Let There Be Light: The Story of Light from Atoms to Galaxies

Cover......Page 1
Contents......Page 16
Preface......Page 8
Acknowledgements......Page 14
1: Introducing Light......Page 36
1.1.2 The Middle Ages......Page 37
1.2.1 The visible spectrum......Page 39
1.3.1 The astronomical method......Page 40
1.3.2 Terrestrial measurement......Page 41
1.3.3 The speed of light in context......Page 43
1.4.2 The journey of a photon......Page 44
1.4.3 The eye is like a digital camera......Page 46
1.4.5 Why is the grass green?......Page 48
1.4.6 Seeing in the dark......Page 49
1.4.7 The branches of optics......Page 50
1.5.2 Light as a wave......Page 51
1.5.3 Maxwell’s electromagnetic waves......Page 52
1.5.4 Light as a particle......Page 53
1.5.5 An illustration of duality?......Page 54
1.6.1 Particles have wave properties......Page 55
1.6.2 The Copenhagen interpretation......Page 56
1.6.3 The universal messenger......Page 57
2: Geometrical Optics: Reflection......Page 58
2.1.1 Light takes the quickest route......Page 59
2.1.3 The quickest path via a reflection......Page 60
2.1.4 The law of reflection......Page 61
2.2.1 A plane mirror......Page 62
2.2.2 Reversal from left to right......Page 63
2.2.4 A spherical concave mirror......Page 64
2.2.5 Applications of concave mirrors......Page 67
2.2.6 The ‘death rays’ of Archimedes......Page 68
A historical interlude: Pierre de Fermat  (1601–1665)......Page 70
Appendix 2.1 The parabolic mirror......Page 72
3: Geometrical Optics: Refraction......Page 76
3.1.1 The refractive index......Page 77
3.1.2 The lifeguard problem......Page 78
3.1.4 Apparent depth......Page 80
3.1.5 The dilemma faced by light trying to leave glass......Page 82
3.1.6 Practical applications of total internal reflection......Page 83
3.1.7 Freedom of choice when a ray meets a boundary......Page 84
3.1.8 The mystery......Page 85
3.1.9 A practical puzzle — two-way mirrors......Page 86
3.2.1 The function of a lens......Page 87
3.2.2 Fermat’s principle applied to lenses......Page 88
3.3.1 Ray tracing through a thin lens......Page 89
3.3.2 Principal rays (thin lenses)......Page 90
3.3.4 Symmetry......Page 91
3.3.5 Breaking the symmetry......Page 92
3.3.6 An intuitive approach — the task of a lens......Page 93
3.4 Objects and images: diverging lenses......Page 95
3.5.2 Examples — lenses in contact......Page 96
3.5.3 The power of a lens......Page 97
3.6.1 The structure of the eye......Page 98
3.6.2 Common eye defects......Page 100
3.7.1 Distant objects......Page 102
3.7.2 Nearer but not clearer......Page 103
3.7.3 Angular magnification......Page 105
3.8.1 Compound microscopes......Page 107
3.8.2 Telescopes......Page 109
3.9 A final note on Fermat’s principle......Page 110
Appendix 3.1 The lifeguard problem......Page 111
Appendix 3.2 The lens equation......Page 113
Appendix 3.3 Calculating the power of spectacles......Page 114
4: Light from Afar — Astronomy......Page 116
4.1.2 Philosophical reasons why the earth should be round......Page 117
4.1.3 Experimental evidence that the earth is round......Page 118
4.2.1 The phases of the moon......Page 119
4.2.2 A lunar eclipse......Page 120
4.2.3 A solar eclipse......Page 122
4.3.1 Relative sizes of the sun and the moon......Page 124
4.3.3 Shrinking shadows......Page 125
4.3.4 The distance to the moon......Page 127
4.3.5 The distance to the sun......Page 128
4.3.6 A practical problem......Page 129
4.3.8 Astronomical distances......Page 131
4.4.2 Ptolemy’s geocentric model......Page 132
4.5.1 Frames of reference......Page 134
