Physics as Flow of Information as Computation as ... - FEniCS Project
Physics as Flow of Information as Computation as ... - FEniCS Project
Physics as Flow of Information as Computation as ... - FEniCS Project
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<strong>Physics</strong>Cl<strong>as</strong>sical Mechanics: ParticlesSolid Mechanics: El<strong>as</strong>tic Bodies: FieldsFluid Mechanics: Continuum: FieldsThermodynamics–Statistical Mech: ParticlesQuantum Mechanics: Atoms: FieldsRelativity Theory: GalaxiesQM Relativity ???Action at Distance???Fields Do Exist, Particles NotClaes Johnson – KTH – p. 3
Automation vs Observation/ControlAutomated:No Observeration, No ControlNo-Mind, No IntelligenceNon-Automated:Observeration, ControlMind(s), IntelligenceClaes Johnson – KTH – p. 4
<strong>Flow</strong> <strong>of</strong> <strong>Information</strong>Collect: Local: CodeCommunicate: Waves/<strong>Flow</strong>: GlobalReceive: Local: DecodeCommunicationPropagation: Node to Neighbor NodeIterated Local: GlobalShannon <strong>Information</strong> Theory: <strong>Flow</strong> EntropyPRECISION–STABILITY–CapacityClaes Johnson – KTH – p. 5
¢¤£¥¦§¢¤£ ¡¥¡ £¡¢¤¨¡¥©¨¨Iterative Poisson SolverGlobalLocal RelaxationJacobi-IterationLocal Communication with NeighborsNo Assembly: No El. Stiffness Matrix: ActionGlobal: Fiction(Iterated) Local: RealityClaes Johnson – KTH – p. 6
One-Mind: Super-IntelligenceFull <strong>Information</strong> Centralized GlobalInfinite Speed <strong>of</strong> CommunicationObservation-ControlParallel Computing: CIMDONE SUPER-PHYSICIST, BIG BROTHERTotalitarianFixed Step Jacobi RelaxationDoes not seem to work well??Claes Johnson – KTH – p. 7
Many-Minds: Limited IntelligencePartial <strong>Information</strong> DecentralizedFinite Speed <strong>of</strong> CommunicationPartial Observation-ControlParallel Computing: MIMDMANY small physicists: DemocraticExplicit Time-SteppingVariable Step Jacobi RelaxationSeems to work re<strong>as</strong>onably well??Claes Johnson – KTH – p. 8
Democratic SystemIndividual Decisions by ManyGeneral Principles: LawParallell <strong>Computation</strong>: MIMDMinimal <strong>Information</strong> for Local <strong>Computation</strong>Nobody Knows EverythingParallel Limited IntelligenceAdaptive by Feed-BackVariable Relaxation JacobiClaes Johnson – KTH – p. 9
Totalitarian SystemBIG BROTHER: Decides 5 Year PlanIndividuals Follow 5 Year PlanBB: Knows EverythingBB: Understands EverythingIndividual: No-MindNon-Adaptive No Feed-BackFixed Relaxation JacobiBB Gaussian Elimination: AssemblyClaes Johnson – KTH – p. 10
¤¥¦¨§¡¡¢£¢¥¥¡¤¥Cl<strong>as</strong>sical Mech: Newton: GravitationParticles: M<strong>as</strong>s, Pos., j=1,...,N,Conservation <strong>of</strong> Momentum ¡Gravitational ConstantGrav. Force: Action at Distance: Non-LocalHow?? Gravitons??Explicit Time-SteppingClaes Johnson – KTH – p. 11
¥¢¤¤¥¢¥¢§¥¥¢¥¥ ¦¥ ¡¡¡¡¤§¢¢Fluids: Cons <strong>of</strong> M<strong>as</strong>s Mom Energysuch that¡¡with¡£¢¤ ¢¡¡Find¦ ¢ ¡¡¡¨ ¥¦ ¢¤¤¡¦ ¢ ¤§¡¤¡¡© ¢¡¢ ¥ ¢ ¢Local Balance: Finite Speed <strong>of</strong> Propag.Explicit Time-SteppingClaes Johnson – KTH – p. 12
¥¢¥¢¥¢¢§¥¥¢¥¥ ¦§¡¦¡¡Cosmology: Grav. Non-Localsuch that¡£¢¤ ¢¡¡¤ ¢Find¦ ¢ ¡¡¡¥¨ ¥¦ ¢¤¤¡¦ ¢ ¡£¢ ¤§¡¤¡¡© ¢¡¢ ¥ ¢Non-Localcreates Gravitational Pot : How??M<strong>as</strong>sExplicit Time-SteppingClaes Johnson – KTH – p. 13
¥¢¡¡¡¢¤¥¢¢§¥¥¥¢¢¡§¥¥ ¦¡¡New Cosmology: M<strong>as</strong>s Creation Local:¤ ¢¤¢¢: FindbyEliminate¦ ¢¥¨ ¥¦ ¢¤¤¡¦ ¢ ¤¤¡¡© ¢¡¢ ¥ ¢¡ ¢¤£relaxation parameter,: Grav Pot Creates M<strong>as</strong>s: How??Local, Time-SteppingClaes Johnson – KTH – p. 14
