PHYSICS IN MANY-SHEETED SPACE-TIME

by Matti Pitkänen

Introduction

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 space-time concept

2. The five threads in the development of quantum TGD

1. Quantum TGD as configuration space spinor geometry

2. p-Adic 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: Many-Sheeted Cosmology and Astrophysics

2. PART II: Topological Field Quantization

PART I:
MANY-SHEETED SPACE-TIME

1) Basic extremals of the Kähler action

1.1. Introduction

1.2. General considerations

1. Long range classical weak and color gauge fields as correlates for dark massless weak bosons
2. Is absolute minimization the correct variational principle
3. Field equations
4. Could Lorentz force vanish identically for all extremals/absolute minima of Kähler action?
5. Topologization of the Kähler current as a solution to the generalized Beltrami condition
6. How to satisfy field equations?
7. D=3 phase allows infinite number of topological charges characterizing the linking of magnetic field lines
8. Is absolute minimization of Kähler action equivalent with the topologization/light-likeness of Kähler current and second law?
9. Generalized Beltrami fields and biological systems
10. About small perturbations of field equations

1.3. Vacuum extremals

1. CP2 type extremals
2. Vacuum extremals with vanishing induced Kähler field

1.4. Non-vacuum extremals

1. Cosmic strings
2. Massless extremals
3. Generalization of the solution ansatz defining massless extremals
4. Maxwell phase
5. Stationary, spherically symmetric extremals
6. The scalar waves of Tesla, bio-systems as electrets, and electric-magnetic duality
7. Maxwell hydrodynamics as a toy model for TGD

1.5. Can one determine experimentally the shape of the space-time surface?

1.6. Measuring classically the shape of the space-time surface

1.7. Quantum measurement of the shape of the space-time surface

2) General View About Physics in Many-Sheeted Space-Time : Part I

2.1. Introduction

1. Various types of topological condensation
2. Implications of the topological non-triviality of macroscopic space-time
3. Topics of the chapter

2.2. What does 3-surface look like?

1. Renormalization group invariance, quantum criticality and topology of 3-space
2. 3-surfaces have outer boundaries
3. Topological field quantization

2.3. Gauge charges in TGD

1. Definition of the gauge charges in TGD
2. Questions related to gravitational interactions
3. The problem of the anomalous gauge charges
4. The concept of the # contact, particle massivation, and weakening of Equivalence Principle

2.4. The new space time picture and some of its consequences

1. Topological condensation and formation of bound states
2. 3-topology and chemistry
3. 3-topology and super-conductivity
4. Macroscopic bodies as a topology of 3-space

2.5. Topological condensation and color confinement

1. Explanation of color confinement using quantum classical correspondence
2. Hadrons as color magnetic/electric flux tubes
3. Color confinement and generation of macro-temporal quantum coherence

2.6. TGD based view about dark matter

1. Dark matter as macroscopic quantum phase with gigantic Planck constant
2. How the scaling of hbar affects physics?
3. Simulating big bang in laboratory
4. Living matter as dark matter
5. Anti-matter and dark matter
6. Are long ranged classical electro-weak and color gauge fields created by dark matter?

2.7. Is it possible to understand coupling constant evolution at space-time level?

1. Overview
2. The evolution of gauge and gravitational couplings at space-time level
3. p-Adic coupling constant evolution
4. About electro-weak coupling constant evolution

2.8. Model for topological evaporation

1. General ideas
2. Estimates for the evaporation of photons and electrons
3. Does vapor phase exist? Astrophysical indications
4. Two velocities of light?
5. How to interpret the red-shift caused by the warping?

3) General View About Physics in Many-Sheeted Space-Time: Part II

3.1. Introduction

1. Parton level formulation of quantum TGD
2. Zero energy ontology
3. Fusion of real and p-adic physics to single one
4. Dark matter hierarchy and hierarchy of Planck constants
5. p-Adic coupling constant evolution

3.2. The new developments in quantum TGD

1. Reduction of quantum TGD to parton level
2. Quantum measurement theory with finite measurement resolution
3. Hierarchy of Planck constants
4. Zero energy ontology
5. U- and S-matrices
6. Number theoretic ideas