4.5.2 Copernicus and the heliocentric model......Page 135
4.5.3 Where did the epicycles come from?......Page 138
4.6 After Copernicus......Page 139
4.7 The solar system in perspective......Page 145
A historical interlude: Galileo Galilei (1564–1642)......Page 147
Appendix 4.1 Mathematics of the ellipse......Page 153
5.1 The birth of astrophysics......Page 156
5.1.1 Isaac Newton and gravitation......Page 157
5.1.2 Falling without getting nearer......Page 158
5.1.4 Newton’s law of gravitation......Page 160
5.1.5 Testing the law......Page 161
5.1.7 The period of the moon’s orbit......Page 164
5.2.1 The moon and the falling apple......Page 165
5.2.2 Predicting the existence of new planets......Page 166
5.3.1 Planets of other suns......Page 168
5.3.2 Other galaxies......Page 171
5.4.1 The steady state cosmological model......Page 173
5.4.2 The ‘big bang’ theory......Page 174
5.4.3 A blast from the past......Page 175
5.5.1 White dwarfs......Page 177
5.5.2 Supernovae......Page 178
5.5.3 Pulsars......Page 180
5.5.4 Black holes......Page 183
5.5.5 Escape velocities......Page 184
5.5.6 How to ‘see’ the invisible......Page 185
5.5.7 A strange event in the Milky Way......Page 186
A historical interlude: Isaac Newton (1642–1727)......Page 187
Appendix 5.1 Kepler’s third law, derived from Newton’s law of universal gravitation......Page 193
Appendix 5.2 Escape velocity......Page 194
6.1 Waves — the basic means of communication......Page 196
6.1.1 Mechanical waves in a medium......Page 198
6.1.2 Transverse waves......Page 199
6.1.3 Longitudinal waves......Page 200
6.2.2 From the sine of an angle to the picture of a wave......Page 203
6.2.3 An expression for a sine wave in motion......Page 205
6.2.4 Wave parameters......Page 206
6.3.1 The superposition principle......Page 207
6.4.2 Path difference and phase difference......Page 208
6.4.3 When two waves travelling in opposite directions meet......Page 209
6.4.4 A string fixed at both ends......Page 211
6.4.5 Standing waves......Page 213
6.5.1 Forced oscillations......Page 214
6.6 Resonance — a part of life......Page 215
6.6.1 The Tacoma Narrows bridge disaster......Page 216
6.6.2 The Mexico City earthquake......Page 217
6.8 The magic of sine and the simplicity of nature......Page 218
6.8.1 The sum of a number of sine waves......Page 219
A historical interlude: Jean Baptiste Joseph Fourier (1768–1830)......Page 220
Appendix 6.1 The speed of transverse waves on a string......Page 223
Appendix 6.2 Dimensional analysis......Page 225
Appendix 6.3 Calculation of the natural frequencies of a string fixed at both ends......Page 226
7.1.1 Sound as a pressure wave......Page 228
7.1.2 The speed of sound......Page 229
7.1.3 Ultrasound and infrasound......Page 230
7.2 Sound as a tool......Page 231
7.3 Superposition of sound waves......Page 240
7.3.1 Standing waves......Page 241
7.4 Sound intensity......Page 243
7.4.1 Real and perceived differences in the intensity of sound......Page 245
7.4.2 Quantifying perception......Page 246
7.4.3 Intensity level (loudness)......Page 248
7.4.4 The ‘annoyance factor’......Page 250
7.5.1 Pitch......Page 251
7.5.3 Propagation of sound in open and confined spaces......Page 253
7.6 Strings and pipes in music......Page 256
7.7 The Doppler effect......Page 257
7.7.2 A moving source......Page 258
7.7.3 Two Doppler effects?......Page 259
7.7.4 Moving away from a source at almost the speed of sound......Page 260
7.7.5 Shock waves......Page 261
7.7.6 Shock waves and light......Page 262
A historical interlude: The sound barrier......Page 263
