Christoph Schiller MOTION MOUNTAIN the adventure of physics – vol.ii relativity www.motionmountain.net Christoph Schiller M M e Adventure of Physics Volume II Relativity 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 isbookiswrittenforanybodywhoiscuriousaboutnatureandmotion.Curiosity about how people, animals, things, images and empty space move leads to many adven- tures. is volume presents the best of them in the domains of relativity and cosmology. In the study of motion – physics – special and general relativity form two important building blocks, as shown in Figure . Special relativity is the exploration of the energy speed limit c. General relativity is the exploration of the force limit c 4 /4G. e text shows that in both domains, all equations follow from these two limit values. is simple, intuitive and unusual way of learning relativity should reward the curiosity of every reader – whether student or professional. e present volume is the second of a six-volume overview of physics that arose from a threefold aim that I have pursued since : to present 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 repeatingevery 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 , , Can one play tennis using a laser pulse as the ball and mirrors as rackets? • Albert Einstein • An invariant limit speed and its consequences •Special relativity with a few lines • Acceleration of light and the Doppler eect • e dierence between light and sound • Can one shoot faster than one’s shadow? • e composition of velocities •Observersandtheprincipleof special relativity •Whatisspace-time? • Can we travel to the past? – Time and causality • Curiosities about special relativity •Fasterthanlight: how far can we travel? •Synchronizationandtimetravel–canamotherstay younger than her own daughter? • Length contraction •Relativisticlms –aberrationandDopplereect •Whichisthebestseatinabus? •How fast can one walk? • Is the speed of shadow greater than the speed of light? • Parallel to parallel is not parallel – omas rotation •Anever-endingstory– temperature and relativity R Mass in relativity • Why relativistic snooker is more dicult •Massand energy are equivalent • Weighing light • Collisions, virtual objects and tachyons • Systems of particles – no centre of mass • Why is most motion so slow? • e history of the mass–energy equivalence formula •4-vectors •4-velocity • 4-acceleration and proper acceleration •4-momentumor energy–momentum or momenergy •4-force • Rotation in relativity •Wavemotion • e action of a free particle – how do things move? • Conformal transformations • Accelerating observers • Accelerating frames of reference • Constant acceleration •Eventhorizons •eimportance of horizons • Acceleration changes colours •Canlightmovefasterthan c? • e composition of accelerations • A curiosity: what is the one-way speed of light? • Limits on the length of solid bodies S Could the speed of light vary? • Where does special relativity break down? S : , - Maximum force – general relativity in one statement • e force and power limits • e experimental evidence • Deducing general relativity • Space-time is curved • Conditions of validity of the force and power limits • Gedanken experiments and paradoxes about the force limit •Gedanken experiments with the power limit and the mass ow limit •Whymaximum force has remained undiscovered for so long • An intuitive understanding of general relativity • An intuitive understanding of cosmology •Exper- imental challenges for the third millennium • A summary of general relativ- ity H , Rest and free fall •Whatclockstellusaboutgravity •Whattidestellus about gravity • Bent space and mattresses •Curvedspace-time • e speed of light and the gravitational constant •Whydoesastonethrown into the air fall back to Earth? – Geodesics • Can light fall? •Curiosities Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Copyright © Christoph Schiller June 1990–November 2012 [...]... speed of light Every electromagnetic device, such as an electric vacuum Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Ref 10 ” Et nihil est celerius annis.* Ovid, Metamorphoses motion of light 21 EasyGlide) F I G U R E 9 Albert Einstein (1879–1955) Vol III, page 46 Vol III, page 46 Challenge 14 ny Copyright © Christoph Schiller June 1990–November... light particles The speed of light would not be invariant, but the massless energy speed would still be so Massive light particles could be captured, stopped and stored in a box Such boxes would make electric illumination unnecessary; it would be sufficient to store some day- Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net x 28 Ref 27, Ref 12 Vol III,... observers Or, as Hendrik Lorentz*** liked to say, the equivalent: Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net O 36 1 maximum speed, observers at rest, and ⊳ The speed of a physical system is bound by ⩽c (10) for all observers, where c is the speed of light Vol III, page 99 Vol III, page 46 — In a closed free-floating (‘inertial’) room, there is... shown in Figure 4, the speed c of the rain is Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net α motion of light then given (approximately) by 17 c = / tan α (1) Challenge 5 s * Umbrellas were not common in Britain in 1726; they became fashionable later, after being introduced from China The umbrella part of the story is made up In reality, Bradley... right instant?) A finite speed of light also implies that a rapidly rotating light beam bends, as shown Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net F I G U R E 5 Fizeau’s set-up to measure the speed of light (photo © AG Didaktik und Geschichte der motion of light 19 F I G U R E 7 A consequence of the finiteness of the speed of light Watch out for... lightning, as you might like to check yourself A century of increasingly precise measurements of the speed have culminated in the modern value Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net TA B L E 1 Properties of the motion of light 20 Ref 9 1 maximum speed, observers at rest, and what is called the theory of special relativity Can one play tennis using... move, we find that there is a maximum force in nature, and we understand why we can see the stars Chapter 1 MA XIMUM SPEED, OBSERVERS AT R EST, AND MOTION OF LIGHT Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net * ‘Nothing is faster than rumour.’ This common sentence is a simplified version of Virgil’s phrase: fama, malum qua non aliud velocius... localized mass or energy) is bound by Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Page 125 Albert Einstein (b 1879 Ulm, d 1955 Princeton) was one of the greatest physicists and of the greatest thinkers ever (The ‘s’ in his name is pronounced ‘sh’.) In 1905, he published three important papers: one about Brownian motion, one about special relativity,... drawing shows that Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net O 26 1 maximum speed, observers at rest, and one moving watch first time second time F I G U R E 11 Moving clocks go slow: moving clocks mark time more slowly than do stationary clocks two fixed watches event Time is indeed different for two observers in relative motion This effect... Schiller June 1990–November 2012 Challenge 18 e 2 c2 Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net F I G U R E 12 Moving clocks go slow: moving lithium atoms in a storage ring (left) read out with lasers (right) confirm the prediction to highest precision (© Max Planck Gesellschaft, TSR relativity team) motion of light y first ladder (first observer) . 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. provide feedback on www.motionmountain.net/ wiki.Helponthespecicpointslistedonthewww.motionmountain.net/help.html web page would be particularly welcome.