1 Introduction 1
1.1 An explanation for the reader 1
1.2 How this book came about 4
1.3 A warning to the reader 5
1.4 The nature of physics and theoretical physics 6
1.5 The influence of our environment 7
1.6 The plan of the book 9
1.7 Apologies and words of encouragement 10
1.8 References 10
Case Study Ⅰ The origins of Newton's laws of motion and of gravity 13
Ⅰ.1 Reference 14
2 From Ptolemy to Kepler-the Copernican revolution 15
2.1 Ancient history 15
2.2 The Copernican revolution 18
2.3 Tycho Brahe-the lord of Uraniborg 21
2.4 Johannes Kepler and heavenly harmonies 25
2.5 References 32
3 Galileo and the nature of the physical sciences 34
3.1 Introduction 34
3.2 Galileo as an experimental physicist 34
3.3 Galileo's telescopic discoveries 40
3.4 The trial of Galileo-the heart of the matter 42
3.5 The trial of Galileo 47
3.6 Galilean relativity 48
3.7 Reflections 50
3.8 References 52
4 Newton and the law of gravity 53
4.1 Introduction 53
4.2 Lincolnshire 1642-61 53
4.3 Cambridge 1661-5 54
4.4 Lincolnshire 1665-7 54
4.5 Cambridge 1667-96 60
4.6 Newton the alchemist 62
4.7 The interpretation of ancient texts and the scriptures 65
4.8 London 1696-1727 67
4.9 References 68
Appendix to Chapter 4:Notes on conic sections and central orbits 68
A4.1 Equations for conic sections 68
A4.2 Kepler's laws and planetary motion 72
A4.3 Rutherford scattering 74
Case Study Ⅱ Maxwell's equations 77
5 The origin of Maxwell's equations 79
5.1 How it all began 79
5.2 Michael Faraday-mathematics without mathematics 82
5.3 How Maxwell derived the equations for the electromagnetic field 88
5.4 Heinrich Hertz and the discovery of electromagnetic waves 98
5.5 Reflections 100
5.6 References 102
Appendix to Chapter 5:Useful notes on vector fields 103
A5.1 The divergence theorem and Stokes'theorem 103
A5.2 Results related to the divergence theorem 103
A5.3 Results related to Stokes'theorem 105
A5.4 Vector fields with special properties 105
A5.5 Vector operators in various coordinate systems 106
A5.6 Vector operators and dispersion relations 108
A5.7 How to relate the different expressions for the magnetic fields produced by currents 109
6 How to rewrite the history of electromagnetism 114
6.1 Introduction 114
6.2 Maxwell's equations as a set of vector equations 115
6.3 Gauss's theorem in electromagnetism 115
6.4 Time-independent fields as conservative fields of force 117
6.5 Boundary conditions in electromagnetism 117
6.6 Ampère'slaw 121
6.7 Faraday's law 121
6.8 The story so far 122
6.9 Derivation of Coulomb's law 123
6.10 Derivation of the Bi？t-Savart law 125
6.11 The interpretation of Maxwell's equations in material media 126
6.12 The energy densities of electromagnetic fields 129
6.13 Concluding remarks 133
6.14 References 134
Case Study Ⅲ Mechanics and dynamics-linear and non-linear 135
Ⅲ.1 References 137
7 Approaches to mechanics and dynamics 138
7.1 Newton's laws ofmotion 138
7.2 Principles of'least action' 140
7.3 The Euler-Lagrange equation 143
7.4 Small oscillations and normal modes 147
7.5 Conservation laws and symmetry 152
7.6 Hamilton's equations and Poisson brackets 155
7.7 A warning 157
7.8 References 158
Appendix to Chapter 7:The motion of fluids 158
A7.1 The equation of continuity 158
A7.2 The equation of motion for an incompressible fluid in the absence of viscosity 161
A7.3 The equation of motion for an incompressible fluid including viscous forces 162
8 Dimensional analysis,chaos and self-organised criticality 165
8.1 Introduction 165
8.2 Dimensional analysis 165
8.3 Introduction to chaos 181
8.4 Scaling laws and self-organised criticality 193
8.5 Beyond computation 199
8.6 References 200
Case Study Ⅳ Thermodynamics and statistical physics 203
Ⅳ.1 References 205
9 Basic thermodynamics 206
9.1 Heat and temperature 206
9.2 Heat as motion versus the caloric theory of heat 207
9.3 The first law of thermodynamics 212
9.4 The origin of the second law of thermodynamics 222
9.5 The second law of thermodynamics 228
9.6 Entropy 238
9.7 The law of increase of entropy 240
9.8 The differential form of the combined first and second laws of thermodynamics 244
9.9 References 244
Appendix to Chapter 9-Maxwell's relations and Jacobians 245
A9.1 Perfect differentials in thermodynamics 245
A9.2 Maxwell's relations 246
A9.3 Jacobians in thermodynamics 248
10 Kinetic theory and the origin of statistical mechanics 250
10.1 The kinetic theory of gases 250
10.2 Kinetic theory of gases-first version 251
10.3 Kinetic theory of gases-second version 252
10.4 Maxwell's velocity distribution 257
