,𝑘 = !!and𝜔 = !!
!.Butinthatcase,themodelisusedtoplotthewavemoving
eitherinspaceorintimewhiletheotherisheldconstant.Aphasordiagramallows
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thembothtochangetogetherasinversesofeachother.SoonephasorinFigure4
mustrotatetotheleftastheotherrotatestotherightatthesameconstantangular
rate.Again,thisleavestheoriginaldiagonalphasor,thetotalenergyofthequantum
particle,toremainunchanged.
Astheleftvectorbeginstorotateleftandgetahigherslope
!!inreference
totherelativisticframe,(asshowninFigure4),thiswouldbeinterpretedtomeanit
isincreasingspeedandsincethevectorcomponentprojectedontothespaceaxisis
gettinglarger,thatsuggeststhattheparticleisgettingbiggerordiffusing.Similarly,
therightvectorprojectsasifitwereslowingdownandgettingsmalleror
collapsing.Sothiswouldmeanthattheparticleisbeginningtoseparateitselfinto
aninnersphereandanoutersphere.Inreality,onewouldarguethatthisisrelated
totheHeisenberguncertaintyprinciple,andnothingishappeningtotheactual
particle.It’sthemodelthatmustchangeinordertorepresentchangethatresults
fromthepassageoftime.Andsincetheappearanceofthephysicalparticledoesn’t
change,thespatialpartoftheexpressionhastoberenormalized,moment-by-
moment,whereasthetemporalpartdoesnot.Thequestionis,whatdefinesthat
“moment”.Thatiswherethegoldenratioappearsinthemodel.
Result:TheGoldenRatio
Thereisapointinthetwophasors’rotationwherethetwoslopesreacha
veryspecialvalue.Figure5showsthisfortheleftphasor(kr)andFigure6forthe
rightphasor(𝜔𝑡).Thatspecialvalueisthepointwheretheslope,whichisaratio,
reachesthegoldenratio,∅ = 1.618…
What’ssospecialaboutthegoldenratio?Itis
thesolutiontotherelation∅ = 1+
!∅.If∅istheslopeoftheleftphasor,thismeans
thatifthereferencescaleshiftsbyoneunitoneitheraxis,i.e.onemomentintime
andonemomentinspace,thentherotatedphasorwiththeslope,∅,canbereplaced
byanewphasor(shownasphasor3)withthesameslopeasphasor2,exceptas
referredtotheoutsidereferenceframe(justascand!!wereshowninFigure1)and
shiftedbyoneunitasshowninbothFigure5andFigure6.
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Andthereisa“twist”:Sincetheangleofeachphasorisfoundbytakingthe
arctan(theoppositeovertheadjacentsidesoftherighttriangle),itiseasyto
calculatethatthetwonewphasorsarerotated(ergotwisted)by13.28oinopposite
directionsascomparedtotheoldvector,phasor1.
Asmentionedabove,justbeforetheshift,the“size”ofthe“newparticle”in
theunshiftedreferenceframe(theprojectionofphasor2onthespaceaxisinboth
figures)isdifferentfromtheoriginalparticle(phasor1).Theprojectionoftheleft
(spatial)phasorinFigure5suggeststhattheparticleisgrowing,butbecauseit
doesn’tappeartobephysicallylarger,thescaleofthespaceaxishastobe
renormalized.Ineffect,the“new”phasor,phasor3,seemstohavecollapsedalong
withthenewrenormalizedcoordinatesystem.Sowecanimaginethattheparticle
expandsfora“goldenmoment”thencollapsesbacktotheoriginalsize.Orwecould
saythattherectangularcoordinatesystemrotatedtoputphasor3backat45!
givingtheparticleitscharacteristicangularmomentumorspin.Whenthat
happens,thetemporalphasormustalsorotatetotherighttoaccountforthe13.28o
tokeep𝜃 =
0.Theresultisthesameparticlethatcontainsa“module”ofinverse-
temporalinformation,i.e.itisafrequencymodulatedunitofinformation(what
NassimHarameincallsaPlanckunitthatmakesuptheunifiedfield).
