PHYSICS IN MANYSHEETED SPACETIME
by Matti Pitkänen
Introduction


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PART I: The notion of manysheeted spacetime

Basic Extremals of the Kähler action


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General View About Physics in ManySheeted SpaceTime: Part I


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General View About Physics in ManySheeted SpaceTime: Part II


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PART II: ManySheeted Cosmology, and Astrophysics

TGD and GR


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Cosmic Strings


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TGD and Cosmology


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TGD and Astrophysics


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Quantum Astrophysics


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PART III: Topological Field Quantization and Generation of Structures

Hydrodynamics and CP2 geometry


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Macroscopic Quantum Phenomena and CP2 Geometry


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Appendix


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1. Basic ideas of TGD
1. TGD as a Poincare invariant theory of gravitation
2. TGD as a generalization of the hadronic string model
3. Fusion of the two approaches via a generalization of the spacetime concept
2. The five threads in the development of quantum TGD
1. Quantum TGD as configuration space spinor geometry
2. pAdic TGD
3. TGD as a generalization of physics to a theory of consciousness
4. TGD as a generalized number theory
5. Dynamical quantized Planck constant and dark matter hierarchy
3. The contents of the book
1. PART I: ManySheeted Cosmology and Astrophysics
2. PART II: Topological Field Quantization
PART I: MANYSHEETED SPACETIME
1.1. Introduction
1.2. General considerations
 Long range classical weak and color gauge fields as correlates for dark massless weak bosons
 Is absolute minimization the correct variational principle
 Field equations
 Could Lorentz force vanish identically for all extremals/absolute minima of Kähler action?
 Topologization of the Kähler current as a solution to the generalized Beltrami condition
 How to satisfy field equations?
 D=3 phase allows infinite number of topological charges characterizing the linking of magnetic field lines
 Is absolute minimization of Kähler action equivalent with the topologization/lightlikeness of Kähler current and second law?
 Generalized Beltrami fields and biological systems
 About small perturbations of field equations
1.3. Vacuum extremals
 CP2 type extremals
 Vacuum extremals with vanishing induced Kähler field
1.4. Nonvacuum extremals
 Cosmic strings
 Massless extremals
 Generalization of the solution ansatz defining massless extremals
 Maxwell phase
 Stationary, spherically symmetric extremals
 The scalar waves of Tesla, biosystems as electrets, and electricmagnetic duality
 Maxwell hydrodynamics as a toy model for TGD
1.5. Can one determine experimentally the shape of the spacetime surface?
1.6. Measuring classically the shape of the spacetime surface
1.7. Quantum measurement of the shape of the spacetime surface
2.1. Introduction
 Various types of topological condensation
 Implications of the topological nontriviality of macroscopic spacetime
 Topics of the chapter
2.2. What does 3surface look like?
 Renormalization group invariance, quantum criticality and topology of 3space
 3surfaces have outer boundaries
 Topological field quantization
2.3. Gauge charges in TGD
 Definition of the gauge charges in TGD
 Questions related to gravitational interactions
 The problem of the anomalous gauge charges
 The concept of the # contact, particle massivation, and weakening of Equivalence Principle
2.4. The new space time picture and some of its consequences
 Topological condensation and formation of bound states
 3topology and chemistry
 3topology and superconductivity
 Macroscopic bodies as a topology of 3space
2.5. Topological condensation and color confinement
 Explanation of color confinement using quantum classical correspondence
 Hadrons as color magnetic/electric flux tubes
 Color confinement and generation of macrotemporal quantum coherence
2.6. TGD based view about dark matter
 Dark matter as macroscopic quantum phase with gigantic Planck constant
 How the scaling of hbar affects physics?
 Simulating big bang in laboratory
 Living matter as dark matter
 Antimatter and dark matter
