The Geometric Universe: Science, Geometry, and the Work of Roger Penrose

Hardcover | March 1, 1998

EditorS. A. Huggett, Lionel J. Mason, K. P. Tod

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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 importantresearchers, 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-commutativegeometry, 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 ofquantum 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.

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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 importantresearchers, including Sir Roger himself, and gives an ...

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Format:HardcoverDimensions:450 pages, 9.21 × 6.14 × 1.18 inPublished:March 1, 1998Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198500599

ISBN - 13:9780198500599

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Table of Contents

I. PLENARY LECTURES1. Roger Penrose - a personal appreciation2. Hypercomplex manifolds and the space of framings3. Gauge theory in higher dimensions4. Noncommutative differential geometry and the structure of space-time5. Einstein's equation and conformal structure6. Twistors, geometry, and integrable systems7. On four-dimensional Einstein manifolds8. Loss of information in black holes9. Fundamental geometry: the Penrose-Hameroff 'Orchor' model of consciousness10. Implications of transience for spacetime structure11. Geometric issues in quantum gravity12. From quantum code-making to quantum code-breaking13. Penrose tilings and quasicrystals revisited14. Decaying neutrinos and the geometry of the universe15. Quantum geometric origin of all forces in string theory16. Space from the point of view of loop groupsII. PARALLEL SESSION I: QUANTUM THEORY AND BEYOND17. The twistor diagram programme18. Geometric models for quantum statistical inference19. Spin networks and topology20. The physics of spin networksIII. PARALLEL SESSION II: GEOMETRY AND GRAVITY21. The Sen conjecture for distinct fundamental monopoles22. An unorthodox view of CG via characteristic surfaces23. Amalgamated Codazzi Raychaudhuri identity for foliation24. Abstract/virtual/reality/complexityIV. PARALLEL SESSION III: FUNDAMENTAL QUESTIONS IN QUANTUM MECHANICS25. Interaction-free measurements26. Quantum measurement problem and the gravitational field27. Entanglement and quantum computationV. PARALLEL SESSION IV: MATHEMATICAL ASPECTS OF TWISTOR THEORY28. Penrose transform for flag domains29. Twistor solution of the holonomy problem30. The Penrose transform and real integral geometry31. Pythagorean spinors and Penrose twistorsVI. AFTERWORD32. Afterword

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'It is always enjoyable to read him,lucid,precise and tinged with enthusiasm, both for what has been done and for those questions whose answers still elude us' General Relativity and Gravitation