Fashion, Faith, and Fantasy in the New Physics of the Universe

Content: Acknowledgements ix  Preface xi  Are fashion, faith, or fantasy relevant to fundamental science? xi  1 Fashion 1  1.1 Mathematical elegance as a driving force 1  1.2 Some fashionable physics of the past 10  1.3 Particle-physics background to string theory 17  1.4 The superposition principle in QFT 20  1.5 The power of Feynman diagrams 25  1.6 The original key ideas of string theory 32  1.7 Time in Einstein\'s general relativity 42  1.8 Weyl\'s gauge theory of electromagnetism 52  1.9 Functional freedom in Kaluza-Klein and string models 59  1.10 Quantum obstructions to functional freedom? 69  1.11 Classical instability of higher-dimensional string theory 77  1.12 The fashionable status of string theory 82  1.13 M-theory 90  1.14 Supersymmetry 95  1.15 AdS/CFT 104  1.16 Brane-worlds and the landscape 117  2 Faith 121  2.1 The quantum revelation 121  2.2 Max Planck\'s E = hnu 126  2.3 The wave-particle paradox 133  2.4 Quantum and classical levels: C, U, and R 138  2.5 Wave function of a point-like particle 145  2.6 Wave function of a photon 153  2.7 Quantum linearity 158  2.8 Quantum measurement 164  2.9 The geometry of quantum spin 174  2.10 Quantum entanglement and EPR effects 182  2.11 Quantum functional freedom 188  2.12 Quantum reality 198  2.13 Objective quantum state reduction: a limit to the quantum faith? 204  3 Fantasy 216  3.1 The Big Bang and FLRW cosmologies 216  3.2 Black holes and local irregularities 230  3.3 The second law of thermodynamics 241  3.4 The Big Bang paradox 250  3.5 Horizons, comoving volumes, and conformal diagrams 258  3.6 The phenomenal precision in the Big Bang 270  3.7 Cosmological entropy? 275  3.8 Vacuum energy 285  3.9 Inflationary cosmology 294  3.10 The anthropic principle 310  3.11 Some more fantastical cosmologies 323  4 A New Physics for the Universe? 334  4.1 Twistor theory: an alternative to strings? 334  4.2 Whither quantum foundations? 353  4.3 Conformal crazy cosmology? 371  4.4 A personal coda 391  Appendix A Mathematical Appendix 397  A.1 Iterated exponents 397  A.2 Functional freedom of fields 401  A.3 Vector spaces 407  A.4 Vector bases, coordinates, and duals 413  A.5 Mathematics of manifolds 417  A.6 Manifolds in physics 425  A.7 Bundles 431  A.8 Functional freedom via bundles 439  A.9 Complex numbers 445  A.10 Complex geometry 448  A.11 Harmonic analysis 458  References 469  Index 491