The Geometric Universe

Science, Geometry, and the Work of Roger Penrose

Edited by S. A. Huggett, L. J. Mason, K. P. Tod, S. T. Tsou, and N. M. J. Woodhouse

The Geometric Universe

Science, Geometry, and the Work of Roger Penrose

Edited by S. A. Huggett, L. J. Mason, K. P. Tod, S. T. Tsou, and N. M. J. Woodhouse

Description

This collection has been inspired by the work of Roger Penrose. It gives an overview of current work on the interaction between geometry and physics, from which many important developments in research have emerged. This volume collects together the contributions of many important researchers, including Sir Roger himself, and gives an overview of the many applications of geometrical ideas and techniques across mathematics and the physical sciences. From the area of pure mathematics papers are included on the topics of classical differential geometry and non-commutative geometry, knot invariants, and the applications of gauge theory. Contributions from applied mathematics cover the topics of integrable systems and general relativity. Current research in experimental and theoretical physics inspired chapters on string theory, quantum gravity, the foundations of quantum mechanics, quasi-crystals and astrophysics. The collection also includes articles on quantum computation, quantum cryptography and the possible role of micro-tubules in a theory of consciousness.

The Geometric Universe

Science, Geometry, and the Work of Roger Penrose

Edited by S. A. Huggett, L. J. Mason, K. P. Tod, S. T. Tsou, and N. M. J. Woodhouse

I. PLENARY LECTURES
1. Roger Penrose - a personal appreciation
2. Hypercomplex manifolds and the space of framings
3. Gauge theory in higher dimensions
4. Noncommutative differential geometry and the structure of space-time
5. Einstein's equation and conformal structure
6. Twistors, geometry, and integrable systems
7. On four-dimensional Einstein manifolds
8. Loss of information in black holes
9. Fundamental geometry: the Penrose-Hameroff 'Orchor' model of consciousness
10. Implications of transience for spacetime structure
11. Geometric issues in quantum gravity
12. From quantum code-making to quantum code-breaking
13. Penrose tilings and quasicrystals revisited
14. Decaying neutrinos and the geometry of the universe
15. Quantum geometric origin of all forces in string theory
16. Space from the point of view of loop groups
II. PARALLEL SESSION I: QUANTUM THEORY AND BEYOND
17. The twistor diagram programme
18. Geometric models for quantum statistical inference
19. Spin networks and topology
20. The physics of spin networks
III. PARALLEL SESSION II: GEOMETRY AND GRAVITY
21. The Sen conjecture for distinct fundamental monopoles
22. An unorthodox view of CG via characteristic surfaces
23. Amalgamated Codazzi Raychaudhuri identity for foliation
24. Abstract/virtual/reality/complexity
IV. PARALLEL SESSION III: FUNDAMENTAL QUESTIONS IN QUANTUM MECHANICS
25. Interaction-free measurements
26. Quantum measurement problem and the gravitational field
27. Entanglement and quantum computation
V. PARALLEL SESSION IV: MATHEMATICAL ASPECTS OF TWISTOR THEORY
28. Penrose transform for flag domains
29. Twistor solution of the holonomy problem
30. The Penrose transform and real integral geometry
31. Pythagorean spinors and Penrose twistors
VI. AFTERWORD
32. Afterword

The Geometric Universe

Science, Geometry, and the Work of Roger Penrose

Edited by S. A. Huggett, L. J. Mason, K. P. Tod, S. T. Tsou, and N. M. J. Woodhouse

Author Information

Contributors:

