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內容簡介

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.

作者簡介

Roger Penrose is Emeritus Rouse Ball Professor of Mathematics at Oxford University. He has received a number of prizes and awards, including the 1988 Wolf Prize for physics, which he shared with Stephen Hawking for their joint contribution to our understanding of the universe. His books include The Emperor's New Mind, Shadows of the Mind, and The Nature of Space and Time, which he wrote with Hawking. He has lectured extensively at universities throughout America. He lives in Oxford.

目錄

Preface
Acknowledgements
Notation
Prologue
1 The roots of science
　1.1 The cluest for the forces that shape the world
　1.2 Mathematical truth
　1.3 Is Plato's mathematical world 'real'?
　1.4 Three worlds and three deep mysteries
　1.5 The Good, the True, and the Beautiful
2 An ancient theorem and a modern question
　2.1 The Pythagorean theorem
　2.2 Euclid's postulates
　2.3 Similar-areas proof of the Pythagorean theorem
　2.4 Hyperbolic geometry: conformal picture
　2.5 Other representations of hyperbolic geometry
　2.6 Historical aspects of hyperbolic geometry
　2.7 Relation to physical space
3 Kinds of number in the physical world
　3.1 A Pythagorean catastrophe?
　3.2 The real-number system
　3.3 Real numbers in the physical world
　3.4 Do natural numbers need the physical world?
　3.5 Discrete numbers in the physical world
4 Magical complex numbers
　4.1 The magic number 'i'
　4.2 Solving equations with complex numbers
　4.3 Convergence of power series
　4.4 Caspar Wessel's complex plane
　4.5 How to construct the Mandelbrot set
5 Geometry of logarithms, powers, and roots
　5.1 Geometry of complex algebra
　5.2 The idea of the complex logarithm
　5.3 Multiple valuedness, natural logarithms
　5.4 Complex powers
　5.5 Some relations to modern particle physics
6 Real-number calculus
　6.1 What makes an honest function?
　6.2 Slopes of functions
　6.3 Higher derivatives; C~-smooth functions
　6.4 The 'Eulerian' notion of a function?
　6.5 The rules of differentiation
　6.6 Integration
7 Complex-number calculus
　7.1 Complex smoothness; holomorphic functions
　7.2 Contour integration
　7.3 Power series from complex smoothness
　7.4 Analytic continuation
8 Riemann surfaces and complex mappings
　8.1 The idea of a Riemann surface
　8.2 Conformal mappings
　8.3 The Riemann sphere
　8.4 The genus of a compact Riemann surface
　8.5 The Riemann mapping theorem
9 Fourier decomposition and hyperfunctions
　9.1 Fourier series
　9.2 Functions on a circle
　9.3 Frequency splitting on the Riemann sphere
　9.4 The Fourier transform
　9.5 Frequency splitting from the Fourier transform
　9.6 What kind of function is appropriate?
　9.7 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 rode in quantum state reduction

The Road to Reality 真實之路 英文原版 [平裝] 下載 mobi epub pdf txt 電子書

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人體中的一個組織細胞，從齣生時候就已經決定瞭它所在的位置，比如一個肝細胞，如果以它自身的能量，想從肝髒移動到心髒，是不可能的，因為它絕沒有這個本領，但是作為醫生——人來說，想把身體中的某一個部分移動到另一個位置，排除生命體徵本身，幾乎是輕而易舉的。因為肝細胞相對於人體來說，無論從質量、大小、能量等等都是無法比擬的，它隻能待在它應該待的地方，如果從人對細胞的角度來說，那就相當於我們人類與幾韆萬光年以外的地方相比，可望而不可及。

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與愛因斯坦的相對論並不矛盾，我們的星球相對於這個巨大的生命體來說，實在是太小瞭，小到可以認為是一個原子，太陽係也不過是這個生命體中的一個小小的細胞，因此，我們無論如何也不可能看到它的邊緣，就象那個肝細胞永遠不會“看”到我們皮膚之外的空間一樣。

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