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Contents

Preface

1.Introduction

1.1A new understanding of reality

1.2A theory of particles and fields

1.3Outline of the book

2.Newtonian Physics

2.1Observation of the night sky

2.2Measurement of time

2.3Ptolemy’s model

2.4The Copernican revolution

2.5Newton’s laws

2.6Work and energy

2.7Determinism

2.8Summary

3.Statistical Mechanics

3.1Atoms

3.2The laws of thermodynamics

3.3Statistical mechanics

3.3.1One-dimensional gas

3.3.2Two-dimensional gas

3.3.3Three-dimensional gas

3.3.4Third law of thermodynamics

3.3.5Second law of thermodynamics

3.4Summary

4.The Concept of a Field

4.1Action at a distance

4.2Electricity and magnetism

4.3Electromagnetism

4.4Electromagnetic waves

4.5Finite speed of fields

4.6Summary

5.The Ultraviolet Catastrophe

5.1A black body

5.2Black body cavity

5.3Standing waves and the catastrophe

5.4Escape from the ultraviolet catastrophe

5.5A small beginning

5.6Summary

6.Absorption and Emission of Radiation

6.1Photelectric effect

6.2Einstein’s explanation

6.3Momentum of electromagnetic radiation

6.4Compton effect

6.5Finite time of interaction

6.6Uncertainty principle

6.7Summary

7.Matter Waves

7.1De Broglie’s hypothesis

7.2Interference

7.2.1Combination of waves

7.3Waves in two or three dimensions

7.4Quantum theory of light

7.5Electron waves

7.6Composite particles

7.7The hydrogen atom

7.8Summary

8.The Special Theory of Relativity

8.1Speed of light

8.2Relative speed in classical mechanics

8.3Motion relative to source of light

8.4Principles of special relativity

8.5Relative speed according to Einstein

8.6Impossible to attain the speed of light

8.7Length is relative

8.8Time ordering of events is relative

8.9Duration of time is relative — time dilation

8.10Mass increases with speed

8.11Mass and energy

8.12Relativity and quantum theory

8.13Summary

9.The Geometry of Space and Time

9.1Space time

9.1.1World lines

9.1.2Space-like, time-like and light-like intervals

9.1.3Minkowski space

9.2Feynman diagrams

9.3Arrow of time

9.3.1Time reversal and Feynman diagrams

9.3.2Information carried by many photons

9.4Summary

10.The Heart of Quantum Theory

10.1How does one study the quantum?

10.2Fields and states

10.3Complex numbers in quantum mechanics

10.4States and operators

10.5Physical meaning of symbols

10.5.1Creation and annihilation of photons

10.5.2Propagation of a photon

10.5.3Probability amplitudes

10.5.4Addition of paths

10.6Classical and quantum probabilities

10.6.1Constructive and destructive interference

10.7Summary

11.Angular Momentum and Spin

11.1Direction of the angular momentum vector

11.2Quantization of angular momentum

11.3Spin of an electron

11.3.1Stern–Gerlach experiment

11.4Pauli exclusion principle

11.4.1Quantum statistics

11.5Summary

12.Quantum Theory and Relativity

12.1Dirac theory

12.1.1Negative energy states

12.1.2Antiparticles

12.1.3Zitterbewegung

12.2Entangled states

12.3Apparent conflict with relativity

12.3.1Action at a distance

12.3.2Action mediated by a field

12.3.3Communication of information

12.4Time ordering of measurements is relative

12.5Feynman graph of entanglement and measurement

12.6Summary

13.Tunneling: Quantum Magic?

13.1Extending the boundaries of the possible

13.2Potential barriers

13.3Tunneling

13.4Tunneling and alpha decay

13.5Summary

14.The Spatial Wave Function

14.1Probability density

14.2Amplitude and probability

14.3The wave function and measurements

14.4A historical note

14.5Summary

15.Conclusion

15.1Summary

15.1.1Wave and particle

15.1.2A statistical result

15.1.3Uncertainty principle

15.1.4Wave functions and operators

15.1.5Spin and statistics

15.1.6Zitterbewegung

15.1.7Antiparticles

15.1.8Entanglement

15.1.9Tunneling

15.2The next step

Appendix A Answers to Exercises

Appendix B Bibliography

Index