# Images of time: mind, science, reality

Plan of this bookWhat is time?ParadigmsEvents in timeTemporal ordering and time labelsThe contextuality of temporal orderingArrows of timeThe thermodynamic arrow of timeThe cosmological arrow of timeThe radiative arrow of timeThe psychological arrow of timeThe biological arrow of timeThe evolutionary arrow of timeThe geological arrow of timeThe causal arrow of timeThe weak arrow of timeThe quantum arrow of timeThe mathematical arrow of timeThe Bayesian (probability) arrow of timeThe spreadsheet arrow of timeThe sociological arrow of timeThe narrative, diachronic arrow of timeArrows versus cyclesObservers and timeMetaphysics, physics, and validationAdvances in technologyTheoretical convenienceObservers and the physical universeThe contextuality of scientific truthAbsolute truthsContextual truthsEmpirical truthsContextual completenessTime and contextualityThe contextuality of the existential quantifierPrimary observersExperimentsHeisenberg cutsGeneralized propositionsSubjective images of timeThe GreeksThe AchillesThe RacetrackThe ArrowAristotleThe dogmatistsThe scepticsThe Age of ReasonThe classical mechanistsThe metaphysicistsThe mathematical physicistsCultural images of timeCosmogony and theogonyStone Age calendarsThe MesopotamiansThe Sumerians and BabyloniansThe ZoroastriansMithraicismThe Middle EastThe Ancient EgyptiansJudaismChristianityIslamThe EuropeansThe Julian CalendarThe Gregorian calendarMedieval EuropeEastern philosophiesHinduismBuddhismAustralian Aboriginal concepts of timeThe Central AmericansThe MayaThe AztecsThe IncasThe Far EastThe ChineseThe JapaneseLiterary images of timeBenefits of science fictionDangers of science fictionLiterary varietiesTime as the fourth dimensionTime as a parameterThe inertia of realityTime and irreversibilityHyperspaceAlternate universesAlternate futuresInformation from the pastTemporal consistencyObjective images of timeOpticsThe optical spectrum is limitedThe speed of light is relatively greatSunlight is strongNormal objects do not shine of their own accordLight momentum is negligibleOptical transparencyOther factorsTimescalesThermodynamicsObservational contextObserver independenceTime in the laboratoryLaboratory frames and observer chorusesChorus protocolFrame geometryStandardizationSynchronizationSuperobserversMathematical images of timeSome reasonable requirementsPrimary observersLocalizationTemporal orderingTemporal architectureSetsTemporal ordering and ordered setsFunctions and the mathematical arrow of timePredictionRetrodictionCardinalityThe finite cardinalsThe natural numbersLinear continuaFurther conceptsLinearly ordered groupsInfinitesimals and Archimedean groupsCyclic timeSignature and multi-dimensional timeThe complex numbers and imaginary timeDiscrete timeFuzzy timeCausal setsp-adic timeIllusionary images of timeThe Block UniversePersistence and transtemporal identityThe problem of time in cosmologyCausal images of timeCausalityBlame and responsibilityDeterminism and known unknownsTeleologyChaosPhysics and timePhysics and persistenceScales of timeThe Planck timeThe natural chrononTime for light to cross an atomPeriod of an electron in a Bohr atomFastest electronicsPeriod of insect wingPeriod of wing of humming birdAverage human heartbeatThe secondThe hundred metresThe Minute WaltzThe period of rotation of the EarthThe lunar monthThe yearThe galactic yearThe decay lifetime of the protonBiological timeThe solar modelThe earliest life on EarthLifetimes of organismsChronobiologyBiological time travelThe dimensions of timePartial differential equations and the flow of informationClassification of second-order PDEs in two independent variablesClassification of second-order PDEs in n independent variablesBoundary conditionsThe signature of spacetimeEmpirical studiesTifft’s analysis of red shiftsThe two-dimensional arrow of biological timeThe architecture of timeWhat is temporal architecture?Process or manifold?Points or intervals?Endo or exo?Examples of temporal architecturesAristotelian space-time architectureGalilean-Newtonian space-timeMinkowski spacetimeMulti-fingered timeContinuous or discrete timeParticle decaysMultiple universesTime travelArchitectural levels of observationLevel 1: classical observationLevel 2: standard quantum mechanical observationLevel 3: quantum detectionLevel 4: theories of observationAbsolute timeClocksThe reparametrization of timeAbsolute spaceAristotelian space-time versus Galilean-Newtonian space-timeParticle worldlinesThe Newtonian mechanical paradigmThe Euler-Lagrange mechanical paradigmPhase spacePoisson bracketsCanonical transformation theoryInfinitesimal transformationsConserved quantitiesTranslation in timeThe reparametrization of timeTemporal parametrizationTemporal reparametrizationAction integralsTemporal reparametrization in detailReparametrization form invarianceThe extended equations of motionTransformation to phase spaceReparametrized primary identityOrigins of relativityInertial framesThe speed of light and Galilean transformationsThe Michelson-Morley experimentFitzGerald length contractionDerivation of FitzGerald length contractionFitzGerald time dilationLorentz transformationsSpecial relativityLorentz transformationsSimultaneity in special relativityTime dilationThe clock hypothesisThe Twin ParadoxLightconesThe Klein-Gordon equationThe causal propagation of special relativistic fieldsFock-Kemmer front velocity and the memory fieldGeneralized transformationsConstraintsGeneral formulaeApplication to generalized transformationsRelative scalingInverse relative scalingThe Michelson-Morley constraintSome standard transformationsThe Minkowski metricGalilean transformationsEinstein-Lorentz transformationsTangherlini-Chang-Rembielinski transformationsThe splitting of causalityEmpirical evidence for a preferred frameGeneral relativistic timeSpace-time versus spacetimeLorentzian signature metricsPseudo-Riemannian manifoldsThe Schwarzschild metricTimelike, lightlike, and spacelike coordinatesTimelike, lightlike, and spacelike vector fieldsGravitational time dilationBlack hole geometryEddington-Finkelstein coordinatesWhite holesThe spinning discTime travelInformation flowPrediction and retrodictionTachyonsSpreadsheet time travelThe Godel metricPhysics of Godel’s spacetimeGeometry of Godel’s spacetimeTimelike geodesicsImaginary timeMinkowski's imaginary timeApplication to wave mechanicsPropagators and Green's functionsPath integralsQuantum gravityQuantum thermodynamicsBlack hole thermodynamicsQuantum cosmologyConclusionsIrreversible timeGlauber's correlationsProbabilityThe expansion of the universePoincare recurrenceDiscrete timeDifference equationsThe action sumCaldirola's proper time chrononCaldirola's microverse modelDiscrete-time classical electrodynamicsThe continuous-time theoryThe discrete-time theoryTime and quantaSchrodinger versus HeisenbergThe Heisenberg picturede Broglie wavesThe time-energy uncertainty relationThe relativistic propagatorTemporal correlationsClassical bit temporal correlationsQuantum bit temporal correlationsThe Leggett-Garg correlationUnderstanding the Leggett-Garg predictionTime reversalClassical active time reversalSchrodinger wave mechanicsThe time-reversal operatorThe Pauli equationThe Dirac wave equationTCP theoremKaonsQuantized spacetimeMach's relationalismEinstein's relationalismPlanck, quanta, photons, and existenceSnyder's quantized spacetimeEpilogueBibliography