3.3. New results related to coupling constant evolution

1. A revised view about Kähler coupling strength and p-adic coupling constant evolution
2. Does the quantization of Kähler coupling strength reduce to the quantization of Chern-Simons coupling at partonic level?
3. What could happen in the transition to non-perturbative QCD?
4. Super-canonical bosons as a particular kind of dark matter

PART II:
MANY-SHEETED COSMOLOGY, AND ASTROPHYSICS

4) The relationship between TGD and GRT

4.1. Introduction

1. The fate of Equivalence Principle
2. Zero energy ontology
3. Dark matter hierarchy and hierarchy of Planck constants
4. The problem of cosmological constant
5. Topics of the chapter

4.2. TGD and GRT descriptions of space-time

1. Many-sheeted space-time defines a hierarchy of smoothed out space-times
2. The dynamics of "gravitational" charges as dynamics without variational principle
3. Equivalence Principle in TGD framework
4. TGD based model for cosmic strings

4.3. Imbedding of the Reissner-Nordström metric

1. Two basic types of imbeddings
2. The condition guaranteing the vanishing of em, Z0, or Kähler fields
3. Imbedding of Reissner-Nordström metric
4. Gravitational energy is not conserved for Reissner-Nordström metric
5. Anomalous time dilation effects due to warping as a basic distinction between TGD and GRT
6. Evidence for many-sheeted space-time from gamma ray flares

4.4. Allais effect and TGD

1. Introduction
2. Could gravitational screening explain Allais effect
3. Allais effect as evidence for large values of gravitational Planck constant?
4. Could Z0 force be present?

4.5. A model for the final state of the star

1. Spherically symmetric model
2. Dynamo model
3. Z0 force and dynamics of compact objects
4. Correlation between γ ray bursts and supernovae and dynamo model for the final state of the star
5. Z0 force and Super Nova explosion
6. Microscopic description of black-holes in TGD Universe

4.6. TGD and gravimagnetism

1. Gravity Probe B and TGD
2. Does horizon correspond to a degenerate four-metric for the rotating counterpart of Schwartshild metric?
3. Has strong gravimagnetism been observed?
4. Is the large gravimagnetic field possible in TGD framework?

4.7. Is gravitational constant really constant

1. The case of bullet cluster
2. Shrinking kilogram

4.8. Machian Principle and TGD

1. Non-conserved gravitational four-momentum and conserved inertial momentum at 4-D space-time level
2. Inertial four-momentum as the average of gravitational four-momentum
3. Non-conserved gravitational four-momentum and conserved inertial momentum at parton level
4. Inertial four-momentum as average of partonic four-momentum and p-adic thermodynamics
5. Various interpretations of Machian Principle

5) Cosmic strings

5.1. Introduction

1. Various strings
2. TGD based model for cosmic strings
3. Correlation between super-novae and cosmic strings

5.2. General vision about topological condensation of cosmic strings

1. The relationship between inertial and gravitational masses
2. Free cosmic strings
3. What happens in the topological condensation of cosmic strings?
4. Negative energy cosmic strings and positive cosmological constant
5. New anomaly in Cosmic Microwave Background

5.3. More detailed view about topological condensation of cosmic strings

1. Topological condensation of a positive energy cosmic string
2. Exterior metrics of cosmic string as extremal of curvature scalar
3. Exterior metric of negative energy cosmic string with large angle excess
4. Geodesic motion in the exterior metric of the negative energy cosmic string
5. Matter distribution around cosmic string
6. Quantization of the cosmic recession velocity

5.4. Cosmic evolution and cosmic strings

1. Cosmic strings and generation of structures
2. Generation of ordinary matter via TGD counterpart of Hawking radiation?
3. How single cosmic string could reduce its Kähler string tension?
4. Zero energy ontology, cosmic strings, and consciousness

5.5. Cosmic string model for galaxies and other astrophysical objects

1. Cosmic strings and the organization of galaxies into linear structures
2. Cosmic strings and dark matter problem
3. Estimate for the velocity parameters
4. Galaxies as split cosmic strings?
5. Cylindrically symmetric model for the galactic dark matter

5.6. Cosmic strings and energy production in quasars

1. Basic properties of the decaying cosmic strings
2. Decaying cosmic string ends as a central engine
3. How to understand the micro-jet structure?
4. Gamma-ray bursts and cosmic strings

