This book explores the fundamental topic of quantum mechanics from a novel perspective, by following its historical development and emphasizing the way the minds of its bright young creators worked, showing how new ideas came through and how conceptual difficulties were overcome, at
east sometimes. We try to convey to the reader the essence of quantum mechanics, discussing how it evolved from the initial concept of Planck's quanta to current developments in quantum entanglement, teleportation and decoherence—cornerstones of the emerging second quantum
revolution.
The book is aimed at the interested non-specialist with some background in mathematics and physics, who seeks to understand modern quantum mechanics and its potential applications. It will also be of value as a complement to lecture notes or textbooks on the subject.
The book starts with a description of the Planck-Einstein revolution which introduced the concept of quanta of energy. The birth and development of a theory of quantum mechanics is then described in the second chapter. The third chapter addresses the principle of superposition, at the very core of quantum mechanics, and the fourth chapter outlines the concepts of observables and operators. A discussion of symmetries and symmetry transformations is presented in chapter five. Heisenberg's uncertainty principle is the subject of the sixth chapter, and the seventh chapter focuses on the notion of entanglement… The book ends in chapter eight with a discussion of the interpretations of quantum mechanics.
THE PLANCK-EINSTEIN REVOLUTION 7
1.1 Blackbody Radiation 9
1.2 The Arrival of h 11
1.3 The Photon 13
2 THE BIRTH OF QUANTUM MECHANICS 17
2.1 Bohr’s Model of the Atom 19
2.2 The Dance of the Quantum Numbers 23
2.3 Einstein on Radiation Transitions 27
2.4 Quantum Mechanics 29
3 THE PRINCIPLE OF SUPERPOSITION 47
3.1 The Polarization of Light 49
3.2 Interference Phenomena 51
3.3 Mathematical Formulation of the Principle 56
3.4 Superpositions of Macroscopically Distinct States 65
4 DYNAMICAL VARIABLES AND OBSERVABLES 69
4.1 Observables and Operators 71
4.2 Representations 76
4.3 The Axioms of Quantum Mechanics 79
4.4 The Density Operator 83
4.5 Revisiting Heisenberg’s Paper of July 1925 89
vi CONTENT S
5 SYMMETRIES 99
5.1 Symmetries and Symmetry Transformations 101
5.2 Symmetries and Group Representations 106
5.3 Examples of Exact and Broken Symmetries 110
5.4 Symmetries in nuclear and particle physics 119
6 UNCERTAINTY 123
6.1 Superposition and Uncertainty 126
6.2 The Heisenberg Microscope 127
6.3 Simple Examples 128
6.4 Young’s Experiment And The Uncertainty Principle 129
6.5 Uncertainty In The Stars 130
6.6 Probabilistic Derivation of the Uncertainty Principle 132
6.7 Trajectories in Cloud Chambers 134
7 ENTANGLEMENT 137
7.1 Introduction 139
7.2 David Bohm’s Description of the EPR experiment 144
7.3 John Bell and the EPR experiment 147
7.4 A Different Analysis of the EPR Thought Experiment 150
7.5 Reduction of the State Vector 151
7.6 Quantum Teleportation 153
7.7 Decoherence 157
8 INTERPRETATIONS OF QUANTUM MECHANICS 163
8.1 The Copenhagen Interpretation 165
8.2 Other Interpretations 170
Appendix: Foundational Attitudes Toward Quantum Mechanics 173
EPILOGUE 175
APPENDIX 177
BIBLIOGRAPHY 179
INDEX
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