The quantum structure of space and time : proceedings of the 23rd Solvay Conference on Physics, Brussels, Belgium, 1-3 December, 2005

Ever since 1911, the Solvay Conferences have shaped modern physics. The 23rd edition, chaired by 2004 Nobel Laureate David Gross, did not break with that tradition. It gathered most of the leading figures working on the central problem of reconciling Einstein's theory of gravity with quantum mechanics.These proceedings give a broad overview with unique insight into the most fundamental issues raised by this challenge for 21st century physics, by distinguished renowned scientists. The contributions cover: the status of quantum mechanics, spacetime singularities and breakdown of classical space and time, mathematical structures underlying the most promising attempts under current development, spacetime as an emergent concept, as well as cosmology and the cosmological constant puzzle. A historical overview of the Solvay conferences by historian of sciences Peter Galison opens the volume.In the Solvay tradition, the volume also includes the discussions among the participants -- many of which were quite lively and illustrate dramatically divergent points of view -- carefully edited and reproduced in full.

Peter GalisonJames B. HartleGary W. GibbonsRobbert DijkgraafNathan SeibergDavid Gross

The International Solvay Institutes	p. v
23rd Solvay Conference on Physics	p. ix
Opening Session	p. xiii
1 History	p. 1
1.1 Rapporteur talk: Solvay Redivivus	p. 1
1.1.1 Three Miracles	p. 1
1.1.2 SOLVAY -1: Einstein-Lorentz, Einstein-Poincare	p. 6
1.1.3 Ignoramus, Ignorabimus at Solvays-5 and Solvay-6	p. 10
1.1.4 Solvay Redivivus	p. 15
1.2 Discussion	p. 19
2 Quantum Mechanics	p. 21
2.1 Rapporteur talk: Generalizing Quantum Mechanics	p. 21
2.1.1 Abstract	p. 21
2.1.2 Introduction	p. 22
2.1.3 Quantum Mechanics Today	p. 24
2.1.4 Spacetime and Quantum Theory	p. 26
2.1.5 The Quantum Mechanics of Closed Systems	p. 27
2.1.6 Quantum Theory in 3+1 Form	p. 30
2.1.7 Generalized Quantum Theory	p. 32
2.1.8 A Quantum Theory of Spacetime Geometry	p. 33
2.1.9 Beyond Spacetime	p. 35
2.1.10 Emergence/Excess Baggage	p. 35
2.1.11 Emergence of Signature	p. 38
2.1.12 Beyond Quantum Theory	p. 39
2.1.13 Conclusion	p. 40
2.2 Discussion	p. 44
3 Singularities	p. 51
3.1 Rapporteur talk: Singularities	p. 51
3.1.1 Introduction	p. 51
3.1.2 Singularity Theorems	p. 51
3.1.3 Cosmic Censorship	p. 53
3.1.4 Classical Boundary Conditions and Stability	p. 54
3.1.5 Boundary Conditions in Cosmology	p. 55
3.1.6 Higher dimensional resolutions	p. 59
3.1.7 Singularities at the end of Hawking Evaporation	p. 61
3.1.8 Maldacena's Conjecture	p. 61
3.2 Discussion	p. 64
3.3 Prepared Comments	p. 65
3.3.1 Gary Horowitz: Singularities in String Theory	p. 65
3.4 Discussion	p. 69
3.5 Prepared Comments	p. 70
3.5.1 Eva Silverstein: Singularities: Closed String Tachyons and Singularities	p. 70
3.6 Discussion	p. 77
3.7 Prepared Comments	p. 77
3.7.1 Thibault Damour: Cosmological Singularities and E[subscript 10]	p. 77
3.8 Discussion	p. 82
3.9 Prepared Comments	p. 83
3.9.1 Abhay Ashtekar: Singularities: quantum nature of the big bang in loop quantum gravity	p. 83
3.10 Discussion	p. 87
4 Mathematical Structures	p. 91
4.1 Rapporteur talk: Mathematical Structures	p. 91
4.1.1 Abstract	p. 91
4.1.2 Quantum Theory and Mathematics	p. 91
4.1.3 The quantum geometry of string theory	p. 97
4.1.4 Non-perturbative string theory and branes	p. 107
4.1.5 D-branes	p. 112
4.1.6 The Role of Mathematics	p. 116
4.2 Discussion	p. 119
4.3 Prepared Comments	p. 123
4.3.1 Renata Kallosh: Stabilization of moduli in string theory	p. 123
4.3.2 Dieter Lust: A short remark on flux and D-brane vacua and their statistics	p. 127
4.3.3 Michael Douglas: Mathematics and String Theory: Understanding the landscape	p. 132
4.4 Discussion	p. 140
4.5 Prepared Comments	p. 143
4.5.1 Nikita Nekrasov: On string theory applications in condensed matter physics	p. 143
4.5.2 Shing-Tung Yau: Mathematical Structures: Geometry of Six-Dimensional String	p. 147
4.6 Discussion	p. 151
4.7 Prepared Comments	p. 153
4.7.1 Hermann Nicolai: E[subscript 10] and K(E[subscript 10]): prospects and challenges	p. 153
4.7.2 Michael Atiyah: Beyond string theory?	p. 157
4.8 Discussion	p. 159
5 Emergent Spacetime	p. 163
5.1 Rapporteur talk: Emergent Spacetime	p. 163
5.1.1 Introduction	p. 163
5.1.2 Ambiguous space	p. 164
5.1.3 Non-standard theories without gravity	p. 168
5.1.4 Derived general covariance	p. 169
5.1.5 Examples of emergent space	p. 170
5.1.6 Emergent time	p. 175
5.1.7 Conclusions and speculations	p. 176
5.2 Discussion	p. 179
5.3 Prepared Comments	p. 182
5.3.1 Tom Banks: The Holographic Approach to Quantum Gravity	p. 182
5.3.2 Igor Klebanov: Confinement, Chiral Symmetry Breaking and String Theory	p. 191
5.3.3 Juan Maldacena: Comments on emergent space-time	p. 195
5.3.4 Alexander Polyakov: Beyond space-time	p. 199
5.4 Discussion	p. 204
6 Cosmology	p. 215
6.1 Rapporteur talk: The cosmological constant and the string landscape, by Joseph Polchinski	p. 216
6.1.1 The cosmological constant	p. 216
6.1.2 The string landscape	p. 225
6.1.3 Conclusions	p. 233
6.2 Discussion	p. 237
6.3 Prepared Comments	p. 242
6.3.1 Steven Weinberg	p. 242
6.3.2 Renata Kallosh: Inflationary models as a test of string theory	p. 246
6.3.3 Andrei Linde: Eternal inflation in stringy landscape and the anthropic principle	p. 250
6.4 Discussion	p. 255
6.4.1 Paul J. Steinhardt: A modest proposal for solving the cosmological constant problem	p. 258
6.5 Discussion	p. 264
7 Closing remarks	p. 269

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