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Christoph Schiller MOTION MOUNTAIN the adventure of physics – vol.iv quantum theory: the smallest change www.motionmountain.net Christoph Schiller Motion Mountain The Adventure of Physics Volume IV Quantum Theory: The Smallest Change Edition 24.1, available as free pdf at www.motionmountain.net Editio vicesima tertia. Proprietas scriptoris © Christophori Schiller secundo anno Olympiadis vicesimae nonae. Omnia proprietatis iura reservantur et vindicantur. Imitatio prohibita sine auctoris permissione. Non licet pecuniam expetere pro aliquo, quod partem horum verborum continet; liber pro omnibus semper gratuitus erat et manet. Twenty-third edition, ISBN 978-300-021946-7. Copyright © 2009 by Christoph Schiller, the second year of the 29th Olympiad. This pdf file is licensed under the Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 Germany Licence,whosefulltextcanbefoundonthewebsite creativecommons.org/licenses/by-nc-nd/3.0/de, with the additional restriction that reproduction, distribution and use, in whole or in part, in any product or service, be it commercial or not, is not allowed without the written consent of the copyright owner. The pdf file was and remains free for everybody to read, store and print for personal use, and to distribute electronically, but only in unmodified form and at no charge. To Britta, Esther and Justus Aaron τῷ ἐμοὶ δαὶμονι Die Menschen stärken, die Sachen klären. PREFACE Primum movere, deinde docere.* Antiquity “ ” Motion Mountain – The Adventure of Physics pdf file available free of charg This book is written for anybody who is curious about nature and motion. Have you ever asked: Why do people, animals, things, images and space move? The answer leads to many adventures; this volume presents those due the discovery that there is a smallest change in nature. This smallest change leads to what is called quantum theory.Inthe structure of modern physics, shown in Figure 1,quantumphysicscoversthreepoints; this volume covers the introduction to the point in the lower right: the foundations of quantum theory. The present introduction to quantum physics arose from a threefold aim I have pur- sued since 1990: to present the basics of motion in a way that is simple, up to date and captivating. In order to be simple, the text focuses on concepts, while keeping mathematics to the necessary minimum. Understanding the concepts of physics is given precedence over using formulae in calculations. The whole text is within the reach of an undergraduate. In order to be up to date, the text is enriched by the many gems – both theoretical and empirical – that are scattered throughout the scientific literature. In order to be captivating, the text tries to startle the reader as much as possible. Read- e at www.motionmountain.net Copyright © Christoph Schiller November 1997– ing a book on general physics should be like going to a magic show. We watch, we are astonished, we do not believe our eyes, we think, and finally we understand the trick. When we look at nature, we often have the same experience. Indeed, every page presents at least one surprise or provocation for the reader to think about. Numerous interesting challenges are proposed. The motto of the text, die Menschen stärken, die Sachen klären,afamousstatementby Hartmut von Hentig on pedagogy, translates as: ‘To fortify people, to clarify things.’ Clar- ifying things requires courage, as changing habits of thought produces fear, often hidden by anger. But by overcoming our fears we grow in strength. And we experience intense and beautiful emotions. All great adventures in life allow this, and exploring motion is one of them. Munich, 27 July 2010. July 2010 * ‘First move, then teach.’ In modern languages, the mentioned type of moving (the heart) is called motivat- ing;bothtermsgobacktothesameLatinroot. 8 preface PHYSICS: Unified description of motion Why does motion Describing motion with action. Adventures: understanding occur? What are motion, intense joy with space, time and thinking, catching a quantum particles? glimpse of bliss, calculating masses Quantum General relativity theory with gravity Quantum field theory Adventures: the Adventures: bouncing Adventures: building night sky, measu- neutrons, under- accelerators, under- ring curved space, standing tree standing quarks, stars, exploring black growth bombs and the basis of Motion Mountain – The Adventure of Physics pdf file available free of charg holes and the life, matter, radiation universe, space How do small and time things move? What are things? How do Classical gravity everyday, Special relativity Quantum theory Adventures: fast and large Adventures: light, Adventures: death, climbing, skiing, things move? magnetism, length sexuality, biology, space travel, contraction, time