¢¤£¥ £¨¦New Cosmology: CreationismPotential Peak:Unit M<strong>as</strong>sDark Matter: Force but no Visible M<strong>as</strong>sMollified Peak: Force but no Visible M<strong>as</strong>s??Create Pot Peaks: fromMatter-Antimatter: Repulsion (Neg Grav)Claes Johnson – KTH – p. 15
¢¢ £¢£¡¥¦¨§¥ £¦¦£¥¥£¦Quantum Mechanics: Schrödinger EqWave function¢£¢¢ £§ ¢forelectrons:Walter Kohn Nobel Prize 1998:Not “Legitimate Scientific Object”does NOT EXIST forNon-Local, Time-Stepping, SpaceDim:Claes Johnson – KTH – p. 16
¥¥¢¦¢¢¥¢¥©¢¨¢¡£¨¥¥¥¥£¡¡§¢£QM: Hartree Approx: Non-Local:¢£¢¢ £¢find ¢¢For £¥¢ ¨¢¤£ £ £¥¦¨§¥¦¨§¡¢£¢¢ £§ ¢ ¢¢ £¢ ¢¢ £§ ¢Non-Local Time-SteppingSystemdim:SpaceDim:Claes Johnson – KTH – p. 17
Special RelativitySpeed <strong>of</strong> LightIndependent <strong>of</strong>Speed <strong>of</strong> Source/ObserverLorenz Transformation: Inertial SystemsInvariance <strong>of</strong> Wave/MaxwellDifficult to Understand:Paradoxes: Time Dilation, Twins....Impossible to Verify ExperimentallyCannot be Wrong (Pseudo-Scientific Popper)Claes Johnson – KTH – p. 19
¢¡¡¡¡¥¡¢Many-Minds RelativityMinds¢: Minds and Agree onMutual DistanceUnit <strong>of</strong> Length: LightsecondSpeed <strong>of</strong> LightBut Not onforlightsecond/second...Minimal Info for Gravitational InteractionNo BIG BROTHERClaes Johnson – KTH – p. 20
¦¦Relativistic Addition <strong>of</strong> Velocities¡§ ¢¡¡¢¡¡§¡¡¡§¡¢¡Claes Johnson – KTH – p. 21
¤ ¡¡¤ ¡¡ ¡¤Relativistic Newton’s LawVelocity/Acc vs Fixed Observer in Approach:Velocity/Acc vs Fixed Observer Moving Away:Acceleration vs Co-Moving Observer (Itself):Claes Johnson – KTH – p. 22
¥¢¦¢¥¥¥Claes Johnson – KTH – p. 23Many-Minds QM-Relativity £¥¦¨§¥¦¨§Electron : Co-Moving Coord SystRelativistic Corr <strong>of</strong> M<strong>as</strong>s if Fixed System
©£ §Claes Johnson – KTH – p. 24outflowonFluid ModelVariable Density Incompress Fluid¢©¢¦¨§¡¢£¥¤Cylinder:¦inflow,¡£ ¤£ ¤¡ §¡ §¡ § output movie on,input movie on
¦¡¡¦¡¡Collection-Transmission-Receptioninput movie,Transport by <strong>Flow</strong>output movie.Turbulent <strong>Flow</strong>Distortion/Error:Point Values vs Mean ValuesClaes Johnson – KTH – p. 25
©©©©¦§¥© ¢©©¡¡¥ ¥¡ ¥¦¡§¡ ¢¤ ¢¡£¢¤ ¢©©¦§¥¢¦©©¦§¢<strong>Physics</strong> <strong>as</strong> Comp: ThermodynamicsCl<strong>as</strong>s 2nd Law:Entropy:Cl<strong>as</strong>s Question: What isNew 2nd Law:New 2nd Law: G2:§¥Local Destruction <strong>of</strong> <strong>Information</strong>Not Trivial Vanishing Viscosity,,Exact!!State Variable? Nobody Knows., No . Forget It.Claes Johnson – KTH – p. 26
<strong>Physics</strong> <strong>as</strong> Comp: Paradox ResolutionLoschmidt: Irreversib in Hamiltonian SystGibbs: Inextensivity <strong>of</strong>PRECISION vs STABILITY (No Statistics)Interprete <strong>Computation</strong> <strong>as</strong> <strong>Physics</strong>Understand <strong>Physics</strong> <strong>as</strong> <strong>Computation</strong>Is the World a G2 World??Galerkin: Res. Weakly Small: Share LocalLS Stab: Res. Pointw. Too Not BigClaes Johnson – KTH – p. 27
G2 LS StabilizationPenalty for Breaking LawPositive Penalty2nd LawDestruction <strong>of</strong> <strong>Information</strong>Claes Johnson – KTH – p. 28
<strong>Physics</strong>: Analog <strong>Computation</strong>M<strong>as</strong>siveParallelLocalPRECISIONSTABILITYDESTRUCTION <strong>of</strong> INFORMATIONNO STATISTICS!!Claes Johnson – KTH – p. 29
FenICs/G2 <strong>as</strong> <strong>Physics</strong> <strong>as</strong> VISIONTurbulence Body Soul Vol 4, Jan 07Thermodynamics Vol 5, 07MM Quantum Mechanics Vol 6, 08??MM Relativity Vol 7, 08??Advanced Applications!!Generality <strong>of</strong> FenICs/G2Simplicity <strong>of</strong> FenICs/G2Efficiency <strong>of</strong> FenICs/G2Claes Johnson – KTH – p. 30
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