 Are long ranged classical electroweak and color gauge fields created by dark matter?
2.7. Is it possible to understand coupling constant evolution at spacetime level?
 Overview
 The evolution of gauge and gravitational couplings at spacetime level
 pAdic coupling constant evolution
 About electroweak coupling constant evolution
2.8. Model for topological evaporation
 General ideas
 Estimates for the evaporation of photons and electrons
 Does vapor phase exist? Astrophysical indications
 Two velocities of light?
 How to interpret the redshift caused by the warping?
3.1. Introduction
 Parton level formulation of quantum TGD
 Zero energy ontology
 Fusion of real and padic physics to single one
 Dark matter hierarchy and hierarchy of Planck constants
 pAdic coupling constant evolution
3.2. The new developments in quantum TGD
 Reduction of quantum TGD to parton level
 Quantum measurement theory with finite measurement resolution
 Hierarchy of Planck constants
 Zero energy ontology
 U and Smatrices
 Number theoretic ideas
3.3. New results related to coupling constant evolution
 A revised view about Kähler coupling strength and padic coupling constant evolution
 Does the quantization of Kähler coupling strength reduce to the quantization of ChernSimons coupling at partonic level?
 What could happen in the transition to nonperturbative QCD?
 Supercanonical bosons as a particular kind of dark matter
PART II: MANYSHEETED COSMOLOGY, AND ASTROPHYSICS
4.1. Introduction
 The fate of Equivalence Principle
 Zero energy ontology
 Dark matter hierarchy and hierarchy of Planck constants
 The problem of cosmological constant
 Topics of the chapter
4.2. TGD and GRT descriptions of spacetime
 Manysheeted spacetime defines a hierarchy of smoothed out spacetimes
 The dynamics of "gravitational" charges as dynamics without variational principle
 Equivalence Principle in TGD framework
 TGD based model for cosmic strings
4.3. Imbedding of the ReissnerNordström metric
 Two basic types of imbeddings
 The condition guaranteing the vanishing of em, Z0, or Kähler fields
 Imbedding of ReissnerNordström metric
 Gravitational energy is not conserved for ReissnerNordström metric
 Anomalous time dilation effects due to warping as a basic distinction between TGD and GRT
 Evidence for manysheeted spacetime from gamma ray flares
4.4. Allais effect and TGD
 Introduction
 Could gravitational screening explain Allais effect
 Allais effect as evidence for large values of gravitational Planck constant?
 Could Z0 force be present?
4.5. A model for the final state of the star
 Spherically symmetric model
 Dynamo model
 Z0 force and dynamics of compact objects
 Correlation between γ ray bursts and supernovae and dynamo model for the final state of the star
 Z0 force and Super Nova explosion
 Microscopic description of blackholes in TGD Universe
4.6. TGD and gravimagnetism
 Gravity Probe B and TGD
 Does horizon correspond to a degenerate fourmetric for the rotating counterpart of Schwartshild metric?
 Has strong gravimagnetism been observed?
 Is the large gravimagnetic field possible in TGD framework?
4.7. Is gravitational constant really constant
 The case of bullet cluster
 Shrinking kilogram
4.8. Machian Principle and TGD
 Nonconserved gravitational fourmomentum and conserved inertial momentum at 4D spacetime level
 Inertial fourmomentum as the average of gravitational fourmomentum
 Nonconserved gravitational fourmomentum and conserved inertial momentum at parton level
 Inertial fourmomentum as average of partonic fourmomentum and padic thermodynamics
 Various interpretations of Machian Principle
5.1. Introduction
 Various strings
 TGD based model for cosmic strings
 Correlation between supernovae and cosmic strings
5.2. General vision about topological condensation of cosmic strings
 The relationship between inertial and gravitational masses
 Free cosmic strings
 What happens in the topological condensation of cosmic strings?
 Negative energy cosmic strings and positive cosmological constant
 New anomaly in Cosmic Microwave Background
5.3. More detailed view about topological condensation of cosmic strings
 Topological condensation of a positive energy cosmic string
 Exterior metrics of cosmic string as extremal of curvature scalar
 Exterior metric of negative energy cosmic string with large angle excess
 Geodesic motion in the exterior metric of the negative energy cosmic string
 Matter distribution around cosmic string
 Quantization of the cosmic recession velocity
5.4. Cosmic evolution and cosmic strings
 Cosmic strings and generation of structures
