Road to reality with Roger Penrose / edited by James Ladyman, Stuart Presnell, Gordon McCabe, Michał Eckstein, Sebastian J. Szybka.

Online resource; title from PDF title page (EBSCO, viewed September 11, 2015).

Includes bibliographical references.

Road to Reality with Roger Penrose -- Authors -- Contents -- Chapter 1. From geometric quantum mechanics toquantum information -- 1.1 Introduction -- 1.2 Geometrical formulation of the Hilbert space picture -- 1.2.1 From Hermitian operators to real-valued functions -- 1.2.2 The Fubini?Study metric seen from the Hilbert space -- 1.2.3 From Hermitian inner products to classical tensor fields -- 1.2.4 Pull-back structures on submanifolds of H -- 1.3 Some applications : composite systems, entanglementand separability -- 1.3.1 Separable and maximal entangled pure states

1.3.2 Quantitative statements1.3.3 Mixed states entanglement and invariant operator valuedtensor fields -- 1.4 From quantum to classical information -- 1.5 Conclusions and outlook -- Chapter 2. Black holes in general relativity -- 2.1 Introduction -- 2.1.1 Newtonian considerations -- 2.1.2 General relativity -- 2.2 Black holes in general relativity -- 2.2.1 Early history -- 2.2.2 Uniqueness -- 2.3 Event horizons and their unforeseen properties -- 2.3.1 Event horizons -- 2.3.2 An unexpected treasure trove -- 2.4 Epilogue -- 2.4.1 Spookiness of event horizons

2.4.2 Quasi-local horizonsChapter 3. Gravitational energy: a quasi-local, Hamiltonian approach -- 3.1 Introduction -- 3.2 Symplectic relations and their generating functions -- 3.3 Lagrangian and Hamiltonian formulations of mechanics -- 3.4 Field dynamics as a symplectic relation -- 3.5 Example: symmetric versus canonical energy in Maxwell electrodynamics -- 3.6 Homogeneous Hamiltonian identity in canonical relativity -- 3.7 Examples of the gravitational boundary control and corresponding Hamiltonians -- 3.8 Concluding remarks

Chapter 4. General relativity and von Neumann algebras4.1 Introduction -- 4.2 Space-time as a noncommutative space -- 4.3 Algebra of random operators -- 4.4 Differential algebra -- 4.5 Generalized space-time geometry -- 4.6 General relativity on random operators -- 4.7 Concluding remarks -- Appendix -- Chapter 5. Penrose?s metalogical argument is unsound -- 5.1 Introduction -- 5.2 Necessary conditions for out-Gödeling -- 5.3 Inconsistency/unsoundness of the antimechanist -- 5.4 A relevant discovery: Gödel?s unknowability thesis -- 5.5 Penrose?s new argument

5.6 Evolution of machines: robots and the mind5.7 A?natural? view of mathematics -- Chapter 6. Mach?s Principle within general relativity -- 6.1 Introduction -- 6.2 A Newtonian non-relativistic mechanics without absolute space -- 6.3 Machian phenomena predicted by general relativity -- 6.3.1 Accelerated inertial frames -- 6.3.2 Rotating inertial frames -- 6.3.3 Induced centrifugal force -- 6.3.4 Mass induction -- 6.4 Closed Universes rotation and the cosmological constant -- Chapter 7. Algebraic approach to quantum gravity I: relative realism -- 7.1 Introduction

English.

Where does the road to reality lie? This fundamental question is addressed in this collection of essays by physicists and philosophers, inspired by the original ideas of Sir Roger Penrose, the English mathematical physicist and philosopher of science. The topics range from black holes and quantum information to the very nature of mathematical cognition itself.--Provided by publisher.

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