On the Emergence Theme of Physics

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More About This Textbook

Overview

The book surveys mathematical relations between classical and quantum mechanics, gravity, time and thermodynamics from various points of view and many sources (with appropriate attribution). The emergence theme is developed with an emphasis on the meaning via mathematics. A background theme of Bohemian mechanics and connections to the quantum equivalence principle of Matone et al. is also developed in great details. Some original work relating the quantum potential and Ricci flow is also included.

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Product Details

  • ISBN-13: 9789814291798
  • Publisher: World Scientific Publishing Company, Incorporated
  • Publication date: 6/28/2010
  • Pages: 288
  • Product dimensions: 6.60 (w) x 9.80 (h) x 0.80 (d)

Table of Contents

Preface ix

Chapter 1 Some Quantum Backgound 1

1 deBroglie-Bohm Mechanics 1

1.1 Subquantum Thermodynamics 3

1.2 Fluctuations And Fisher Information 7

1.3 The Quantum Equivalence Princicple-Qep 12

2 On The Gutzwiller Trace Formula 15

2.1 Propagatprs, Kernels, and the Wigner Function 17

2.2 Remarks On the Trace Formula 18

2.3 Coherent States and the Trace Formula 20

2.4 Some Mathematical Variations 26

3 More On Metaplectic Techniques 32

Chapter 2 Some Geometric Aspects 37

1 Introduction 37

2 Remarks On Weyl Geometry 39

3 Emergence Of Q in Geometry 44

3.1 Quantum Potential as a Dynamical Field 48

4 Other Geometric Aspects 49

5 The Qantum Potential and Geometry 54

6 Conformal and Quantum Mass 58

7 Ricci Flow and the Quantum Potential 59

7.1 Expansion 62

8 Remarks on the Friedman Equations 65

9 Enhancement 67

10 Some Heuristic Results 71

Chapter 3 Aspects Of Emergence 75

1 Introduction 75

2 Some Classical Quantum Relations 77

3 Nc Fields and Gravity 82

3.1 Review Of Some Ideas 85

4 Gerbes And Structure 87

Chapter 4 Kaluza-Klein and Cosmology 95

1 Introduction 95

2 Kaluza-Klein Theory 97

3 Induced Matter Theory 99

4 More On Electromagnetism 101

5 5-D Physics 102

6 Some Quantum Connections 106

7 Remarks On Cosmology 108

8 Extensions 110

8.1 More Examples 114

Chapter 5 Remarks On Thermodynamics and Gravity 121

1 Introduction 121

1.1 Information Dynamics 124

1.2 Entropy and the Einstein Equations 124

2 Horizons, Entropy, and All That 127

3 Thermodynamics And Frw Formats 129

3.1 Metrics From (1) 129

3.2 Metrics From (3) 130

3.3 Metrics From (2) 133

4 The Geometry Of Thermodynamics 135

4.1 Unified Legendre Forms 138

5 Frw Following (4) and (5) 141

5.1 Higher Derivative Gravities 143

6 Thermodynamics and Quantum Gravity - I 144

6.1 Thermodynamics of the Universe 153

7 Thermodynamics and Quantum Gravity - II 154

7.1 Boson Fields and Quantization 156

7.2 Fock Space Constructions 157

8 Thermodynamics And Quantum Gravity - III 159

8.1 Quantum Cosmology 160

8.2 Partial Summary 162

Chapter 6 Geometry And Mechanics 167

1 More On Emergence 167

1.1 Fluctuations And Dissipation 172

1.2 Prequantization And Born's Rule 173

2 Quantum Mechanics, Gravity, And Ricci Flow 176

3 Thermodynamics, Gravity, And Quantum Theory 184

3.1 Geometric Flows and Entropy 185

4 More On Gravitation 191

5 Black Holes and Thermodynamics 196

Chapter 7 On Time and the Universe 205

1 Time 205

2 Spacetime, Mathematics, And Physics 211

3 Non-Commutative Geometry 216

4 More On Fundamental Matters 219

4.1 Nc Geometry, Gravity, And Strings 219

4.2 Time And Geometry 221

Chapter 8 Gravity and the Quantum Potential 225

1 Introduction 225

2 Background 226

3 Qep And Gravity 230

3.1 Weyl Geometry and the Quantum Potential 235

4 On The Klein-Gordon Equation 238

4.1 Enhancement 241

5 Quantization 243

Bibliography 247

Index 271

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