5.7. The light particles associated with dark matter and the correlation between gamma ray bursts and supernovae

1. Correlations between gamma ray bursts and supernovae
2. Lepto-pions as a signature dark matter?

3) TGD and Cosmology

6.1. Introduction

1. Zero energy cosmology
2. Dark matter hierarchy and hierarchy of Planck constants
3. Quantum criticality and quantum phase transitions
4. Critical and over-critical cosmologies are highly unique
5. Equivalence Principle in TGD framework
6. Cosmic strings as basic building blocks of TGD inspired cosmology

6.2. Basic ingredients of TGD inspired cosmology

1. Many-sheeted space-time defines a hierarchy of smoothed out space-times
2. Robertson-Walker cosmologies
3. Cosmic strings and cosmology
4. Thermodynamical considerations

6.3. TGD inspired cosmology

1. Primordial cosmology
2. Critical phases
3. Radiation dominated phases
4. Matter dominated phases
5. Stationary cosmology

6.4. Inflationary cosmology or TGD?

1. Comparison with inflationary cosmology
2. Balloon measurements of the cosmic microwave background favor flat cosmos
3. Quantum critical fractal cosmology as TGD counterpart of the inflationary cosmology
4. The problem of cosmological missing mass
5. TGD based explanation of the results of the balloon experiments

6.5. Some problems of cosmology

1. Why some stars seem to be older than the Universe? /font>
2. Mechanism of accelerated expansion in TGD Universe
3. Could many-sheeted cosmology explain the claimed time dependence of the fine structure constant?
4. Apparent time dependence of the fine structure constant
5. The problem of fermion families

6.6. Simulating Big Bang in laboratory

1. Experimental arrangement and findings
2. TGD based model for the quark-gluon plasma
3. Further experimental findings and theoretical ideas
4. Are ordinary black-holes replaced with super-canonical black-holes in TGD Universe?
5. Conclusions

7) TGD and Astrophysics

7.1. Introduction

1. p-Adic length scale hypothesis and astrophysics
2. The high temperature of the solar corona and dark matter
3. Quantum criticality, hierarchy of dark matters, and dynamical hbar
4. Dark matter as large hbar phase
5. Dark matter as a source of long ranged weak and color fields
6. How gravitational and inertial Bohr rules relate to each other?
7. Consciousness and cosmology

7.2. p-Adic length scale hypothesis at astrophysical and cosmological length scales

1. List of long p-adic length scales
2. p-Adic evolution of cosmological constant
3. Evidence for a new length scale in cosmology

7.3. Solar magnetic fields and Sunspot cycle

1. Sunspot cycle
2. Sunspots as helical vortices
3. A model for the Sunspot cycle
4. Helical vortex as a model for a magnetic flux tube
5. Estimates for the vacuum parameters of magnetic flux tube

7.4. Explanation for the high temperature of solar corona

1. Topological model for the magnetic field of Sun
2. Quantitative formulation

7.5. General ideas about dark matter and condensed matter

1. General view about dark matter hierarchy and interactions between relatively dark matters
2. Dark atoms and dark cyclotron states
3. Gravitational Schrödinger equation as a quantum model for the formation of astrophysical structures and dark matter?

1. Model for planetary orbits without v0→ v0/5 scaling
2. The interpretation of the parameter v0
3. The interpretation of hbargr and pre-planetary period
4. Inclinations for the planetary orbits and the quantum evolution of the planetary system
5. Eccentricities and comets
6. Why the quantum coherent dark matter is not visible?
7. Quantum interpretation of gravitational Schrödinger equation
8. How do the magnetic flux tube structures and quantum gravitational bound states relate?
9. p-Adic length scale hypothesis and v0--> v0/5 transition at inner-outer border for planetary system
10. About the interpretation of the parameter v0
11. Further evidence for dark matter

7.4. Explanations of some astrophysical and cosmological anomalies

1. Apparent shrinking of solar system
2. Pioneer anomaly
3. Flyby anomaly
4. New anomaly in Cosmic Microwave Background

8) Quantum Astrophysics

8.1. Introduction

1. Generalization of the notion of imbedding space
2. Gravitational Bohr orbitology

8.2. Basic objections against planetary Bohr orbitology

1. Also exoplanets obey Bohr rules
2. How General Coordinate Invariance and Lorentz invariance are achieved?

8.3. General quantum vision about formation of structures

1. Simple quantitative model
2. Could one understand the different values of gravitational Planck constant for inner and outer planetary systems?
3. Formation of rings like structures
4. A quantum model for the dark part of the central mass and rings
5. Two stellar components in the halo of Milky Way

8.4. Quantum chaos in astrophysical length scales

1. Brief summary about quantum chaos
2. What does the transition to quantum chaos mean?
3. Quantum chaos in astrophysical scales?