10.5 The viscosity of gases 263
10.6 The statistical nature of the second law of thermodynamics 266
10.7 Entropy and probability 268
10.8 Entropy and the density of states 272
10.9 Gibbs entropy and information 276
10.10 Concluding remarks 278
10.11 References 278
Case Study Ⅴ The origius of the concept of quanta 281
Ⅴ.1 References 282
11 Black-body radiation up to 1895 283
11.1 The state of physics in 1890 283
11.2 Kirchhoff's law of emission and absorption of radiation 284
11.3 The Stefan-Boltzmann law 289
11.4 Wien's displacement law and the spectrum of black-body radiation 297
11.5 References 301
12 1895-1900:Planck and the spectrum of black-body radiation 303
12.1 Planck's early career 303
12.2 Oscillators and their radiation in thermal equilibrium 305
12.3 The equilibrium radiation spectrum of a harmonic oscillator 311
12.4 Towards the spectrum of black-body radiation 315
12.5 The primitive form of Planck's radiation law 318
12.6 Rayleigh and the spectrum of black-body radiation 320
12.7 Comparison of the laws for black-body radiation with experiment 323
12.8 References 325
Appendix to Chapter 12:Rayleigh's paper of 1900'Remarks upon the law of complete radiation' 326
13 Planck's theory of black-body radiation 329
13.1 Introduction 329
13.2 Boltzmann's procedure in statistical mechanics 329
13.3 Planck's analysis 333
13.4 Planck and'natural units' 336
13.5 Planck and the physical significance of h 338
13.6 Why Planck found the right answer 340
13.7 References 343
14 Einstein and the quantisation of light 345
14.1 1905-Einstein's annus mirabilis 345
14.2 'On an heuristic viewpoint concerning the production and transformation of light' 348
14.3 The quantum theory of solids 354
14.4 Debye's theory of specific heats 358
14.5 The specific heats of gases revisited 360
14.6 Conclusion 363
14.7 References 364
15 The triumph of the quantum hypothesis 366
15.1 The situation in 1909 366
15.2 Fluctuations of particles in a box 366
15.3 Fluctuations of randomly superposed waves 369
15.4 Fluctuations in black-body radiation 371
15.5 The first Solvay conference 373
15.6 Bohr's theory of the hydrogen atom 375
15.7 Einstein(1916)'On the quantum theory ofradiation' 383
15.8 The story concluded 388
15.9 References 390
Appendix to Chapter 15:The detection of signals in the presence of noise 391
A15.1 Nyquist's theorem and Johnson noise 391
A15.2 The detection of photons in the presence of background noise 393
A15.3 The detection of electromagnetic waves in the presence of noise 394
Case Study Ⅵ Special relativity 397
Ⅵ.1 Reference 399
16 Special relativity-a study in invariance 400
16.1 Introduction 400
16.2 Geometry and the Lorentz transformation 407
16.3 Three-vectors and four-vectors 410
16.4 Relativistic dynamics-the momentum and force four-vectors 416
16.5 The relativistic equations describing motion 419
16.6 The frequency four-vector 422
16.7 Lorentz contraction and the origin of magnetic fields 423
16.8 Reflections 425
16.9 References 426
Case Study Ⅶ General relativity and cosmology 429
17 An introduction to general relativity 431
17.1 Introduction 431
17.2 Essential features of the relativistic theory of gravity 434
17.3 Isotropic curved spaces 444
17.4 The route to general relativity 448
17.5 The Schwarzschild metric 452
17.6 Particle orbits about a point mass 454
17.7 Advance of perihelia of planetary orbits 461
17.8 Light rays in Schwarzschild space-time 464
17.9 Particles and light rays near black holes 466
17.10 Circular orbits about Schwarzschild black holes 468
17.11 Refefences 471
Appendix to Chapter 17:Isotropic curved spaces 472
A17.1 A brief history of non-Euclidean geometries 472
A17.2 Parallel transport and isotropic curved spaces 473
18 The technology of cosmology 478
18.1 Introduction 478
18.2 Joseph Fraunhofer 478
18.3 The invention of photography 479
18.4 The new generation of telescopes 481
18.5 The funding of astronomy 487
18.6 The electronic revolution 491
18.7 The impact of the Second World War 493
18.8 Ultraviolet,X-ray and y-rayastronomy 495
18.9 Reflections 497
18.10 References 498
19 Cosmology 499
19.1 Cosmology and physics 499
19.2 Basic cosmological data 500
19.3 The Robertson-Walker metric 505
19.4 Observations in cosmology 509
19.5 Historical interlude-steady state theory 515
19.6 The standard world models 517
19.7 The thermal history of the Universe 528
19.8 Nucleosynthesis in the early Universe 536
19.9 The best-buy cosmological model 540
19.10 References 543
Appendix to Chapter 19:The Robertson-Walker metric for an empty universe 543
20 Epilogue 547
Index 548