The Road to Reality: A Complete Guide to the Laws of the Universe
Roger Penrose |
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Summary: Roger Penrose, one of the most accomplished scientists of our time, presents the only comprehensive and comprehensible account of the physics of the universe. From the very first attempts by the Greeks to grapple with the complexities of our known world to the latest application of infinity in physics, "The Road to Reality" carefully explores the movement of the smallest atomic particles and reaches into the vastness of intergalactic space. Here, Penrose examines the mathematical foundations of the physical universe, exposing the underlying beauty of physics and giving us one the most important works in modern science writing.
Table of Contents 1 The roots of science 7 2 An ancient theorem and a modern question 25 3 Kinds of number in the physical world 51 4 Magical complex numbers 71 5 Geometry of logarithms, powers, and roots 86 6 Real-number calculus 103 7 Complex-number calculus 122 8 Riemann surfaces and complex mappings 135 9 Fourier decomposition and hyperfunctions 153 10 Surfaces 179 11 Hypercomplex numbers 198 12 Manifolds of n dimensions 217 13 Symmetry groups 247 14 Calculus on manifolds 292 15 Fibre bundles and gauge connections 325 16 The ladder of infinity 357 17 Spacetime 383 18 Minkowskian geometry 412 19 The classical fields of Maxwell and Einstein 440 20 Lagrangians and Hamiltonians 471 21 The quantum particle 493 22 Quantum algebra, geometry, and spin 527 23 The entangled quantum world 578 24 Dirac's electron and antiparticles 609 25 The standard model of particle physics 627 26 Quantum field theory 655 27 The Big Bang and its thermodynamic legacy 686 28 Speculative theories of the early universe 735 29 The measurement paradox 782 30 Gravity's role in quantum state reduction 816 31 Supersymmetry, supra-dimensionality, and strings 869 32 Einstein's narrower path; loop variables 934 33 More radical perspectives; twistor theory 958 34 Where lies the road to reality? 1010 |