Hidden Unity In Nature's Laws

HIDDEN UNITY IN NATURE’S LAWS As physics has progressed through the ages it has succeeded in explaining more and more diverse phenomena with fewer and fewer underlying principles. This lucid and wide-ranging book explains how this understanding has developed by periodically uncovering unexpected “hidden unities” in nature. The author deftly steers the reader on a fascinating path that goes to the heart of physics – the search for and discovery of elegant laws that unify and simplify our understanding of the intricate universe in which we live. Starting with the ancient Greeks, the author traces the development of major concepts in physics right up to the present day. Throughout, the presentation is crisp and informative, and only a minimum of mathematics is used. Any reader with a background in mathematics or physics will find this book provides fascinating insight into the development of our fundamental understanding of the world, and the apparent simplicity underlying it. John C. Taylor is professor emeritus of mathematical physics at the University of Cambridge. A pupil of the Nobel Prize–winner Abdus Salam, Professor Taylor has had a long and distinguished career. In particular, he was a discoverer of equations that play an important role in the theory of the current “standard model” of particles and their forces. In 1976, he published the first textbook on the subject, Gauge Theories of Weak Interactions. He has taught theoretical physics at Imperial College, London, and the Universities of Oxford and Cambridge, and he has lectured around the world. In 1981 he was elected a Fellow of the Royal Society. HIDDEN UNITY IN NATURE’S LAWS JOHN C. TAYLOR University of Cambridge           The Pitt Building, Trumpington Street, Cambridge, United Kingdom    The Edinburgh Building, Cambridge CB2 2RU, UK 40 West 20th Street, New York, NY 10011-4211, USA 477 Williamstown Road, Port Melbourne, VIC 3207, Australia Ruiz de Alarcón 13, 28014 Madrid, Spain Dock House, The Waterfront, Cape Town 8001, South Africa http://www.cambridge.org © Cambridge University Press 2004 First published in printed format 2001 ISBN 0-511-03690-6 eBook (Adobe Reader) ISBN 0-521-65064-X hardback ISBN 0-521-65938-8 paperback CONTENTS Preface 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 xi Motion on Earth and in the Heavens Galileo’s Telescope 1 The Old Astronomy 2 1 Aristotle and Ptolemy: Models and Mathematics Copernicus: Getting Behind Appearances 9 Galileo 11 Kepler: Beyond Circles 14 Newton 19 Conclusion 30 Energy, Heat and Chance Introduction 32 5 32 Temperature and Thermometers 33 Energy and Its Conservation 34 Heat as Energy 42 Atoms and Molecules 43 Steam Engines and Entropy 50 Entropy and Randomness 58 Chaos 62 Conclusion 69 Electricity and Magnetism Electric Charges 70 Magnets 77 70 Electric Currents and Magnetism 80 Faraday and Induction of Electricity by Magnetism v 88 CONTENTS 3.5 3.6 Maxwell’s Synthesis: Electromagnetism Conclusion 97 4 Light 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 Waves 99 Sound 102 Light 104 The Principle of Least Time What Is Light? 113 Light Waves 119 Waves in What? 127 Light Is Electromagnetism Conclusion 136 91 99 108 129 5 Space and Time 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 Electrons 137 Is the Speed of Light Always the Same? 139 The Unity of Space and Time 143 Space, Time and Motion 144 The Geometry of Spacetime 147 Lorentz Transformations 151 Time Dilation and the “Twin Paradox” 155 Distances and the Lorentz-Fitzge