Christoph Schiller MOTION MOUNTAIN the adventure of physics – vol.iv the quantum of change www.motionmountain.net Christoph Schiller M M e Adventure of Physics Volume IV e Quantum of Change Edition ., available as free pdf at www.motionmountain.net Editio vicesima quinta. Proprietas scriptoris © Chrestophori Schiller primo anno Olympiadis trigesimae. Omnia proprietatis iura reservantur et vindicantur. Imitatio prohibita sine auctoris permissione. Non licet pecuniam expetere pro aliqua, quae partem horum verborum continet; liber pro omnibus semper gratuitus erat et manet. Twenty-h edition. Copyright © by Christoph Schiller, the rst year of the th Olympiad. is pdf le is licensed under the Creative Commons Attribution-Noncommercial-No Derivative Works . Germany Licence,whosefulltextcanbefoundonthewebsite creativecommons.org/licenses/by-nc-nd/./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. e pdf le was and remains free for everybody to read, store and print for personal use, and to distribute electronically, but only in unmodied form and at no charge. To Britta, Esther and Justus Aaron τ µο δαµονι Die Menschen stärken, die Sachen klären. PREFACE “ Primum movere, deinde docere.* ” Antiquity is 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? e answer leads to many adventures; this volume presents those due to the discovery that there is a smallest change value in nature. is smallest change value, the quantum of action, leads to what is called quantum physics.Inthestructureofmodernphysics,showninFigure ,quantum physics covers three points; this volume covers the introduction to the point in the lower right: the foundations of quantum theory. e present introduction to quantum physics arose from a threefold aim I have pur- sued since : 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. e 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 scientic literature. In order to be captivating, the text tries to startle the reader as much as possible. Read- 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 nally we understand the trick. When we look at nature, we oen 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. e 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 – and adhering only to the truth – requires courage, as changing the habits of thought produces fear, oen 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. Enjoy it! Munich, November . * ‘First move, then teach.’ In modern languages, the mentioned type of moving (the heart) is called motivat- ing;bothtermsgobacktothesameLatinroot. Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Copyright © Christoph Schiller June 1990–November 2012 Galilean physics, heat and electricity Adventures: sport, music, sailing, cooking, describing beauty and understanding its origin (vol. I), using electricity, light and computers, understanding the brain and people (vol. III). Special relativity Adventures: light, magnetism, length contraction, time dilation and E 0 = mc 2 (vol. II). Quantum theory Adventures: death, reproduction, biology, chemistry, evolution, enjoying colours and art, all high-tech business, medicine (vol. IV and V). Quantum theory with gravity Adventures: bouncing neutrons, under- standing tree growth (vol. V). Final, unified description of motion Adventures: understanding motion, intense joy with thinking, calculating couplings and masses, catching a glimpse of bliss (vol. VI). G c h, e, k PHYSICS: Describing motion with the least action principle. Quantum field theory Adventures: building accelerators, under- standing quarks, stars, bombs and the basis of life, matter, radiation (vol. V). How do everyday, fast and large things move? How do small things move? What are things? Why does motion occur? What are space, time and quantum particles? General relativity Adventures: the night sky, measu- ring curved space, exploring black holes and the universe, space and time (vol. II). Classical gravity Adventures: climbing, skiing, space travel, the wonders of astronomy and geology (vol. I). 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. A 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 images and words, aloud.Ifyouareunabletodo so, read the section again. Repeat this until you can clearly summarize what you read in your own images and 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 signicantly. e most inecient learning method is to use a marker or to underline text: it wastes time, provides false comfort and makes the text unreadable. Nobody marking text is an Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Copyright © Christoph Schiller June 1990–November 2012 ecient learner. Instead, by repeating every section in your own images and words, aloud, youwillsavetimeandmoney,enjoylearningfromgoodtextsmuchmoreandhatebad 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. U 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 classied as research level (r), dicult (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). F is text is and will remain free to download from the internet. I would be delighted to receive an email from you at fb@motionmountain.net, especially on the following issues: What was unclear and should be improved? Challenge 1 s What story, topic, riddle, picture or movie did you miss? What should be corrected? In order to simplify annotations, the pdf le allows adding yellow sticker notes in Adobe Reader. Alternatively, you can provide feedback on www.motionmountain.net/ wiki.Helponthespecicpointslistedonthewww.motionmountain.net/help.html web page would be particularly welcome. All feedback will be used to improve the next edi- tion. 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. Your donation to the charitable, tax-exempt non-prot organisation that produces, translates and publishes this book series is welcome! For details, see the web page www. motionmountain.net/donation.html. If you want, your name will be included in the sponsor list. ank you in advance for your help, on behalf of all readers across the world. A paper edition of this book, printed on demand and delivered by mail to any ad- dress, can be ordered at www.lulu.com/spotlight/motionmountain.Butaboveall,enjoy the reading! Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Copyright © Christoph Schiller June 1990–November 2012 C M – e eects of the quantum of action on rest • e consequences of the quantum of action for objects • Why ‘quantum’? • e eect of the quantum of action on motion • e surprises of the quantum of action • Transformation, life and Democritus • Randomness – a consequence of the quantum of action • Waves – a consequence of the quantum of action •Particles–aconsequenceof the quantum of action • Quantum information • Curiosities and fun chal- lenges about the quantum of action • e dangers of buying a can of beans • A summary: quantum physics, the law and indoctrination L – How do faint lamps behave? •Photons •Whatislight? •esize of photons • Are photons countable? – Squeezed light •epositions of photons • Are photons necessary? • Interference: how can a wave be made up of particles? • Interference of a single photon •Reection and diraction deduced from photon arrows • Refraction and partial reection from photon arrows •Fromphotonstowaves •Canlightmovefasterthan light? – Virtual photons • Indeterminacy of electric elds •Curiositiesand fun challenges about photons • A summary on light: particle and wave M – Wine glasses, pencils and atoms – no rest • No innite precision •Cool gas • Flows and the quantization of matter •Fluidowsandquan- tons • Knocking tables and quantized conductivity •Matterquantonsand their motion – matter waves • Mass and acceleration of quantons •Why are atoms not at? Why do shapes exist? • Rotation, quantization of angular momentum, and the lack of north poles • Rotation of quantons •Silver, Stern and Gerlach – polarization of quantons • Curiosities and fun challenges about quantum matter • First summary on the motion of quantum particles T States and measurements • Visualizing the wave function: rotating arrows and probability clouds • e state evolution – the Schrödinger equation •Self- interference of quantons • e speed of quantons • Dispersion of quan- tons • Tunnelling and limits on memory – damping of quantons •e quantum phase • Can two photons interfere? •Cantwoelectronbeamsin- terfere? Are there coherent electron beams? •eleastactionprincipleinquan- tum physics • e motion of quantons with spin • Relativistic wave equa- tions • Composite vs. elementary quantons • Curiosities and fun challenges about quantum motion of matter • A summary on motion of quantons P – ? Distinguishing macroscopic objects • Distinguishing atoms •Why does indistinguishability appear in nature? • Can quantum particles be counted? • What is permutation symmetry? • Indistinguishability and wave function symmetry • e behaviour of photons •Bunchingand antibunching • e energy dependence of permutation symmetry •In- distinguishability in quantum eld theory • How accurately is permutation symmetry veried? • Copies, clones and gloves • Summary Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Copyright © Christoph Schiller June 1990–November 2012 [...]... Credits Film credits 243 • Image credits 243 Copyright © Christoph Schiller June 1990–November 2012 6 Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net 113 contents 12 Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Copyright © Christoph Schiller June 1990–November 2012 The Quantum of Change In our... ” limbing Motion Mountain up to this point, we completed three legs We ame across Galileo’s mechanics (the description of motion for kids), then ontinued with Einstein’s relativity (the description of motion for science-fiction enthusiasts), and finally explored Maxwell’s electrodynamics (the description of motion for business people) These three classical descriptions of motion are impressive, beautiful... the Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net C “ Natura [in operationibus suis] non facit saltus.* 15th century 1 minimum action – quantum theory for poets 15 All attempts to observe physical actions values smaller than this fail.** In other words, Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net... a discovery as important as universal gravity Indeed, Planck knew that he had found the key to understanding many of the effects that were then unexplained Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Forget all you have learnt so far: Inertial motion is an approximation! An object can move in straight, uniform motion only approximately, and... He was right in unifying all change in nature – from transport to transformation and growth – as motion of particles But he was wrong in assuming that the small particles behave like stones The smallest particles behave like quantons: they behave randomly, and they behave partly as waves and partly as particles What happens if we try to measure a change smaller than the quantum of action? Nature has... it is expected that their particle-like aspects, the gravitons, exist also in this case.) In summary, the quantum of action states: Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net The quantum of action, the smallest change, implies that flows cannot be arbitrary weak This applies to all flows: in particular, it applies to rivers, solid matter flows,... Motion Mountain The consequences of the quantum of action are so strange, so incredible, and so numerous, that quantum physics can rightly be called the description of motion for crazy scientists In a sense, this generalizes our previous definition of quantum physics as the description of motion related to pleasure Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net... as combinations of length, time and mass units, we find: Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net F I G U R E 6 Max Born (1882–1970) 1 minimum action – quantum theory for poets 21 TA B L E 2 Some small systems in motion and the observed action values for their changes System and change Motion 1ħ 2ħ c 5 ħ 1ħ c 3 ħ c 1017 ħ quantum quantum quantum... all other quantum matter particles): this was the essence of his doctoral thesis The prediction was first confirmed experimentally a few years later, in 1927 For the prediction of the wave nature of matter, de Broglie received Copyright © Christoph Schiller June 1990–November 2012 E = ħω Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Vol I, page... distance becomes small enough, the two particles can switch roles, without anybody being able to avoid, or notice, it Thus, in a volume of gas it is impossible – thanks to the quantum of action – to follow particles moving around and to say which particle is which Can you confirm this deduction, and specify the conditions, using the indeterminacy relations? In summary Motion Mountain – The Adventure of Physics . Alternatively, you can provide feedback on www.motionmountain.net/ wiki.Helponthespecicpointslistedonthewww.motionmountain.net/help.html web page would be particularly. called motivat- ing;bothtermsgobacktothesameLatinroot. Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net