Cover image for The geometric universe : science, geometry, and the work of Roger Penrose
The geometric universe : science, geometry, and the work of Roger Penrose
Huggett, S. A.
Publication Information:
Oxford ; New York : Oxford University Press, 1998.
Physical Description:
xviii, 431 pages : illustrations ; 24 cm
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Central Library QC20.7.G44 G463 1998 Adult Non-Fiction Central Closed Stacks

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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.

Author Notes

Mathematical Institute, 24-29 St Giles', OXFORD, OX1 3LB. Tel: +44 1865 273525; fax: +44 1865 273583

Reviews 1

Choice Review

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. D. V. Feldman; University of New Hampshire

Table of Contents

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

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