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TopologicalGeometroDynamics (TGD) PowerPoint presentation
Matti Pitkänen 08/09/2000
Postal address:
Köydenpunojankatu 2 D 11
10940, Hanko, Finland
E-mail:
URL-address: http://tgdtheory.com
(former address: http://www.helsinki.fi/~matpitka )
"Blog" forum: http://matpitka.blogspot.com/
Abstract
A. How to end up with TGD
B. p-Adic physics
C. Quantum dynamics as classical dynamics for classical spinor fields in the world of classical worlds.
D. Superconformal symmetries
E. p-Adicization program and number theoretic universality
F. TGD and von Neumann algebras, quantization of Planck constant, and dark matter.
G. About the construction of S-matrix
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A. How to end up with TGD
(mhtml:http://www.helsinki.fi/~matpitka/tgdppt/TGDideasweb.mht!TGDideasweb_files/frame.htm )
1. Short FAQ about TGD
2. Physics as generalized number theory
3. TGD predicts the Standard Model of particle physics
4. TGD as solution to the energy problem of GRT and as generalization of string models
5. Geometrization
6. Some implications of new notion of classical gauge field
7. Kähler action and vacuum extremals
8. TGD Universe
9. Quantum-Classical correspondence
1. Short FAQ about TGD
Why TGD
● Why TGD (1978)? Energy problem of General Relativity. Generalization of string models by replacing strings with 3-surfaces. Geometrization of fundamental interactions using sub-manifold geometry.
● Why TGD (2006): landscape crisis of M-theory. Failure to even reproduce Standard Model physics. Super-symmetry might be misunderstood physically. Higgs might not be what it is.
What are the great ideas about TGD?
● Space-time as 4-D surface in M4£CP2. Geometrization of classical fields and elementary particle quantum numbers. 3-D light-like surfaces basic dynamical objects.
● Generalization of Einstein’s geometrization program. Quantum states as classical spinor fields in the world of classical worlds. Do not quantize.
2. Physics as generalized number theory
● Physics as generalized number theory. p-Adic mass calculations. p-Adic physics as physics of cognition and intention. Unification of p-adic and real physics by number theoretic universality. Classical number fields and dimensions 8,4,2,0 of imbedding space, space-time, parton, strand of number theoretic braid. Riemann Zeta and physics.
● Clifford algebra of world of classical worlds and hyper-finite factors of type II1. Key to the understanding of Quantum TGD and its generalization. Quantum measurement theory with finite measurement resolution in terms of Jones inclusions. Emergence of TGD Universe from number theory. Planck constants dynamical and quantized. Dark matter as Macroscopically quantum coherent phases with large value of h.
● Super-conformal symmetries. Magic conformal properties of 3-D light-like partonic surfaces and boundary of 4-D light-cone as key aspects of theory.
● Extension of quantum measurement theory to a theory of Consciousness. New view about relation of geometric and experienced time. Self hierarchy.
3. TGD predicts the Standard Model of particle physics
What is common to TGD and the Standard Model?
● TGD predicts standard model (gauge) symmetries and particle spectrum.
What distinguishes TGD from the Standard Model?
● Reductionistic philosophy given up and replaced with fractality. Various fractal hierarchies. Many-sheeted space-time, p-adic scaling hierarchy, dark matter hierarchy, hierarchy of selves. Scaled up variants of standard model physics. Scaling arguments make theory predictive.
● New view about energy and time. Also negative energies possible. Zero energy ontology.
● Hierarchy of dark matters with nonstandard values of Planck constants. Macroscopic quantum phases in all length scales. Applications in biology especially interesting.
4. TGD as solution to the energy problem of GRT and as generalization of string models
● Energy not well-defined concept in GRT since Poincare invariance is lost in curved space-time. Space-time as 4-surface in H = M4£S: Poincare symmetries are symmetries of imbedding space.
● Space-time as orbit of particle like object: generalization of string models. String à 3-D surface. Actually light-like 3-surface: parton orbit.
● S = CP2 codes for the symmetries of standard model. Isometries: color group SU(3).
Holonomies: ew gauge group U(2). CP2= SU(3)/U(2). Symmetric/constant curvature space.
5. Geometrization
● Geometrization of classical gauge fields. Projections of Killing vector fields of CP2 as color gauge potentials. Electroweak gauge potentials as projections of CP2 spinor connection.
● Geometrization of Standard Model quantum numbers. Leptons and quarks correspond to different H-chiralities. Color partial waves. Triality 1 color partial waves for quarks. Conformal symmetries essential for understanding details.
● Family replication phenomenon topologically. Generation-genus correspondence. 3 fermion families. Hyper-ellipticity key notion.
6. Some implications of new notion of classical gauge field
● Topological field quantization. The imbeddability of, say, constant magnetic field possible for finite space-time region only. Physical objects possess field identity: notion of field (magnetic) body.
● Only the topological half of YM equations satisfied.
