ProofWiki:Books/Roger Penrose/The Road to Reality: A Complete Guide to the Laws of the Universe

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Roger Penrose: The Road to Reality: A Complete Guide to the Laws of the Universe

Published 2004, Vintage.

ISBN 0-099-44068-7


Subject Matter


Contents

Preface
Acknowledgements
Notation
Prologue
1 The roots of science
2 An ancient theorem and a modern question
3 Kinds of number in the physical world
4 Magical complex numbers
5 Geometry of logarithms, powers, and roots
6 Real-number calculus
7 Complex-number calculus
8 Riemann surfaces and complex mappings
9 Fourier decomposition and hyperfunctions
10 Surfaces
11 Hypercomplex numbers
12 Manifolds of $n$ dimensions
13 Symmetry groups
14 Calculus on manifolds
15 Fibre bundles and gauge connections
16 The ladder of infinity
17 Spacetime
18 Minkowskian geometry
19 The classical fields of Maxwell and Einstein
20 Lagrangians and Hamiltonians
21 The quantum particle
22 Quantum algebra, geometry, and spin
23 The entangled quantum world
24 Dirac's electron and antiparticles
25 The standard model of particle physics
26 Quantum field theory
27 The Big Bang and its thermodynamic legacy
28 Speculative theories of the early universe
29 The measurement paradox
30 Gravity's role in quantum state reduction
31 Supersymmetry, supra-dimensionality, and strings
32 Einstein's narrower path; loop variables
33 More radical perspectives; twistor theory
34 Where lies the road to reality?
Epilogue
Bibliography
Index