Quantum Mechanics: Its Early Development and the Road to Entanglement Book

Acknowledgements xvii

Preface xix

1 Setting the Scene 1

1.1 Introduction 1

1.2 Light and Heat: Kirchhoff's 'Black-body Radiation' 2

1.3 Kirchhoff's Work on Optical Spectra 4

1.4 Planck's Route to Tackling the Black-body Radiation Problem 5

1.5 Light and the Aether 6

1.6 Post 1900 7

2 Light: The 'Aether' and the Special Theory of Relativity 11

2.1 Introduction 11

2.2 The 'Aether' 13

2.2.1 The stellar 'aberration of light' 13

2.2.2 Arago's experiments 14

2.2.3 Fresnel's 'drag' mechanism (1818) 15

2.2.4 The 1887 Michelson-Morley experiment 15

2.2.5 The FitzGerald contraction 16

2.2.6 The Lorentz contraction 16

2.3 Einstein's Special Theory of Relativity (1905) 17

2.3.1 Introduction: reference frame transformations 17

2.3.2 Energy and momentum 23

3 Thermal Radiation and Planck's 'Energy Elements' 26

3.1 Introduction 26

3.2 Planck and 'Energy Elements' 32

3.2.1 Introduction: background 32

3.2.2 Stage 1 34

3.2.3 Stage 2: Planck's final distribution function 39

3.2.4 Summary of the main features of Planck's final derivation of the distribution function 45

4 Einstein and the Quantum 48

4.1 Introduction 48

4.2 Overview 49

4.3 Volume Dependence of Entropy: Light Quanta and the Photoelectric Effect 56

4.4 Fluctuations 62

4.4.1 Energy fluctuations 62

4.4.2 Momentum fluctuations 65

4.5 Statistics: Planck's Radiation Formula and Specific Heat Theory 66

5 The Quantum in the Atom: Optical Spectra 69

5.1 Introduction 69

5.2 Classical Mechanics of an Electron in a Circular Atomic Orbit 71

5.3 The Quantum is Introduced: The Correspondence Principle 72

6 Einstein's Transition Probabilities:Bohr's Theory and Planck's Law 80

7 Wave Mechanics 85

7.1 Introduction 85

7.2 de Broglie's Matter Waves 86

7.2.1 Freely moving particles 87

7.2.2 Orbital electrons as waves 91

7.3 Schrodinger's Wave Mechanics 93

7.3.1 Introduction 93

7.3.2 Background role of Einstein's Gas Theory 95

7.3.3 Classical wave optics and geometrical optics compared: a note 98

7.3.4 Fermat's principle of least time 99

7.3.5 Maupertuis's principle of least action 101

7.3.6 Hamilton's mechanics and Schrodinger's wave mechanics 103

7.3.7 Schrodinger's time-independent wave equation of 1926 105

7.3.8 Schrodinger's time-dependent equation 112

7.3.9 The probabilistic interpretation of the wave equation 116

7.3.10 Operator representations 119

7.4 Relativistic Wave Equation: The Dirac Equation 120

8 Matrix Mechanics 124

8.1 Introduction 124

8.2 Heisenberg's Approach 126

8.2.1 Heisenberg invokes the correspondence principle 128

8.2.2 Outside the range of the correspondence principle 130

8.3 The Reconciliation of Matrix Mechanics and Wave Mechanics 132

8.4 Dirac and Matrix Mechanics 133

9 Complementarity, the Uncertainty Principle, and the Copenhagen Interpretation 135

9.1 Introduction 135

9.2 Heisenberg's Uncertainty Principle 138

9.3 The Como Meeting and the 'Copenhagen Interpretation' 142

9.4 Copenhagen Interpretation Challenged 146

9.4.1 Background 146

9.4.2 Einstein's objections 150

10 Indeterminacy and Entanglement (Sara M. McMurry) 159

10.1 Introduction 159

10.2 Entangled Pairs of Particles and Bell's Inequality 161

10.2.1 Photon polarisation and indeterminacy 162

10.2.2 An EPR experiment with photons 166

10.2.3 Hidden variables and Bell's Inequality 168

10.2.4 Experimental tests of Bell's Inequality 172

10.3 Quantum Information Theory 173

10.3.1 Quantum computing 175

10.3.2 Quantum cryptography 176

10.3.3 Quantum cloning and quantum teleportation 177

10.4 The Quantum Measurement Problem 179

10.4.1 Schrodinger's Cat and the collapse of the wave function 180

10.5 Further Reading 183

Appendices

A Entropy 184

B Classical Thermodynamics; Kinetic Theory; Statistical Mechanics; Statistical Thermodynamics 191

C Phase Space 196

D A Note on Rayleigh's Radiation Formula 204

E Debye: Specific Heat Theory of Solids and Derivation of Planck's Radiation Formula 206

F The Photoelectric Effect 209

G The General Wave Equation; Wave Groups; Dispersion 211

H The Harmonic and Anharmonic Oscillator 214

I Chronology of Main Developments Leading to the Copenhagen Interpretation 219

J Biographical Notes: The Central Characters 223

Bibliography 231

References 238

Index 247