Appendix 7.1 Derivation of Doppler frequency changes......Page 268
8: Light as a Wave......Page 274
8.1.1 The mystery of waves in nothing......Page 275
8.2.1 Superposition......Page 276
8.2.2 Huygens’ principle......Page 277
8.2.3 Huygen’s principle and refraction......Page 278
8.2.4 Diffraction......Page 280
8.2.5 Huygens’ principle and diffraction......Page 281
8.3.1 Diffraction of light......Page 282
8.3.2 The experiment with light......Page 283
8.3.3 Other apertures......Page 284
8.3.4 The curious case of the opaque disc......Page 285
8.4.2 The Rayleigh criterion......Page 286
8.5 Other electromagnetic waves......Page 288
8.5.1 Message from the stars......Page 289
8.6 Light from two sources......Page 290
8.6.1 Young’s experiment......Page 291
8.6.2 A pattern within a pattern......Page 294
8.7.1 The Michelson interferometer......Page 295
8.8 Thin films......Page 297
8.8.1 Newton’s rings......Page 298
8.8.2 Non-reflective coatings......Page 299
8.9 Diffraction gratings......Page 301
8.9.1 Practical diffraction gratings......Page 302
8.10.1 X-ray diffraction......Page 304
8.10.2 Electron diffraction......Page 308
8.11 Coherence......Page 309
8.11.1 The question of phase......Page 310
8.12.1 Polarisation of electromagnetic waves......Page 311
8.12.2 What happens to light as it passes through a polaroid?......Page 312
8.12.3 Polarisation by reflection......Page 314
A historical interlude: Thomas Young (1773–1829)......Page 315
Appendix 8.1 Single slit diffraction......Page 317
Appendix 8.2 Reflectance of thin films......Page 322
9.1.1 Photography......Page 324
9.1.2 History of the photograph......Page 326
9.1.4 Interpretation of photographic images......Page 331
9.2.1 The inventor......Page 332
9.2.2 The principle......Page 333
9.2.3 Making a hologram......Page 334
9.2.5 Applications of holography......Page 336
10.1.1 The gravitational force......Page 338
10.1.2 The electrostatic force......Page 340
10.1.3 Coulomb’s law......Page 341
10.2.1 Vector fields......Page 343
10.2.2 A picture to represent a physical law......Page 344
10.2.3 Gauss’s theorem......Page 346
10.2.4 The energy in an electric field......Page 350
10.3.1 Magnetic materials......Page 352
10.4.1 Electric currents......Page 353
10.4.2 Ampère’s discovery......Page 354
10.4.4 Oersted’s discovery......Page 355
10.4.5 Ampère’s law......Page 358
10.4.6 The effect of a magnetic field on an electric charge......Page 361
10.4.7 Electromagnetism......Page 362
10.4.8 The interaction between moving charges......Page 363
10.5.1 Faraday’s discovery......Page 364
10.6.1 Putting facts together......Page 367
10.6.2 An important extension to Ampère’s law......Page 368
10.6.3 The four laws......Page 370
10.6.4 As we turn on a current…......Page 371
10.6.5 The propagating magnetic field......Page 372
10.7.1 Cause and effect — A summary......Page 376
10.7.2 Making an electromagnetic pulse......Page 377
10.7.4 Putting theory into practice......Page 378
A historical interlude: James Clerk Maxwell (1831–1879)......Page 381
Appendix 10.1 Energy density of a uniform electric field......Page 385
Appendix 10.2 Units and Dimensions......Page 386
11: ‘Atoms of Light’ — The Birth of Quantum Theory......Page 388
11.1.1 How does matter emit electromagnetic energy?......Page 389
11.1.3 The Blackbody radiation spectrum......Page 390
11.1.4 The Stefan–Boltzmann law......Page 391
11.1.5 Wien’s displacement law; the spectral distribution......Page 392
11.2.1 Cavity radiation......Page 394
11.2.3 Wien’s displacement law......Page 396
11.2.5 Second try — a model which incorporates the wave nature of light......Page 398