 Generation of ordinary matter via TGD counterpart of Hawking radiation?
 How single cosmic string could reduce its Kähler string tension?
 Zero energy ontology, cosmic strings, and consciousness
5.5. Cosmic string model for galaxies and other astrophysical objects
 Cosmic strings and the organization of galaxies into linear structures
 Cosmic strings and dark matter problem
 Estimate for the velocity parameters
 Galaxies as split cosmic strings?
 Cylindrically symmetric model for the galactic dark matter
5.6. Cosmic strings and energy production in quasars
 Basic properties of the decaying cosmic strings
 Decaying cosmic string ends as a central engine
 How to understand the microjet structure?
 Gammaray bursts and cosmic strings
5.7. The light particles associated with dark matter and the correlation between gamma ray bursts and supernovae
 Correlations between gamma ray bursts and supernovae
 Leptopions as a signature dark matter?
6.1. Introduction
 Zero energy cosmology
 Dark matter hierarchy and hierarchy of Planck constants
 Quantum criticality and quantum phase transitions
 Critical and overcritical cosmologies are highly unique
 Equivalence Principle in TGD framework
 Cosmic strings as basic building blocks of TGD inspired cosmology
6.2. Basic ingredients of TGD inspired cosmology
 Manysheeted spacetime defines a hierarchy of smoothed out spacetimes
 RobertsonWalker cosmologies
 Cosmic strings and cosmology
 Thermodynamical considerations
6.3. TGD inspired cosmology
 Primordial cosmology
 Critical phases
 Radiation dominated phases
 Matter dominated phases
 Stationary cosmology
6.4. Inflationary cosmology or TGD?
 Comparison with inflationary cosmology
 Balloon measurements of the cosmic microwave background favor flat cosmos
 Quantum critical fractal cosmology as TGD counterpart of the inflationary cosmology
 The problem of cosmological missing mass
 TGD based explanation of the results of the balloon experiments
6.5. Some problems of cosmology
 Why some stars seem to be older than the Universe? /font>
 Mechanism of accelerated expansion in TGD Universe
 Could manysheeted cosmology explain the claimed time dependence of the fine structure constant?
 Apparent time dependence of the fine structure constant
 The problem of fermion families
6.6. Simulating Big Bang in laboratory
 Experimental arrangement and findings
 TGD based model for the quarkgluon plasma
 Further experimental findings and theoretical ideas
 Are ordinary blackholes replaced with supercanonical blackholes in TGD Universe?
 Conclusions
7.1. Introduction
 pAdic length scale hypothesis and astrophysics
 The high temperature of the solar corona and dark matter
 Quantum criticality, hierarchy of dark matters, and dynamical hbar
 Dark matter as large hbar phase
 Dark matter as a source of long ranged weak and color fields
 How gravitational and inertial Bohr rules relate to each other?
 Consciousness and cosmology
7.2. pAdic length scale hypothesis at astrophysical and cosmological length scales
 List of long padic length scales
 pAdic evolution of cosmological constant
 Evidence for a new length scale in cosmology
7.3. Solar magnetic fields and Sunspot cycle
 Sunspot cycle
 Sunspots as helical vortices
 A model for the Sunspot cycle
 Helical vortex as a model for a magnetic flux tube
 Estimates for the vacuum parameters of magnetic flux tube
7.4. Explanation for the high temperature of solar corona
 Topological model for the magnetic field of Sun
 Quantitative formulation
7.5. General ideas about dark matter and condensed matter
 General view about dark matter hierarchy and interactions between relatively dark matters
 Dark atoms and dark cyclotron states
 Gravitational Schrödinger equation as a quantum model for the formation of astrophysical structures and dark matter?
 Model for planetary orbits without v0→ v0/5 scaling
 The interpretation of the parameter v0
 The interpretation of hbargr and preplanetary period
 Inclinations for the planetary orbits and the quantum evolution of the planetary system
 Eccentricities and comets
 Why the quantum coherent dark matter is not visible?
 Quantum interpretation of gravitational Schrödinger equation
 How do the magnetic flux tube structures and quantum gravitational bound states relate?
 pAdic length scale hypothesis and v0> v0/5 transition at innerouter border for planetary system
 About the interpretation of the parameter v0
 Further evidence for dark matter
7.4. Explanations of some astrophysical and cosmological anomalies
