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

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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

Roger Penrose, one the world's foremost theoretical physicists, has won numerous prizes, including the Albert Einstein Medal, for his fundamental contributions to general relativity and cosmology. He is the bestselling author, with Stephen Hawking, of The Nature of Space and Time (Princeton). Penrose's other books include Cycles of Time: An Extraordinary New View of the Universe and The Road to Reality: A Complete Guide to the Laws of the Universe (both Vintage). He is the Rouse Ball Professor of Mathematics Emeritus at the University of Oxford and lives in Oxford, England.

Winner of the 2017 PROSE Award in Chemistry & Physics, Association of American Publishers "Physics has been at an awkward impasse for the past century. Two theories--quantum mechanics and general relativity--are widely believed to be true... But they contradict each other in basic ways--they cannot both be entirely true. InFashion, Faith, and Fantasy in the New Physics of the Universe... Roger Penrose, an elder statesman of physics, considers the problem. As intellectually offbeat as he is eminent... he ventures here some novel ways in which the two theories might be reconciled."--Wall Street Journal "Penrose gets to the heart of modern physics' problem with subjectivity in this insightful and provocative pop-sci title... [A] rewarding discussion of scientific stumbles in the search for truth."--Publishers Weekly "It is always inspiring to read Penrose's uncompromisingly independent perspec-tive on physics."--Richard Dawid, Nature "An extremely original, rich, and thoughtful survey of today's most fashionable attempts to decipher the cosmos on its smallest and largest scales."--Science "I can't recommend [Fashion, Faith, and Fantasy in the New Physics of the Universe] too highly to anyone with a serious interest in fundamental questions about physics."--Peter Woit, Not Even Wrong blog "In standing outside the fray and criticising the central dogmas of fundamental physics, Penrose is playing the role of Einstein, who forced quantum theorists to defend and hone their ideas, and Sir Fred Hoyle, who persistently challenged Big Bang theorists to sharpen their ideas. This is an extremely important role, and long may Penrose fulfill it."--Times Higher Education "[A] beautifully produced, beautifully laid-out and diagrammed book... There is possibly no better or more original expositor than Penrose to draw from. If modern physics theory is of interest to you, you certainly won't want to ignore this book."--Math Frolic "The book is replete with phenomenal visual representations of the physics under discussion, a reminder of Penrose's ability to see and describe physics in a unique way... Ultimately, what is most valuable about the book is the excellent example he offers in how to ask questions."--Chanda Prescod-Weinstein, Physics World "Something is rotten in the state of physics... The eminent mathematician and physicist Roger Penrose identifies several possible sources of the rot... He is not one to be intimidated by an overwhelming majority, no matter how illustrious and vocal it is. He sets out his objections politely and with exemplary patience towards the keepers of physics orthodoxy... Time will tell whether any of his judgments are correct. In the meantime, his critics would do well to remember George Bernard Shaw's warning: 'The minority is sometimes right; the majority is always wrong.'"--Graham Farmelo, Guardian "A valuable insight into what one of the most prominent theoretical physicists of recent times makes of reality's relationship to ideas in quantum theory, standard cosmology, and theories that pretend to replace them."--Richard Webb, New Scientist "The strength of this book is how the reader can appreciate science as a human undertaking."--Choice "The most important thing is not exactly what he writes about string theory, cosmology and quantum mechanics in his latest book ... but that a book so wide and deep in its erudition could be written at all. If his successors cannot do the same, science will be all the poorer."--Philip Ball, Prospect

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