11.2.6 How can the theoretical models be ‘half right’?......Page 399
11.3.1 A guess to start......Page 400
11.3.2 Showing that Planck’s ‘lucky guess’ formula works at all wavelengths......Page 401
11.3.4 Nature’s secret......Page 402
11.4.1 The quantum hypothesis......Page 403
11.4.2 Quantum discrimination......Page 404
11.4.4 What does the quantum do after it is emitted?......Page 405
11.4.5 How does the quantum hypothesis solve the ‘ultraviolet catastrophe’?......Page 406
11.5.2 The average energy......Page 408
11.5.4 Quantum theory......Page 409
A historical interlude: Max Planck (1858–1947)......Page 412
Appendix 11.1 Deriving the Stefan– Boltzmann law from Planck’s radiation formula and calculating the value of Stefan’s constant......Page 416
12: The Development of Quantum Mechanics......Page 418
12.1.1 From oscillators to photons to other things......Page 419
12.1.3 The quantum enters the picture......Page 420
12.1.4 Quantum jumps — light comes out of the atom......Page 421
12.1.6 The demise of determinism......Page 422
12.1.7 A new way of thinking......Page 423
12.2.1 Heisenberg’s approach......Page 424
12.2.3 A matrix for everything......Page 425
12.2.4 Rules of the game......Page 426
12.2.6 An example of the Heisenberg method......Page 427
12.2.7 Matrices do not commute!......Page 428
12.2.8 Laws of nature must be built into the matrices......Page 429
12.3.2 A ‘table top’ experiment with polaroids......Page 430
12.3.3 Experimenting with a series of polaroids......Page 432
12.3.4 The uncertainty principle......Page 435
12.4.2 De Broglie’s original idea......Page 437
12.4.3 Adapting de Broglie waves......Page 440
12.4.4 Uncertainty from another aspect......Page 441
12.5.1 A wider view......Page 442
12.5.2 Relativity and quantum mechanics......Page 443
12.5.3 Triumph out of difficulty......Page 444
12.5.5 Positron emission tomography......Page 445
12.5.6 Antiprotons and antihydrogen......Page 447
12.6.1 Critics of the Copenhagen interpretation......Page 448
12.6.2 Bell’s theorem......Page 449
12.6.3 A precursor of quantum reality......Page 450
A historical interlude: Niels Bohr (1885–1963)......Page 451
Appendix 12.1 Calculating the radius of atomic orbits for hydrogen......Page 456
13: Atoms of Light Acting as Particles......Page 458
13.1.2 Short sharp shocks......Page 459
13.1.3 An accidental discovery......Page 460
13.1.4 How long would we expect to wait? An order-ofmagnitude calculation......Page 461
13.1.5 The ‘lucky’ electron......Page 462
13.1.6 Einstein’s photoelectric equation......Page 463
13.1.7 Millikan’s Experiment......Page 464
13.1.8 Current flowing uphill......Page 466
13.1.9 The photoelectric work function......Page 468
13.1.10 Practical applications......Page 469
13.2.1 Real bullets have momentum......Page 471
13.2.3 Collision dynamics revisited......Page 472
13.2.5 The photon loses energy but does not slow down......Page 473
13.2.6 Experimental verification......Page 475
A historical interlude: Robert A. Millikan (1868–1953)......Page 476
Appendix 13.1 Mathematics of the Compton effect......Page 481
14: Atoms of Light Behaving as Waves......Page 486
14.1.2 Detecting a single photon......Page 487
14.1.4 Single slit diffraction......Page 489
14.1.5 Double slit diffraction and interference......Page 490
14.1.6 Measuring ‘clicks’ as photons arrive one by one......Page 491
14.1.7 Separating the possible paths......Page 494
14.2.1 Partial reflection......Page 496
14.2.2 The strange theory of the photon......Page 499
