Evolution and Development of the Universe 8 - 9 October 2008, Paris, France ARE PARTICLES SELF-ORGANIZED SYSTEMS ? Vladimir A.
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Evolution and Development of the Universe 8 - 9 October 2008, Paris, France ARE PARTICLES SELF-ORGANIZED SYSTEMS ? Vladimir A. Manasson Sierra Nevada Corporation Irvine, California [email protected] ARE PARTICLES SELF-ORGANIZED SYSTEMS ? Self-organized systems are complex systems that acquire stability of their dynamical variables through dynamical feedback http://astrocanada.ca/_photos/a4201_ univers1_g.jpg http://farm2.static.flickr.com /1287/588319871_a2304d8 7bf.jpg?v=0 http://www.astronomycast.c om/wpcontent/uploads/2007/05/ab ell2218.jpg http://img.dailymail.co.uk/i/p ix/2007/07_01/galaxy11_46 8x468.jpg http://www.spacetoday.org/i mages/DeepSpace/Stars/S tarWR124Hubble.jpg SELF-ORGANIZED SYSTEMS http://www.wnps.org/ecosy stems/images/middle_lake s_wl.jpg http://www.moneypit.com/me mbers2/AardvarkPublisher/99 90261456922/image1.jpg ??? http://www.ices.dk/marinew orld/photogallery/images/jel lyfish.jpg http://www.pasteur.fr/actu/press http://addiandcassi.com/wordp http://radio.weblogs.com/0105 ress/wp-content/uploads/dna- 910/images/hiphop_atom.jpg e/images/plasmodium.jpg image.jpg V Manasson, EDU-2008 WHICH THEORY? Standard Model (QT) ? Self-Organized Systems (SOS) ? ? ? ? http://www-d0.fnal.gov/Run2Physics/WWW/results/final/NP/N04C/N04C_files/standardmodel.jpg V Manasson, EDU-2008 STABILITY and DYNAMICAL PHASE PORTRAITS Classical Conservative Dynamics Idealistic (Closed Systems) CONDITIONAL STABILITY Realistic (Open Systems) SOS ABSOLUTE (ASYMPTOTIC) STABILITY j Center J Limit cycle Attractor J+DJ Quantum Systems ABSOLUTE STABILITY Center Center with selected orbits constrained by fundamental constants like ħ ħ Realistic (Open Systems) ħ +DJ Jn=nħ Bohr-Sommerfeld V Manasson, EDU-2008 Quantum systems resemble SOS Heisenberg's uncertainty principle Dt ~ ħ /DE Dissipation time? Permitted Orbit = Attractor? QT SOS Y-function collapses Non-reversibility Perturbation technique Renormalization Nonlinearity Non-Abelian Yang-Mills fields V Manasson, EDU-2008 PHENOMENON of QUANTIZATION in Nonlinear Dissipative Dynamics V Manasson, EDU-2008 LOGISTIC MAP AS A SOS PARADIGM yn+1 Jj yn+1 8 y J A Ji yn y 8 yn+1=FJ(yn) yn xn+1=Axn(1-xn) A parameterizes limit points in the same way generalized angular momentum J parameterizes attractors J i Jj J V Manasson, EDU-2008 BIFURCATIONS CHANGE DIMENSIONALITY AND TOPOLOGY OF THE PHASE SPACE U(1) Vector y 2p F(y) SU(2) Spinor y1 y2 4p F(F(y)) Feigenbaum point http://www.lactamme.polytechnique.fr/ Mosaic/images/MOB2.11.D/image.jpg V Manasson, EDU-2008 UNIVERSAL BEHAVIOR AND FEIGENBAUM DELTA 0 F(y) a) xn1 Axn 1 xn ) 2 y b) x 0 n 1 0.4 2 4 d=DJn/DJn+1=4.669.. Asinpxn ) 0.6 0.8 1 c) xn1 A xn2 0 y yn+1=FJ(yn) 0 -2 DJ 1 DJ 2 8 1 3 1. UNIMODAL 2. QUADRATIC EXTREMUM 8 1 1 2 J V Manasson, EDU-2008 J1 J2 J3 y 8 Superattractors QUANTIZATION SPRINGS from SUPERATTRACTORS Lyapunov exponent Dissipation Rate, D F(y) J J1 J2 J3 http://web.mst.edu/~vojtat/class_355/ch apter1/lyapunov_logistic.jpg V Manasson, EDU-2008 Discrete spectrum Coulomb-wave potential Bifurcation diagram J J3 8 E 8 Continuous spectrum One More Similarity between SOS and QT J2 E3 E2 E1 J1 Hydrogen atom V Manasson, EDU-2008 QUANTIZATION OF GENERALIZED ANGULAR MOMENTUM 8 J y 8 J J 3 1 2pd 2 1 137 J3 J2 J 2 1 2pd 1 29 J1 1 2p 0.16 Sn J n dj 2pJ n J1 S1 1 V Manasson, EDU-2008 QUANTIZATION OF COUPLING CONSTANTS? 8 a a 1 2pd 1 137 a3 2 aW 1 2pd 1/ 29 GUT aS 1 2p 0.16 a2 a y 8 J a ELECTROMAGNETIC WEAK a1 STRONG http://webplaza.pt.lu/public/fklaess/pix/merging_forces.gif V Manasson, EDU-2008 MAJOR RESULT Fine structure constant a 1 2pd 2 a e 4p0c 2 Accuracy ~ 0.04% 0 2 de ) 0 2 Presence of d implies routes to chaos, which are dynamics that cannot be properly described by QT Presence of d underscores the relevance of perioddoubling bifurcation dynamics and SU(2) symmetry Value d = 4.669.. suggests that we are dealing with dissipative dynamics Quantization of charge (e) and quantization of action (ħ) have the same origin V Manasson, EDU-2008 SU(2) SYMMETRY, SPINORS, and 4p ROTATION ANGLE Family I Leptons p Family I n Family I Quarks e e e e e e e e e e e e u u u d u d d e e u u u d d d d y1 y2 y3 y4 y1 y2 V Manasson, EDU-2008 e Family I Leptons e Family I u Family I Quarks e e e e u u d d Family II Leptons Family II c Family II Quarks s Family III Leptons Family III t Family III Quarks d c c s s t t b b b e e e e e e e e u u u u d d d d c c c c s s s s t t t t b b b b BIFURCATION DIAGRAM and PARTICLE "PHYLOGENETIC" TREE EXCITATION DIAGRAM EXCITATION RELAXATION (SPONTANEOUS SYMMETRY BREAK) Electromagnetic Excitation Level Spin 2 Graviton? Bosons (2 photons) Spin 1 Spin 1/2 Dirac spinor Electron Branch Fermions (4, including charge and spin) V Manasson, EDU-2008 EXCITATION DIAGRAM Weak Excitation Level Lepton Branch Bosons (4 electroweak) Fermions (8) Electron Branch Neutrino Branch V Manasson, EDU-2008 EXCITATION DIAGRAM GUT Strong Excitation Level Lepton Branch Bosons (8 gluons) Fermions (16) Quark Branch Electron Branch Neutrino Branch V Manasson, EDU-2008 Is QT a quasi-linear surrogate of Nonlinear Dynamics? Nonlinear Dynamics Classical Conservative Dynamics Statistical Physics Quantum Theory F(F(F(y))) Duffing Oscillator Numerical Perturbation Theory Renormalization time A. L. Fetter, J. D. Walecka, Nonlinear Mechanics, Dover Publications, 2006 Nonlinear Dynamics Quantum Theory V Manasson, EDU-2008