8.5. Gravitational radiation and large value of gravitational Planck constant

1. Standard view about gravitational radiation
2. Model for dark gravitons
3. Detection of gravitational radiation
4. Quantitative model
5. Generalization to gauge interactions

8.6. New view about blackholes

1. Super-canonical bosons
2. Are ordinary blackholes replaced with super-canonical blackholes?

8.7. Piece-wise accelerated cosmic expansion as basic prediction of quantum cosmology

1. Experimental evidence for accelerated expansion is consistent with TGD based model
2. Quantum version of Expanding Earth theory

8.8. About the anomalies of the cosmic microwave background

1. Background
2. Anomalies CMB
3. What TGD could say about the anomalies?

8.9. Appendix

1. Generalization of the notion of imbedding space
2. Orbital radii of exo-planets as a test for the theory

PART III:
TOPOLOGICAL FIELD QUANTIZATION

9) Hydrodynamics and CP2 geometry

9.1. Introduction

1. Basic ideas and concepts
2. Z0 magnetic fields and hydrodynamics
3. Topics of the chapter

9.2. Many-sheeted space-time concept

1. Basic concepts related to topological condensation and evaporation
2. Can one regard #resp. #B contacts as particlesresp. string like objects?
3. Number theoretical considerations
4. Physically interesting p-adic length scales in condensed matter systems

9.3. Hydrodynamical and thermodynamical hierarchies

1. Dissipation by the collisions of condensate blocks
2. Energy transfer between different condensate levels in turbulent flow
3. The magnetic fields associated with vortex and rigid body flows
4. Criticality condition
5. Sono-luminescence and hydrodynamical hierarchy
6. p-Adic length scale hypothesis, hydrodynamic turbulence, and distribution of primes
7. Thermodynamic Hierarchy

9.4. Configuration space geometry and phase transitions

1. Basic ideas of catastrophe theory
2. Configuration space geometry and catastrophe theory
3. Quantum TGD and catastrophe theory
4. TGD based description of phase transitions

9.5. Imbeddings of the cylindrically symmetric flows

1. The general form of the imbedding of the cylindrically symmetric rotational flow.
2. Orders of magnitude for some vacuum parameters
3. Critical radii for some special flows

9.6. Transition to turbulence in channel flow

1. Transition to turbulence
2. Definition of the model
3. Estimates for the parameters
4. Kähler fields associated with the cascade process
5. Order of magnitude estimate for the change of the Kähler action and Reynolds criterion
6. Phase slippage as mechanism for the decay of vortices

10) Macroscopic quantum phenomena and CP2 geometry

10.1. General Theory

1. Identification of the topological field quanta
2. Formation of the supra phase
3. Generalized quantization conditions
4. Dissipation in super fluids: critical velocities
5. Meissner effect
6. Phase slippage

10.2. Models for topological field quanta

1. The Kähler field created by a constant mass distribution
2. The imbedding of a constant magnetic fields
3. Magnetic fields associated with constant velocity flows

10.3. Quantum Hall effect from topological field quantization

1. The effect
2. The model

10.4. TGD and condensed matter

1. Electronic conductivity and topological field quantization
2. Dielectrics and topological field quantization
3. Magnetism and topological field quantization

11) Appendix

11.1. Basic properties of CP2

1. CP2 as a manifold
2. Metric and Kähler structures of CP2
3. Spinors in CP2
4. Geodesic sub-manifolds of CP2

11.2. CP2 geometry and standard model symmetries

1. Identification of the electro-weak couplings
2. Discrete symmetries

11.3. Basic facts about induced gauge fields

1. Induced gauge fields for space-times for which CP2 projection is a geodesic sphere
2. Space-time surfaces with vanishing em, Z0, or Kähler fields

11.4. p-Adic numbers and TGD

1. p-Adic number fields
2. Canonical correspondence between p-adic and real numbers