14.2.4 The rotating amplitude vector......Page 500
14.2.5 How can we believe all this?......Page 503
14.2.6 It all comes together......Page 504
14.2.7 Quantum electrodynamics......Page 505
A historical interlude: Richard Feynman (1918–1988)......Page 507
15: Relativity Part 1: How It Began......Page 514
15.1.1 Space and the ancient philosophers......Page 515
15.1.3 Space and time — according to Isaac Newton......Page 517
15.2.1 Starting with a clean slate......Page 518
15.2.2 Frames of reference — defining a point of view......Page 519
15.2.3 Specifying the prejudices......Page 521
15.3.1 The Michelson–Morley experiment......Page 523
15.3.2 Timing the ferry......Page 524
15.3.3 Details of the experiment......Page 526
15.3.4 A powerful conclusion......Page 527
15.4.2 The new model......Page 528
15.5.1 Nature does not discriminate......Page 529
15.5.2 Galileo had the right idea!......Page 531
15.5.3 The Galilean transformation......Page 532
15.5.4 The speed of a bullet......Page 533
15.6.2 An imaginary experiment with light......Page 535
15.6.3 A paradox?......Page 536
15.6.4 ‘The impossible’ in mathematical form......Page 537
15.6.5 The Lorentz transformation......Page 539
15.6.6 The gamma factor......Page 541
15.6.7 Addition of velocities — a classical example......Page 542
15.6.8 Addition of velocities when the speeds are relativistic......Page 543
15.6.9 Playing with the formula......Page 544
15.7 The fourth dimension......Page 545
15.7.1 Definition of an ‘event’......Page 546
15.7.3 Pythagoras revisited......Page 547
15.7.4 Time as a fourth dimension......Page 549
15.7.5 The smoking astronaut......Page 550
15.8 A philosophical interlude......Page 551
A historical interlude: Hendrik A. Lorentz (1852–1928)......Page 552
16: Relativity Part 2: Verifiable Predictions......Page 560
16.1.1 Time dilation in action......Page 561
16.1.2 Living on borrowed time?......Page 562
16.2.1 Bringing energy into the picture......Page 563
16.2.2 Conservation of momentum — a thought experiment with snooker balls......Page 564
16.2.3 Interacting with another time frame......Page 566
16.2.4 Momentum from another frame of reference......Page 567
16.2.5 A new look at the concept of mass......Page 568
16.2.6 The relativistic formula for momentum......Page 569
16.2.7 Energy in different frames of reference......Page 571
16.2.8 High energy particle accelerators......Page 572
16.2.9 Nuclear structure......Page 577
16.2.10 Nuclear fusion — nature’s way of powering the sun......Page 578
16.2.11 Nuclear fission......Page 579
16.4.1 The ‘recoiling gun’ revisited......Page 580
16.4.2 Radioactive decay......Page 582
A historical interlude: Albert Einstein (1879–1955)......Page 584
Appendix 16.1 Deriving the relativistic formula for kinetic energy T = mc2 -m0c2......Page 589
Appendix 16.2 Dimensions and units of energy......Page 591
Appendix 16.3 Relativistic analysis of the beta decay of bismuth 210......Page 593
17: Epilogue......Page 596
17.1.1 Collisions make particles......Page 597
17.1.2 Prediction and discovery of
the πmeson......Page 598
17.1.3 The forces between the particles......Page 600
17.1.4 The laws of the world of fundamental particles......Page 602
17.1.5 Quarks......Page 604
17.1.6 Charm......Page 606
17.1.7 The return of photographic emulsion......Page 608
17.1.8 More quarks......Page 611
17.2.1 The role of light as the carrier of the electromagnetic force......Page 612
17.2.2 Unification — the long hard road......Page 613
17.2.3 The heavy photon......Page 614
17.2.4 The full circle......Page 617
Index......Page 620