CONTENTS Foreword ... ⅶ Quantum Gravity ... xxxi Lecture 1 ... 1 1.1 A Field Approach to Gravitation ... 1 1.2 The Characteristics of Gravitational Phenomena ... 3 1.3 Quantum Effects in Gravitation ... 10 1.4 On the Philosophical Problems in Quantizing Macroscopic Objects ... 11 1.5 Gravitation as a Consequence of Other Fields ... 15 Lecture 2 ... 17 2.1 Postulates of Statistical Mechanics ... 17 2.2 Difficulties of Speculative Theories ... 22 2.3 The Exchange of One Neutrino ... 23 2.4 The Exchange of Two Neutrinos ... 25 Lecture 3 ... 29 3.1 The Spin of the Graviton ... 29 3.2 Amplitudes and Polarizations in Electrodynamics, Our Typical Field Theory ... 31 3.3 Amplitudes for Exchange of a Graviton ... 35 3.4 Physical Interpretation of the Terms in the Amplitudes ... 38 3.5 The Lagrangian for the Gravitational Field ... 42 3.6 The Equations for the Gravitational Field ... 43 3.7 Definition of Symbols ... 44 Lecture 4 ... 47 4.1 The Connection Between the Tensor Rank and the Sign of a Field ... 47 4.2 The Stress-Energy Tensor for Scalar Matter ... 49 4.3 Amplitudes for Scattering (Scalar Theory) ... 50 4.4 Detailed Properties of Plane Waves. Compton Effect ... 52 4.5 Nonlinear Diagrams for Gravitons ... 54 4.6 The Classical Equations of Motion of a Gravitating Particle ... 56 4.7 Orbital Motion of a Particle About a Star ... 59 Lecture 5 ... 63 5.1 Planetary Orbits and the Precession of Mercury ... 63 5.2 Time Dilation in a Gravitational Field ... 66 5.3 Cosmological Effects of the Time Dilation. Machs Principle ... 69 5.4 Machs Principle in Quantum Mechanics ... 71 5.5 The Self Energy of the Gravitational Field ... 74 Lecture 6 ... 77 6.1 The Bilinear Terms of the Stress-Energy Tensor ... 77 6.2 Formulation of a Theory Correct to All Orders ... 81 6.3 The Construction of Invariants with Respect to Infinitesimal Transformations ... 82 6.4 The Lagrangian of the Theory Correct to All Orders ... 85 6.5 The Einstein Equation for the Stress-Energy Tensor ... 87 Lecture 7 ... 89 7.1 The Principle of Equivalence ... 89 7.2 Some Consequences of the Principle of Equivalence ... 93 7.3 Maximum Clock Rates in Gravity Fields ... 95 7.4 The Proper Time in General Coordinates ... 97 7.5 The Geometrical Interpretation of the Metric Tensor ... 99 7.6 Curvatures in Two and Four Dimensions ... 101 7.7 The Number of Quantities Invariant under General Transformations ... 103 Lecture 8 ... 107 8.1 Transformations of Tensor Components in Nonorthogonal Coordinates ... 107 8.2 The Equations to Determine Invariants of g μ ν ... 110 8.3 On the Assumption that Space Is Truly Flat ... 112 8.4 On the Relations Between Different Approaches to Gravity Theory ... 113 8.5 The Curvatures as Referred to Tangent Spaces ... 115 8.6 The Curvatures Referred to Arbitrary Coordinates ... 118 8.7 Properties of the Grand Curvature Tensor ... 120 Lecture 9 ... 123 9.1 Modifications of Electrodynamics Required by the Principle of Equivalence ... 123 9.2 Covariant Derivatives of Tensors ... 124 9.3 Parallel Displacement of a Vector ... 127 9.4 The Connection Between Curvatures and Matter ... 132 Lecture 10 ... 135 10.1 The Field Equations of Gravity ... 135 10.2 The Action for Classical Particles in a Gravitational Field ... 140 10.3 The Action for Matter Fields in a Gravitational Field ... 143 Lecture 11 ... 151 11.1 The Curvature in the Vicinity of a Spherical Star ... 151 11.2 On the Connection Between Matter and the Curvatures ... 153 11.3 The Schwarzschild Metric, the Field Outside a Spherical Star ... 154 11.4 The Schwarzschild Singularity ... 156 11.5 Speculations on the Wormhole Concept ... 159 11.6 Problems for Theoretical Investigations of the Wormholes ... 161 Lecture 12 ... 163 12.1 Problems of Cosmology ... 163 12.2 Assumptions Leading to Cosmological Models ... 166 12.3 The Interpretation of the Cosmological Metric ... 169 12.4 The Measurements of Cosmological Distances ... 171 12.5 On the Characteristics of a Bounded or Open Universe ... 173 Lecture 13 ... 177 13.1 On the Role of the Density of the Universe in Cosmology ... 177 13.2 On the Possibility of a Nonuniform and Nonspherical Universe ... 180 13.3 Disappearing Galaxies and Energy Conservation ... 181 13.4 Machs Principle and Boundary Conditions ... 184 13.5 Mysteries in the Heavens ... 186 Lecture 14 ... 189 14.1 The Problem of Superstars in General Relativity ... 189 14.2 The Significance of Solutions and their Parameters ... 192 14.3 Some Numerical Results ... 194 14.4 Projects and Conjectures for Future Investigations of Superstars ... 196 Lecture 15 ... 199 15.1 The Physical Topology of the Schwarzschild Solutions ... 199 15.2 Particle Orbits in a Schwarzschild Field ... 201 15.3 On the Future of Geometrodynamics ... 202 Lecture 16 ... 207 16.1 The Coupling Between Matter Fields and Gravity ... 207 16.2 Completion of the Theory: A Simple Example of Gravitational Radiation ... 211 16.3 Radiation of Gravitons with Particle Decays ... 212 16.4 Radiation of Gravitons with Particle Scattering ... 215 16.5 The Sources of Classical Gravitational Waves ... 218 Bibliography ... 221 Index ... 229