 Apparent shrinking of solar system
 Pioneer anomaly
 Flyby anomaly
 New anomaly in Cosmic Microwave Background
8.1. Introduction
 Generalization of the notion of imbedding space
 Gravitational Bohr orbitology
8.2. Basic objections against planetary Bohr orbitology
 Also exoplanets obey Bohr rules
 How General Coordinate Invariance and Lorentz invariance are achieved?
8.3. General quantum vision about formation of structures
 Simple quantitative model
 Could one understand the different values of gravitational Planck constant for inner and outer planetary systems?
 Formation of rings like structures
 A quantum model for the dark part of the central mass and rings
 Two stellar components in the halo of Milky Way
8.4. Quantum chaos in astrophysical length scales
 Brief summary about quantum chaos
 What does the transition to quantum chaos mean?
 Quantum chaos in astrophysical scales?
8.5. Gravitational radiation and large value of gravitational Planck constant
 Standard view about gravitational radiation
 Model for dark gravitons
 Detection of gravitational radiation
 Quantitative model
 Generalization to gauge interactions
8.6. New view about blackholes
 Supercanonical bosons
 Are ordinary blackholes replaced with supercanonical blackholes?
8.7. Piecewise accelerated cosmic expansion as basic prediction of quantum cosmology
 Experimental evidence for accelerated expansion is consistent with TGD based model
 Quantum version of Expanding Earth theory
8.8. About the anomalies of the cosmic microwave background
 Background
 Anomalies CMB
 What TGD could say about the anomalies?
8.9. Appendix
 Generalization of the notion of imbedding space
 Orbital radii of exoplanets as a test for the theory
PART III: TOPOLOGICAL FIELD QUANTIZATION
9.1. Introduction
 Basic ideas and concepts
 Z0 magnetic fields and hydrodynamics
 Topics of the chapter
9.2. Manysheeted spacetime concept
 Basic concepts related to topological condensation and evaporation
 Can one regard #resp. #B contacts as particlesresp. string like objects?
 Number theoretical considerations
 Physically interesting padic length scales in condensed matter systems
9.3. Hydrodynamical and thermodynamical hierarchies
 Dissipation by the collisions of condensate blocks
 Energy transfer between different condensate levels in turbulent flow
 The magnetic fields associated with vortex and rigid body flows
 Criticality condition
 Sonoluminescence and hydrodynamical hierarchy
 pAdic length scale hypothesis, hydrodynamic turbulence, and distribution of primes
 Thermodynamic Hierarchy
9.4. Configuration space geometry and phase transitions
 Basic ideas of catastrophe theory
 Configuration space geometry and catastrophe theory
 Quantum TGD and catastrophe theory
 TGD based description of phase transitions
9.5. Imbeddings of the cylindrically symmetric flows
 The general form of the imbedding of the cylindrically symmetric rotational flow.
 Orders of magnitude for some vacuum parameters
 Critical radii for some special flows
9.6. Transition to turbulence in channel flow
 Transition to turbulence
 Definition of the model
 Estimates for the parameters
 Kähler fields associated with the cascade process
 Order of magnitude estimate for the change of the Kähler action and Reynolds criterion
 Phase slippage as mechanism for the decay of vortices
10.1. General Theory
 Identification of the topological field quanta
 Formation of the supra phase
 Generalized quantization conditions
 Dissipation in super fluids: critical velocities
 Meissner effect
 Phase slippage
10.2. Models for topological field quanta
 The Kähler field created by a constant mass distribution
 The imbedding of a constant magnetic fields
 Magnetic fields associated with constant velocity flows
10.3. Quantum Hall effect from topological field quantization
 The effect
 The model
10.4. TGD and condensed matter
 Electronic conductivity and topological field quantization
 Dielectrics and topological field quantization
 Magnetism and topological field quantization
11.1. Basic properties of CP2
 CP2 as a manifold
 Metric and Kähler structures of CP2
 Spinors in CP2
 Geodesic submanifolds of CP2
11.2. CP2 geometry and standard model symmetries
 Identification of the electroweak couplings
 Discrete symmetries
11.3. Basic facts about induced gauge fields
 Induced gauge fields for spacetimes for which CP2 projection is a geodesic sphere
 Spacetime surfaces with vanishing em, Z0, or Kähler fields
11.4. pAdic numbers and TGD
 pAdic number fields
 Canonical correspondence between padic and real numbers