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Figure5
Figure6
Soevenifnothingphysicalabouttheparticleitselfchanged,theobserver’s
perceptionchangedbecausetheparticleappearstohaverotatedinspaceandtime.
Wesensethemotioninspacebecauseithasmomentum,and“pulls”the
surroundingspaceinward,whichwemeasureasgravity.Andwesensethatithas
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movedintime,butweinterpretittobeunchangingintime.Ratherthanthinking
thattheparticlechangedintime,wethinkthattimehaschangedindependentofthe
particle.Andthatisaperfectlylegitimateinterpretationformostpracticalpurposes.
Butifthatistrue,wheredidthetimego?
Itwentinwardasamomentofinversetimeanditsreflectionwentoutward
asournormalnotionofamomentintime:i.e.theclassic“arrowoftime”.Because
thespaceaxiswasrenormalizedbutthetemporalaxiswasnot,theoldtemporal
phasorstillappearstorepresentasmallerparticle(projectionofphasor3onthe
spaceaxis),whichwecouldimagineobjectivelyasan“event-particle”(atermfrom
ProcessPhilosophy(Whitehead1929))orqbitofinformationcollapseinsidetoward
theinfinitesimalcenterofthephysicalparticle.Thissuggeststhatatorusisabetter
modelthanaspheretorepresentquantumparticles.Anditmightcorrespondto
energylevelsthatrepresentelectronorbitalsinthecurrentmodelsofphysics,but
thathasnotbeenverified.Andifthismodelrepresentsalivingbeing,itsuggests
thattheinner“event-particle”mightbeassociatedwithourmemoryandwithour
geneticcodestoredasquantumunits,twistedinthehelicalformofDNA,being
programmedinrealtime.
Keepinmindthattheprojectionsonthespaceandtimeaxesdonot
representtotalenergyoftheparticle,butratherwavesinspaceandtime.Butthe
differenceinphaseanglesbetweenthenewandoldparticlecanberepresentedasa
differentwavethatmodulatestheparticlefrequency.Andasawave,itisaunitof
information.ThissupportstheideathatperhapsInformationTheoryprovidesa
betterapproachtounderstandingrealitythantheStandardModelofParticle
Physics.(DaviesandGregersen2010)
Itisalsoimportanttonotethatthegoldenratiocanbewrittenintheform
∅! = 1+
∅.Sothisreferstheslopebacktotheinsidedomainoftheoriginal
referenceframeandpresentstheoldenergytermasbeingsquared.Inclassical
wavetheory,thesquareofawaveamplitudereferstointensity,i.e.theamountof
energythatpassesthroughaunitareaperpendiculartothewavedirectionintime.
Inthiscase,thatdirectionisinward.
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Thegoldenratiohasbeenknownforcenturiesandusedinartand
architecturebecauseapplyingittodetermineproportionsforfiguresandbuildings
createsaestheticallypleasingresults.Anditappearsasacommonpatterninleaves,
plants,fruitsandflowers(veryobviousinpineapplesandpinecones)aswellas
seashells(forexamplethenautilus)andanimals,includinghumans.Clearlythe
goldenratioismuchmorethanatoolforart.AccordingtotheSTMmodelpresented
here,itistherelationshipthatshapeseveryfiberofourbeingandeverymomentof
spaceandtime.Andasprojectionsoflife,weliterallyresonatewithit.
Conclusion
Thisprocess,whichIcalltheholomorphicprocess,bywhichtheunifiedfield
separatesintotwodomains,projectsitselfinwardandoutward,reflectsonitself(at
thepointthatitsmotionreachesthegoldenratio)andreunifies,ishowthree
dimensionsofspacearemixedwithonedimensionoftimetomakespacetimeseem
tobesomekindofweirdphenomenondifferentthanenergywheninfactitisjust
information-modulatedenergy,whichiscalled“truth”sinceitactuallyhappened.If
spaceisrepresentedasasphereonthree-dimensionalcoordinatesystem,thentime
isjusttheinward-outwarddirection.Itisassimpletounderstandasconsideringthe
radiusofaspheretobeafourthdimension,exceptthateachspherecapturesthe
implicitprocessasinformation.Wejusthappentoscaleitbyastandardclock.