Jeeva Anandan, Max-Planck-Institut für Physik Föhringer Ring 6, D-80805 Munich, Germany and Department of Physics and Astronomy, University of South Carolina, Columbia, SC 20208, USA Abhay Ashtekar, The Center for Gravitational Physics and Geometry, The Physics Department, Penn State University, University Park, PA 16802-6300, USA Sir Michael Atiyah, The Master's Lodge, Trinity College, Cambridge, CB2 1TQ Toby Bailey, Department of Mathematics, University of Edinburgh, James Clerk Maxwell Building, The King's Buildings, Mayfield Road, Edinburgh EH9 3JZ Dorje C Brady, Blackett Laboratory, Imperial College, South Kensington, London SW7 2BZ Brandon Carter,Department d'Astrophysique Relativiste et de Cosmologie, Observatoire de Paris, Place J Janssen, F-92195 Meudon Cedex, France Alain Connes, Department of Mathematics, Collège de France, 11 Place Marcellin Berthelet, 75005 Paris Cedex 05, France Simon Donaldson, Mathematical Institute, 24 - 29 St Giles', Oxford, OX1 3LB Artur Ekert, The Clarendon Laboratory, Parks Road, Oxford, OX1 3PU Helmut Friedrich, The Albert Einstein Institute, The Max-Planck-Institute für Gravitationaphysik, Schlaatzweg 1, D-14473 Potsdam, Germany Simonetta Frittelli, Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, USA Gary Gibbons, Department of Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge, CB3 9EW Simon Gindikin, Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA Stuart Hameroff, Department of Anaesthesiology, University of Arizona, Tucson AZ 8572, USA Stephen Hawking, Department of Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge, CB3 9EW Nigel Hitchin, Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB Andrew Hodges , Wadham College, Oxford, OX1 3BN Richard Josza, School of Mathematics and Statistics, University of Plymouth, Plymouth, PL4 8AA Lane Hughston, Merrill Lynch International, 25 Ropemaker Street, London, EC2Y 9LY Louis Kauffman, Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 South Morgan Street, Chicago, Illinois 60607-7045, USA Carlos Kozameh, FaMAF, Universidad Nacional de Córdoba, 5000 Córdoba, Argentina Claude Lebrun, Department of Mathematics, State University of New York at Stonybrook, Stonybrook, NY 11794, USA Sergei Merkulov, Department of Mathematics, University of Glasgow, G12 8QW Ted Newman, The Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, USA Sir Roger Penrose, Mathematical Institute, 24 - 29 St Giles', OXFORD, OX1 3LB L J Schwachhöfer, Universität Leipzig Dennis Sciama, SISSA/ISAS, Via Beirut 2-4, 34013 Trieste, Italy Graeme Segal, Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge, CB2 1SB Abner Shimony, Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, MA 02215 , USA Lee Smolin, The Center for Geometry and Gravity, The Physics Department, Penn State University, University Park, PA 16802-6300, USA George Sparling, The Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh , PA 15260, USA Paul Steinhardt, Department of Physics and Astronomy, David Rittenhouse Laboratory, University of Pennsylvania, Philadelphia, PA 19104-6396, USA R P Thomas, The Mathematical Institute, 24 - 29 St Giles', Oxford, OX1 3LB Andrzej Trautman, Instytut Fizyki Teoretycznej, Uniwersytet Warszawski, ul Hoza 69, PL-00681 Warszawa, Poland Lev Vaidman, School of Physics and Astronomy, Raymond and Beverly Sackler, Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel Gabriele Veneziano, Theory Division, CERN, Geneva, Switzerland Richard Ward, Department of Mathematical Sciences, University of Durham, Durham, DH1 3LE John A Wheeler, Department of Physics, Princeton University, Princeton, New Jersey, USA

The Geometric Universe

Science, Geometry, and the Work of Roger Penrose

Edited by S. A. Huggett, L. J. Mason, K. P. Tod, S. T. Tsou, and N. M. J. Woodhouse

Reviews and Awards

"Internationally renowned theoretical physicist Penrose invented twistor theory, a radical new approach to space-time where geometric points no longer enter the theory as primitives. More recently, he has stirred controversy with two books that invoke modern physics to plumb the nature of human consciousness. This festschrift honoring Penrose on his 65th birthday contains survey articles by some of the most eminent mathematicians (Atiyah, Donaldson, Connes, et al.) and physicists (Hawking, Astekar, Veneziano, among others) of our time. Besides browsing the most formidable contributions, undergraduates may particularly benefit from Artur Ekert's introduction to quantum cryptography, Paul Steinhardt's new approach to Penrose tilings, and particularly, biologist Stuart Hameroff's defense of Penrose's theories of consciousness from the charge of merely constituting a 'minimization of mysteries.' Highly recommended. Undergraduates through faculty."--Choice

"This book grew out of a symposium ... honoring Roger Penrose (b. 1931) at the age of 65. Even at an early age, it was noted about Penrose that he 'thinks geometrically.' His geometrical thinking led him, in 1974, to a solution of a problem that had eluded Johannes Kepler and Albrecht Dürer, that is, how to cover a surface with motifs of pentagonal symmetry without gaps and overlaps, the Penrose tiling. ... In this volume, Paul Steinhardt ... revisits the Penrose tiling and quasicrystals, reports recent results in modeling, and points out the still unresolved problems. ... The Penrose tiling was an inadvertent discovery, a result of almost idle doodling. The main areas of Penrose's research include time-space, quantum theory, and the workings of the mind ... [and m]ost of the 32 contributions in this book, including Penrose's own Afterword, concern Penrose's main activities. The book is introduced by a brief and charming Laudatio by John A. Wheeler."--The Chemical Intelligencer