The Arrows of Time: A Debate in Cosmology (Fundamental Theories of Physics Book 172)

The concept of time has fascinated humanity throughout recorded history, and it remains one of the biggest mysteries in science and philosophy. Time is clearly one of the fundamental building blocks of the universe and thus a deeper understanding of nature at a fundamental level also demands a comprehension of time. Furthermore, the origins of the universe are closely intertwined with the puzzle of time: Did time emerge at the Big Bang? Why does the arrow of time ‘conspire’ with the order of the initial state of the universe? This book addresses many of the most important questions about time: What is time, and is it fundamental or emergent? Why is there such an arrow of time, closely related to the initial state of the universe, and why do the cosmic, thermodynamic and other arrows agree? These issues are discussed here by leading experts, and each offers a new perspective on the debate. Their contributions delve into the most difficult research topic in physics, also describing the latest cutting edge research on the subject. The book also offers readers a comparison between the different outlooks of philosophy, physics and cosmology on the puzzle of time. This volume is intended to be useful for research purposes, but most chapters are also accessible to a more general audience of scientifically educated readers looking for deeper insights. The Arrows of Time 3 Contents 5 Introduction 6 Time After Time — Big Bang Cosmology and the Arrows of Time 9 1 The Direction of Time 10 2 Ten Arrows of Time 11 3 Four Kinds of Answers 14 4 Fundamental Issues 16 5 Gravity, Entropy, and Improbability 17 6 Beyond the Big Bang 19 7 Big Fluctuation 21 8 Big Bounce 24 9 A Fundamental Asymmetry? 25 10 A Universe With or Without a Beginning 26 11 Microtime, Macrotime and the Pseudo-Beginning Proposal 29 12 Conformal Cyclic Cosmology 36 13 The End of Time 39 References 41 Fundamental Loss of Quantum Coherence from Quantum Gravity 47 1 Introduction 47 2 Quantum Mechanics with Real Clocks 48 3 Fundamental Limits to Realistic Clocks 50 4 Possible Experimental Implications 51 5 Conceptual Implications 52 5.1 The Black Hole Information Paradox 52 5.2 The Measurement Problem in Quantum Mechanics 53 5.3 Quantum Computing 54 6 Discussion 55 References 56 The Clock Ambiguity: Implications and New Developments 57 1 Introduction 57 2 Summary of the Clock Ambiguity 58 3 The Time Independence of H 60 4 Field Theory and the Wigner Semicircle 61 4.1 Our Basic Approach 61 4.2 The Value of and the Dimensions of Space 63 4.3 Wigner's Tail 64 5 Including Gravity 66 6 Heat Capacity and N 67 7 Summary and Conclusions 71 References 72 Holographic Cosmology and the Arrow of Time 73 1 General Relativity Is Not a Quantum Field Theory! 73 1.1 The Arena 78 1.2 The Variables 82 1.3 SUSY and the Holographic Screens 84 1.4 The Hamiltonian Constraint 88 1.5 Executive Summary 91 2 Holographic Cosmology 92 2.1 The Dense Black Hole Fluid 92 2.2 Our World As the Cosmology of DBHF Defects 95 2.3 Phenomenology 104 2.3.1 Spectral Tilt and Over the Top Inflation 106 2.3.2 Executive Summary 108 2.4 The Thermodynamic Arrow of Time 109 References 111 The Emergent Nature of Time and the Complex Numbers in Quantum Cosmology 113 1 Introduction 113 2 The Structure of Quantum Mechanics 114 2.1 A Precautionary Principle 116 2.2 Dyson's Threefold Way 117 2.3 Relation to Jordan Algebras 118 2.4 Special Cases: Low Order Isomorphisms 119 3 Spacetime Signature and the Real Numbers 120 3.1 Clifford Algebras 120 3.2 Chiral Rotations 121 3.3 Majorana Spinors 122 3.4 Dirac Spinors 122 3.5 Weyl Spinors 123 3.6 Signature Reversal Non-invariance 123 4 More Than One Time: Signature Change 125 5 Examples 127 5.1 Quantum Field Theory in Curved Spacetime 127 5.2 The Wave Function of the Universe 128 5.3 Euclidean Quantum Field Theory 129 5.4 Lorentzian Creation ex nihilo 129 6 Topology, Time Reversal and the Arrow of Time 130 7 Unification and Spin (10) 131 8 Gravitational CP Violation? 133 8.1 Behaviour in a Gravitational Field 135 9 Pure States -3mu Mixed States? 135 9.1 Density Matrices 136 9.2 Gibbs Entropy 136 9.3 Evolution by an S-Matrix 137 9.4 Tracing Out 137 9.5 Evolution by an $ Matrix 138 9.6 Invertibility and Factorisability 139 9.7 Irreversibility and CPT 140 9.8 Strong CPT 140 9.9 Weak CTP 140 9.10 Pauli Master Equation 141 9.11 Consequence of Symmetries 142 9.12 S-Matrix Case 143 9.13 $-Matrix Case 143 10 Superscattering and the Reals 144 11 Conclusion 144 References 148 The Phantom Bounce: A New Proposal for an Oscillating Cosmology 153 1 Introduction 153 2 The Bouncing Cosmology 155 3 Destruction of Black Holes 158 4 Discussion 159 References 160 Notes on Time's Enigma 161 1 Introduction 161 2 The Three Enigmas of Time and the Multiverse 162 2.1 Time's Arrow and the Birth of the Universe 163 2.2 Fundamental Time and the Multiverse 165 2.3 Time-Reversal Symmetry for the Laws of Physics 168 3 Discussion 169 References 171 A Momentous Arrow of Time 173 1 Introduction 173 2 The Problem and the Arrow of Time 174 3 Classical Dynamics 176 4 Quantum Dynamics 177 4.1 Monotonicity 179 4.2 Before the Big Bang 180 5 Beyond Exactitude 184 6 An Arrow of Moments 187 7 Conclusions 188 References 191 Can the Arrow of Time Be Understood from Quantum Cosmology? 194 1 Introduction 194 2 Entropy and Cosmology 196 3 Quantum Geometrodynamics 198 4 Arrow of Time from Quantum Cosmology 199 References 205 Open Questions Regarding the Arrow of Time 207 1 Laws and Facts 207 2 The Arrow in Classical Physics 210 3 The Arrow in Quantum Theory and Quantum Cosmology 213 4 A Brief History of Timelessness 217 References 218 Index 220 The concept of time has fascinated humanity throughout history, and remains one of the biggest mysteries in science and philosophy. Yet a deeper understanding of nature at a fundamental level can only be achieved through a comprehension of this strange fourth dimension. Furthermore, the origin of the universe is closely intertwined with the puzzle of time: Did time emerge at the big bang? Why does the direction of time 'conspire' with the remarkably ordered initial state of the universe? This book addresses many of the most important questions about time: What is time, and is it fundamental or emergent? Why is there such an arrow of time, closely related to the initial state of the universe, and why do the cosmic, thermodynamic and other arrows agree? These issues are discussed here by leading experts, and each offers a new perspective on the debate. Their contributions delve into the most difficult research topic in physics, also describing the latest cutting edge research on the subject. The book also offers readers a comparison between the different outlooks of philosophy, physics and cosmology on the puzzle of time. This volume is intended to be useful for research purposes, but most chapters are also accessible to a more general audience of scientifically educated readers looking for deeper insights