There’snothingspecialaboutstandardclocktime.Itwasameasureofmotionthat
wasrecordedandisnow“clocked”asareferenceattheNationalInstituteof
StandardsandTechnology(NIST).Soitiseffectivelyanointedandtreatedasbeinga
sacredunit.
Thelogicaltwist(thinkingthattimeitselfisdifferentthaninversefrequency)
andstrictdefinitionoftimeasanunchangingunit,objectifiesandhidesthemeaning
oftime,becauseitignorestheconvolutionprocess.Convolutionmeansthatspace
andtimeformaconvolutedwhole,i.e.theinformationpresentontheoutsideis
continuouslyconvolved,withtheparticle.Thisprocessshapestheparticleintoa
formthatcanbeperceivedatthemacroscopiclevelasbeingatrest.It’stheformor
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shapethatimpliestheinformationanddictatesitsbehavior.Thisisexactlyhow
anatomicalinformationgetsinfusedorimpliedinanx-rayorholographicfilm.But,
whereastheinformationinahologrammustbedeconvolvedbyilluminatingitwith
anotherlaser,theinformationinaquantumparticleisautomaticallydeconvolved
byrelativemotion(itsbehavior).
Oneexample,ofhowrelativemotiondeconvolvesinformation,was
demonstratedbyAlbertEinsteinwhenheusedstatisticalanalysisofBrownian
motion(randommotionofdustparticles)toprovethattheirmotionimpliedthe
existenceofformswenowknowasmolecules.Inhis1956paper,InvestigationsOn
TheTheoryoftheBrownianMovement,hehypothesizedthatthemovementofdust-
particlesonthesurfaceofasphericaldropofliquidwasthevisiblemacroprocess
impliedbyrandomcollisionswithmolecules.Hedevelopedanequationforthe
distributionofthenumberofparticlesperunitvolumeasafunctionoftime(t)and
position(x).Hesaid,“wewillcalculatethedistributionoftheparticlesatatime
𝑡 +
𝜏fromthedistributionatthetimet.”Thenhesolvedforthemomentofthe
distribution.Aswithanystatisticaldistribution,the“moment”providesuswitha
singlemeasureofacollectivebehavior,deducedfromtheshapeofthedistribution.
Thatmeansthattheshapeevolvesbyconvolvingthefunction,definedbythe
implicitnatureofthemicrosystem,withtime.Byexpandingandrearrangingit,he
effectivelydeconvolveditandsolvedforthediffusioncoefficient.Thisdeconvolved
expressionwasthenverifiedbyexperimentalobservationofdustparticles.
Aseachmomentoftimepasses,thequantumbitsofinformationthatare
present–inthepresent–(onthesurfaceofeveryquantumparticle)collapseinward
andbecomeinfusedintotheparticleasbitwiserecordings,collectivelycalled“the
past”.Soaunitofinverse-timeisinterpretedasa“momentofthepast”–asingle
“logical”quantumbitofinformationstoredinthree“physical”dimensions.
Collective,itformsafour-bitqbit.Aspartofalargerquantumcomputer,itself-
programs,self-correctsandrunsitself,whichisanideathatiscurrentlybeing
studied.(Lloydd’Arbelofn.d.)(Lloyd2007)(Almheiri,DongandHarlow2015)
(Wolchover2019)Theoutward-pointingvectorsimplycorrespondstothe
mysteriousarrowoftime.
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18
Themostprofoundimplicationofthisisthatallphysicalmatter,includinga
livingorganism,isrecordingeverymomentintime.Soweareareflectionofevery
event,actionandwordthatweexperienceincludingthosethatwegenerate.These
interpretationsprovidesabridgebetweenphysics,asaphysicalscience,andthelife
sciences,whichmustincludeinformationfromtheenvironmentthatconvolveswith
particlestoallowlifetogrow,changeandadapt.
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