enjoying art and the wonders of dilation and colours, all high-tech 2 astronomy and E0 = mc business, medicine, geology chemistry, evolution G c h, e, k Galilean physics, heat and electricity Adventures: sport, music, sailing, cooking, describing beauty and understanding its origin, e at www.motionmountain.net Copyright © Christoph Schiller November 1997– using electricity and computers, understanding the brain and people FIGURE 1 A complete map of physics: the connections are defined by the speed of light c,the gravitational constant G, the Planck constant h, the Boltzmann constant k and the elementary charge e. Advice for learners In my experience as a teacher, there was one learning method that never failed to trans- form unsuccessful pupils into successful ones: if you read a book for study, summarize every section you read, in your own words, aloud.Ifyouareunabletodoso,readthe section again. Repeat this until you can clearly summarize what you read in your own words, aloud. You can do this alone in a room, or with friends, or while walking. If you do this with everything you read, you will reduce your learning and reading time signif- icantly. In addition, you will enjoy learning from good texts much more and hate bad July 2010 texts much less. Masters of the method can use it even while listening to a lecture, in a low voice, thus avoiding to ever take notes. preface 9 Usingthis book Text in green, as found in many marginal notes, marks a link that can be clicked in a pdf reader. Such green links are either bibliographic references, footnotes, cross references to other pages, challenge solutions, or pointers to websites. Solutions and hints for challenges are given in the appendix. Challenges are classified as research level (r), difficult (d), standard student level (s) and easy (e). Challenges of type r, d or s for which no solution has yet been included in the book are marked (ny). Arequest The text is and will remain free to download from the internet. In exchange, I would be delighted to receive an email from you at [email protected], especially on the Motion Mountain – The Adventure of Physics pdf file available free of charg following issues: Challenge 1 s — What was unclear and should be improved? — What story, topic, riddle, picture or movie did you miss? — What should be corrected? Alternatively, you can provide feedback online, on www.motionmountain.net/wiki.The feedback will be used to improve the next edition. On behalf of all readers, thank you in advance for your input. For a particularly useful contribution you will be mentioned – if you want – in the acknowledgements, receive a reward, or both. But above all, enjoy the reading! e at www.motionmountain.net Copyright © Christoph Schiller November 1997– July 2010 Contents 14 1 Minimum action – quantum theory for poets The effects of the quantum of action on rest 17 • The consequences of the quan- tum of action for objects 18 • Why ‘quantum’? 19 • The effect of the quantum of action on motion 22 • Quantum limits and surprises 23 • Transformation, life and Democritus 24 • Randomness – a consequence of the quantum of action 28 • Waves – a consequence of the quantum of action 29 •Particles–aconsequenceof the quantum of action 30 • Quantum information 30 • Curiosities and fun chal- lenges about the quantum of action 31 • The dangers of buying a can of beans 32 • A summary: quantum physics, the law and indoctrination 34 35 2 Light – the strange consequences of the quantum of action What is the faintest lamp? 35 •Photons 39 •Whatislight? 41 •Thesizeofpho- Motion Mountain – The Adventure of Physics pdf file available free of charg tons 42 • Are photons countable? – Squeezed light 42 • The positions of pho- tons 44 • Are photons necessary? 47 • How can a wave be made up of parti- cles? 49 • Can light move faster than light? – Virtual photons 54 • Indetermi- nacy of electric fields 55 • Curiosities and fun challenges about photons 56 •A summary on light: particle and waves 57 60 3 Motion of matter – beyond classical physics Wine glasses, pencils and atoms – no rest 60 • No infinite precision 61 •Cool gas 61 • Flows and the quantization of matter 62 • Fluid flows and quantons 62 • Knocking tables and quantized conductivity 62 •Matterquantonsandtheirmo- tion – matter waves 63 • Mass and acceleration of quantons 66 •Whyareatoms not flat? Why do shapes exist? 67 • Rotation, quantization of angular momentum, andthelackofnorthpoles 68 • Rotation of quantons 70 •Silver,SternandGer- lach – polarization of quantons 70 • Curiosities and fun challenges about quantum matter 72 • First summary on the motion of quantum particles 72 74 4 The quantum description of matter and its motion e at www.motionmountain.net Copyright © Christoph Schiller November 1997–
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