● Classical color and EW fields in all length scales: Hierarchy of fractal copies of Standard Model highly suggestive. Interpretation in terms of dark matter?!
● Classical color holonomy Abelian. Quantum-classical correspondence suggests vanishing of U(2) quantum numbers for physical states. Weak form of confinement. Note: elementary bosons correspond to so-called CP2-type vacuum extremals rather than quantized classical fields.
7. Kähler action and vacuum extremals
● Kähler action: Maxwell action for induced Kähler form of CP2.
● Vacuum degeneracy of Kähler action key to the understanding of TGD!
● Spin glass degeneracy of Kähler action . Canonical transformations of CP2 act as U(1) gauge transformations but are dynamical symmetries of vacuum extremals only. CP2 projection Lagrangian manifold for vacuum extremal.
● Path integral does not make sense nor does canonical quantization.
● Generalize Wheeler's superspace: the world of classical worlds, space CH of 3-surfaces X3. Realization of 4-D general coordinate invariance requires that CH geometry assigns to X3 a unique four-surface X4(X3), as preferred extremals of Kähler action, generalized Bohr orbit. Path integralà functional integral over 3-surfaces using as vacuum functional the exponent of Kähler function K identified as Kähler action for X4(X3). Reference: TGD: Physics as infinite-dimensional geometry.
● K a non-local functional of X3: local divergences cancel. Ill-defined Gaussian and metric determinants cancel each other.
8. TGD Universe
● TGD Universe quantum critical. Kähler coupling strength corresponds to critical temperature and invariant under renormalization group evolution. Kähler coupling strength turns out to correspond to the value of electroweak U(1) coupling at electron Compton length.
● RW cosmologies vacuum extremals. Poincare/inertial energy density zero in cosmological length scales. The sign of Poincare energy can be also negative. Gravitational mass has definite sign. Reference: TGD and Cosmology.
● Zero energy ontology: all physical states have vanishing conserved quantum numbers. Reference: Construction of Quantum Theory: S-matrix.
9. Quantum-Classical correspondence
● Interpretation of classical non-determinism. Space-time provides a symbolic representation of quantum dynamics.
● Maximal deterministic space-time regions as “Bohr orbits” representing quantum states.
● Also a representation of quantum jump sequences (and contents of conscious experience).
● What about quantum measurement theory? Interior of space-time surface represents classical dynamics and defines classical correlates for the parton dynamics at -dimensional light-like surfaces carrying partonic quantum numbers. Interior degrees of freedom zero modes for metric of CH.
● Conformal invariance: light like partonic 3-surfaces are metrically 2-dimensional. Chern Simons action for induced Kähler gauge potential the only possible dynamics at parton level. TGD as almost topological QFT. Only light-likeness brings in metric implicitly!
● Reference: Construction of Quantum Theory: Symmetries
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B. p-Adic physics
(mhtml:http://www.helsinki.fi/~matpitka/tgdppt/TGDpadmassweb.mht!TGDpadmassweb_files/frame.htm )
1. p-Adic mass calculations
2. Particle massivation by p-adic thermodynamics and Higgs mechanism
3. Family replication phenomenon topologically
4. How to fuse p-adic and real physics together?
5. Higgs as a wormhole contact
1. p-Adic mass calculations
● Mass calculations using p-adic thermodynamics for Virasoro generator L0 (scaling). Mass squared essentially thermal expectation value of the conformal weight (no problems with Lorentz invariance!). Quantization of p-adic temperature number theoretically when exp(-E/T) replaced with p^(L0/T), T= 1/n. Canonical identification maps p-adic mass squared to its real counterpart. Universal mass formula with real mass squared proportional to 1/pn.
● Reduction of fundamental length scales to number theory. p-Adic length scale hypothesis: primes p~2k , k integer, preferred physically. Prime powers especially so -- in particular Mersenne primes Mn=2n-1 and Gaussian Mersennes MGn=(1+i)n-1.
● Charged leptons correspond to Mersennes or Gaussian Mersennes. 'e' to M127, 'm' to MG113, 't' to M107. Light quarks to MG113. Gluons to M107, electroweak gauge bosons to M89, graviton to M127, the largest non-super-astronomical Mersenne.
● Reference: p-Adic length scale hypothesis and dark matter hierarchy.
2. Particle massivation by p-adic thermodynamics and Higgs mechanism
● Elementary particles as CP2-type vacuum extremals: M4 coordinates arbitrary functions of some CP2 coordinate such that M4 projection light-like random curve. Virasoro conditions. More generally: partonic 3-surfaces light-like. Super-conformal invariance.
● Light-like randomness analogous to zitterbewegung. Gravitational momentum light-like but changes direction. Inertial 4-momentum for a given space-time sheet as a time average of gravitational four-momentum. p-Adic thermodynamics describes the randomness.
