ENERGY, THE SUBTLE CONCEPT Nicolas Poussin, A Dance to the Music of Time, c. 1640 (By kind permission of the Trustees of the Wallace Collection, London). Energy, the Subtle Concept The discovery of Feynman’s blocks from Leibniz to Einstein JENNIFER COOPERSMITH Revised Edition 1 1 Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries © Jennifer Coopersmith 2015 The moral rights of the author have been asserted First Edition published in 2010 Revised Edition published in 2015 Impression: 1 All rights reserved. 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Oxford disclaims any responsibility for the materials contained in any third party website referenced in this work. 9780198716747-Coopersmith.indb 4 12/03/15 6:04 PM To Bertie Coopersmith and Murray Peake, sages both Preface to the Revised Edition This book is both a history of the emergence of the concept of energy and an explanation of energy through that history. As it is primarily a book of explanation, the historical coverage is not exhaustive, and also ‘energy’ is brought in ahead of its final discovery, wherever an explan- ation in modern terms would be an aid to understanding. The level is popular science but hard thinking is required—we might call it serious popular science. The facts do not, in general, speak for themselves, and the aim is not only to explain, but, most of all, to imbue the reader with a sense of awe—over these very facts, and the genius of their discoverers. This second edition is more comprehensive in its coverage, especially in Chapter 17, ‘A Forward Look’, but at the same time it is more stream- lined in order to better bring out the logic of the arguments—argu- ments that will lead to the concept of energy. The expertise gained while researching The Lazy Universe: the Principle of Least Action Explained (Oxford University Press, in preparation) has led to some changes in Chapter 7, Part IV, and Chapter 13, ‘Hamilton’, and to some new ma- terial in Chapter 18, ‘Impossible Things, Difficult Things’. ‘Energy’ is a huge topic, and to keep the book at a reasonable length, and in one volume, energy in the current era has not been considered; in fact, the aim has been to cover material, and to provide insights, not easily found by a computer search. Likewise, the amount of biographical detail is mostly in inverse proportion to the fame of the given scientist. Some ‘housekeeping’: Quotation marks appear all over the place, sometimes in thickets, and with little attempt at consistency. This is because as new ideas arrive, new words hover over them, and it takes a few decades for the right word to land. (There are also many commas—this is the OUP house style.) Mathematical notation: ‘height ∝ age’ means ‘height is proportional to age’, ‘<x >’ means ‘the average value of x’, ‘Δx’ means ‘a small increment in x’, ‘∫Edt’ is the ‘integral of E with respect to t’ or ‘the integral of E over t’, or, less often, ‘the integral of E through t’, and is roughly equivalent to a summation of the separate increments, E1dt + E2dt + E3dt + . Vectors are quantities that have a direction as well as a magnitude (a bit like an arrow, of length 40 cm, pointing due west). They are indicated in bold; viii Preface to the Revised Edition for example v is velocity, whereas v is just the magnitude of velocity, also known as speed. The history has been given in roughly chronological order, but ‘heavy’ chapters on theoretical developments are interspersed with ‘lighter’ chapters on experiments and phenomenology. Chapters 7 (the last sec- tion), 13, 17, and 18 assume some background knowledge in the physi- cal sciences: readers with this background will enjoy the broad sweep across the whole of physics (Chapter 17), and other readers should not be discouraged as much knowledge can seep in by osmosis. Also, all chapters contain gentle introductions, summaries, and occasional dis- cursive sections (for example, on interactions between physicists, energy in the public domain, and global warming). The summaries were vari- ously called conclusions, summary, resumé, review, comments, remarks, and so on, but the copy editor swept these aside and insisted on a uni- form descriptor—‘overview’. Just one ‘Remarks’ has survived, in the middle of Chapter 8 (the end of the section on Watt), as the remarks really are . remarkable—there is even a mention of sex. Acknowledgements Six marvellous books have guided me and been my constant com- panions: Donald Cardwell’s From Watt to Clausius: the Rise of Ther- modynamics in the Early Industrial Age, Cornelius Lanczos’ The Variational Principles of Mechanics, Richard Feynman’s Lectures on Physics, Richard Westfall’s Force in Newton’s Physics, Charles Gillispie’s The Edge of Objectivity, and Brian Pippard’s The Elements of Classical Thermodynamics. In the case of the last two books, I have been privileged to have a cor- respondence with the authors. Both have been extremely enthusiastic and encouraging (Professor Sir Brian Pippard died last year). Professor Gillispie (Emeritus Professor at Princeton and founding father of the discipline of the history of science) has read many of my draft chap- ters and made invaluable suggestions. Professor Paul Davies (physicist, science writer, and founder and director of ‘Beyond, Center for Funda- mental Concepts in Science’), and Emeritus Professor Rod Home (De- partment of History and Philosophy of Science, Melbourne University) read some early draft chapters and were likewise very encouraging. I would like to thank past colleagues and friends at King’s College London, TRIUMF, UBC, Logica SDS, and the Open University. I would especially like to thank the Open University students (London, Winchester, and Oxford, 1986–96) who asked all those difficult-to- answer questions. My present colleagues at La Trobe University, Bendigo Campus, and Swinburne University of Technology in Melbourne have been very sup- portive. In particular, I would like to thank the late Rob Glaisher, Kath- erine Legge, Glenys Shirley, John Schutz, Mal Haysom, Joe Petrolito, John Russell, Glen Mackie, and Sarah Maddison. For special tasks: Mal Haysom took the cover photos, Andrew Kilpatrick was tireless in draw- ing diagrams, even randomizing the position of dot-molecules by hand (mind you, I assisted with his marking-avoidance strategies), Sabine Wilkens translated Euler and trawled through Helmholtz’s endless ac- counts of indigestion, and Glenys Shirley helped with anything and eve- rything, and with characteristic good humour. I thank the University of La Trobe, Faculty of Science, Technology and Engineering, Bendigo Campus, for providing me with an office, x Acknowledgements computing and library facilities, and the intangible but crucially import- ant ambience of learning, research, and cooperation. The library staff at La Trobe University, Bendigo showed great for- bearance in my constant requests for inter-library loans and my loss of magnetic belts, late returns, and so on. (Having previously lived a stone’s throw from the Blackwell bookshop and the Bodleian in Oxford, I naturally didn’t embark on this project until I had moved to central Victoria.) I thank Howard Doherty, of Doherty’s Garage in Bendigo, for inter- esting conversations about cars, their design, and their impact on society. Thank you to Wikimedia Commons and Google Books for making source documents available online. In material reproduced in this book, every reasonable effort has been made to contact the original copyright holders. Any omissions will be rectified in future printings if notice is given to the publisher. I am unusually fortunate in having not one but two sages to call upon in my family (I am daughter of one and married to the other). My father (a physicist-turned-programmer) is a deep and highly original thinker, always aiming to get back to the essentials. When I asked him where my grandfather had come from in Russia and what the family name was (before ‘Coopersmith’ was adopted upon arrival in South Africa around 1910), he replied ‘I don’t know. Anyway it’s just contingent.’ My husband, Murray, has a profound understanding of mathematics and physics (he was a prize-winning physics student and applied math- ematician before being drawn down that well-trodden path of computer programming). His compendious knowledge of pre-twentieth-century arts and crafts has also been useful in the writing of this book. After one of his weekday ‘Murraycles’ (for example, being instrumental in a quiet revolution in the calculation of risk in banking), he turns to tying knots, grinding wheat, making rope, bread, tofu, and soap; restoring gas lamps, kerosene burners, sextants, and clocks; and calculating lunar motions using Stumpf’s method.