The theory of the quantum world : proceedings of the 25th Solvay Conference on Physics, Brussels, Belgium, 19th-22nd October, 2011

Ever since 1911, the Solvay Conferences have shaped modern physics. The 25th edition held in October 2011 in Brussels and chaired by David Gross continued this tradition and celebrated the first centennial of this illustrious series of conferences. The development and applications of quantum mechanics have always been the main threads in the history of the Solvay Conferences, hence the 25th Solvay conference gathered many of the leading figures working on a wide variety of profound problems in physics where quantum mechanical effects play a central role. The conference addressed some of the most pressing open questions in the field of physics. The proceedings contain the "rapporteur talks" which give a broad overview with unique insights by distinguished and renowned scientists. These lectures cover the seven sessions: "History and Reflections", "Foundations of Quantum Mechanics and Quantum Computation", "Control of Quantum Systems", "Quantum Condensed Matter", "Particles and Fields", "Quantum Gravity and String Theory" and it ended with a general discussion attempting to arrive at a synthesis. In the Solvay tradition, the proceedings also include the prepared comments to the rapporteur talks. The discussions among the participants — some of which quite lively and involving dramatically divergent points of view — have been carefully edited and are reproduced in full. Readership: Graduate students and researchers in physics. Contents 24 The International Solvay Institutes 6 In Memoriam Jacques Solvay (1920-2010) 9 25th Solvay Conference on Physics 10 Opening Session 14 Session 1: History and Reflections Chair: M. Henneaux 26 John L. Heilbron: The First Solvay Council “A sort of private conference”a 26 1. Introduction 26 2. Soda and Energy 27 3. Positivism and Progress 30 4. International Connections 32 5. The Council of 1911 34 Works Cited 37 References 39 Murray Gell-Mann: From Solvay 1961 to Solvay 2011 42 Session 2: Foundations of Quantum Mechanics and Quantum Computation Chair: A. Aspect 46 Rapporteur talk by A. Leggett: The Structure of a World Described by Quantum Mechanics 46 References 60 Prepared comments 61 Discussion 69 Prepared comments 77 Discussion 84 Rapporteur talk by J. Preskill: Quantum Entanglement and Quantum Computing 88 1. Introduction: Toward Quantum Supremacy 88 2. Quantum Entanglement and the Vastness of Hilbert Space 89 3. Separating Classical from Quantum 91 4. Easiness and Hardness 92 5. Local Hamiltonians 94 6. Quantum Error Correction 96 7. Scalable Quantum Computing 98 8. Topological Quantum Computing 99 9. Quantum Computing vs. Quantum Simulation 100 10. Conclusions and Questions 101 Acknowledgments 102 References 102 Prepared comment 106 Discussion 109 Session 3: Control of Quantum Systems Chair: P. Zoller 116 Rapporteur talk by I. Cirac: Quantum Computing and Simulation with Atoms and Photons 116 1. Introduction 116 2. Bottom-up Approach: Quantum Information 118 3. Top-down Approach: Quantum Simulations 121 4. Conclusions 125 References 126 Prepared comments 127 Discussion 134 Rapporteur talk by S. Girvin: Quantum Machines: Coherent Control of Mesoscopic Solid-State Systems 141 1. Introduction 141 2. Superconducting Qubits and Quantum Microwave Circuits 141 2.1. Quantum Limited Amplification, Measurement and Feedback 142 2.2. Future Directions for Superconducting Qubits 144 3. Quantum Optomechanics 147 4. Summary 148 Acknowledgments 148 References 148 Prepared comment 152 Discussion 154 Prepared comments 157 Discussion 161 Prepared comments 164 Discussion 168 Session 4: Quantum Condensed Matter Chair: B. Halperin 170 Rapporteur talk by S. Sachdev: The Quantum Phases of Matter 170 1. Introduction 170 2. Gapped Quantum Matter 173 3. Conformal Quantum Matter 178 4. Compressible Quantum Matter 185 5. Connections to String Theory 190 Acknowledgments 196 References 196 Discussion 203 Prepared comments 206 Discussion 209 Prepared comments 211 Discussion 215 Prepared comments 222 Discussion 227 Session 5: Particles and Fields Chair: H. Georgi 235 Rapporteur talk by F. Wilczek: A Long View of Particle Physics 235 1. Origins: Understanding Matter 235 2. Phenomena: New Questions and Surprising Answers 236 3. Questions That the Standard Model Begs 238 3.1. Questions from the Core 238 3.2. Loose Ends 238 3.3. Gravity 239 4. Approaches: “Modest” Improvements 240 4.1. Unification and Supersymmetry 240 4.2. Θ Problem and Axions 242 5. Experimental Frontiers 243 6. Cosmic Questions: Way Beyond the Standard Model 244 6.1. Kinematics and Dynamics 244 6.2. Dynamics and Initial Values 244 6.3. The Ubiquity of Spinors 245 6.4. Information as Foundation? 245 Acknowledgments 246 Discussion 247 Prepared comments 254 Discussion 265 Prepared comments 268 Discussion 273 Session 6: Quantum Gravity and String Theory Chair: J. Polchinski 275 Rapporteur talk by J. Maldacena: The Quantum Spacetime 275 1. Classical Spacetime Dynamics 275 2. Quantum Spacetime 276 3. Two Surprising Predictions 276 4. Quantization at Low Energies 276 5. UV Completion in Field Theory 277 6. UV Completion in Gravity? 277 7. Perturbative String Theory 277 8. Unification 278 9. Beyond Perturbation Theory? 278 10. Beyond Perturbation Theory 278 11. Non Perturbative Quantum Spacetimes 279 12. Hyperbolic Space 279 13. Quantum Hyperbolic Space 279 14. Emergent Space 280 15. Black Holes in AdS 280 16. The Information Problem 280 17. The Information Problem 281 18. Lessons 281 19. String Theory and the Real World 282 20. Some Unsolved Problems 283 Acknowledgments 283 References 283 Discussion 285 Prepared comments 290 Discussion 296 Rapporteur talk by A. Guth: Quantum Fluctuations in Cosmology and How they Lead to a Multiverse 301 1. Introduction 301 2. Origin of Density Perturbations During the Inflationary Era 301 3. Evolution of the Density Perturbations Through the End of Inflation 309 4. Simplifying the Description 312 5. Deducing the Consequences, Comparing with Observation 314 6. Outstanding Questions About Density Perturbations 317 7. Fluctuations on Larger Scales: Eternal Inflation? 318 References 321 Prepared comments 325 Discussion 333 Session 7: General Discussion and Conclusions Chair: D. Gross 342 Alain Aspect: Foundations of Quantum Mechanics and Quantum Computation 342 Peter Zoller: Control of Quantum Systems 350 Bertrand Halperin: Quantum Condensed Matter 357 Howard Georgi: Particles and Fields 363 Joseph Polchinski: Quantum Gravity and String Theory 372 David Gross: Conclusions 380 Closing Session Chair of the Conference David Gross 386 Address by the Director of the International Solvay Institutes Marc Henneaux 387 History And Reflections -- Foundations Of Quantum Mechanics And Quantum Computation -- Control Of Quantum Systems -- Quantum Condensed Matter -- Particles And Fields -- Quantum Gravity And String Theory -- General Discussion And Conclusions. Editors, David Gross, Marc Henneaux, Alexander Sevrin. Includes Bibliographical References.