● Also Higgs needed to understand weak boson masses. Higgs as wormhole contact: a piece of CP2-type extremal connecting 2 space-time sheets with M4 signature. Light-like 3-surfaces associated with the contact carry fermionic and antifermionic quantum numbers and have opposite M4 chiralities. Higgs contributes very little to fermionic masses. Couplings to fermions very weak: explains why Higgs not detected. Rate for Higgs production could be by a factor ~1/100 slower than in Standard Model.
● Overall view about Quantum TGD
3. Family replication phenomenon topologically
● Parton as 2-surface X2 whose orbit is light-like 3-surface. Handle number g of X2, genus, labels particle families. Topological mixing gives rise to CKM mixing. Thermodynanics in conformally invariant degrees of freedom contributes to particle mass. Elementary particle vacuum functionals which are modular invariant.
● Why g>2 families experimentally absent? Possible answer: g≤2 surfaces always hyper-elliptic unlike g>2 surfaces. g≤2 particles decouple from of g>2 particles in topology changing dynamics since the vacuum functionals for latter vanish for hyper-elliptic surfaces. g>2 particles dark matter?
● What about bosons? It seems that for gauge bosons maximal mixing of families occurs in p-adic thermodynamics. Possibly because p-adic temperature T= ½ rather than T=1 in modular.
● Reference: Construction of elementary particle vacuum functionals
4. How to fuse p-adic and real physics together?
● Generalization of number concept by gluing of reals and p-adics along common rationals (algebraics for algebraic extensions of p-adics). Generalization of the notion of imbedding space by gluing real and p-adic imbedding spaces together along common rationals (algebraics).
● p-Adic physics as physics of cognition of intention. p-Adic space-time sheets correlates for intention and cognition. p-Adic-to-real transition corresponds to transformation of intention to action.
● Real space-time sheets possess effective p-adic topology: large number of common points with p-adic space-time sheet transforming in quantum jump to a real space-time sheet as intention becomes action! Only zero energy ontology (all states have vanishing conserved quantum numbers) makes possible these transitions!
● Effective p-adic topology justifies the use of p-adic thermodynamics in p-adic mass calculations.
5. Higgs as a wormhole contact
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C. Quantum dynamics as classical dynamics for classical spinor fields in the world of classical worlds.
(mhtml:http://www.helsinki.fi/~matpitka/tgdppt/TGDinfgeomweb.mht!TGDinfgeomweb_files/frame.htm )
1. Generalization of Einstein's geometrization program to infinite-dimensional context.
2. Infinite-dimensional geometric existence is highly unique
3. Geometrization of fermionic statistics and super symmetries
4. Basic objection
5. Magic properties of lightcone boundary dM4+
6. Light-like 3-surfaces of H/X4 as partons
7. Quantum dynamics at parton level
8. Superconformal symmetries
9. Breaking of superconformal symmetries
10. Isometries of the world of classical worlds
10. How classical dynamics emerges?
Problem
● Path integrals and canonical quantization do not work. Vacuum degeneracy and extreme nonlinearity the basic problems. Perturbation theory fails completely around canonically imbedded M4.
Outcome
● Quantum dynamics as classical dynamics for classical spinor fields in the infinite-dimensional “world of classical worlds” consisting of 3-surfaces in H= M4×CP2.
1. Generalization of Einstein's geometrization program to infinite-dimensional context.
● The world of classical worlds identified as space CH of 3-surfaces in H the arena of dynamics. Analog of Wheeler's superspace or of loop space.
● 4-D(!) General Coordinate invariance: definition of CH metric must assign to a given 3-surface four-surface as a generalized Bohr orbit. Bohr orbitology as part of configuration space geometry.
● Kähler geometry as a manner to geometrize Hermitian conjugation. Kähler function defining the metric absolute extremum of Kähler action?
● Complexification of configuration space highly non-trivial problem: effective 2-dimensionality.
● Reference: TGD: Physics as Infinite-Dimensional Geometry.
2. Infinite-dimensional geometric existence is highly unique
● Existence of Riemann connection forces infinite-dimensional symmetries: generalization of Kac-Moody symmetries of loop spaces (thesis of Dan Freed).
● Configuration space as a union of infinite-dimensional symmetric spaces. Constant curvature spaces. All points metrically equivalent.
● Symmetric spaces in union labeled by zero modes not contributing to the metric. Identifiable as classical observables crucial for quantum measurement theory. Vanishing curvature scalar: Einstein's vacuum equations satisfied from mere finiteness.
● Choice of compact Cartesian factor S of H also uniquely S=CP2? Number theoretic considerations suggest this.
3. Geometrization of fermionic statistics and super symmetries
● Gamma matrices of configuration space provide geometrization of fermionic statistics.
● Gamma matrices expressible in terms of fermionic oscillator operators assignable to second quantized free induced spinor fields at space-time surface. Gamma matrices and isometry algebra combine to form a super algebra. Geometrization of super algebra concept.