Christoph Schiller MOTION MOUNTAIN the adventure of physics – vol.vi the strand model – a speculation on unification www.motionmountain.net Christoph Schiller M M e Adventure of Physics Volume VI e Strand Model – A Speculation on Unication 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 is book is written for anybody who is intensely curious about nature and motion. Have youeverasked:Whydopeople,animals,things,imagesandemptyspacemove?e answer leads to many adventures, and this book presents one of the best of them: the search for a precise, unied and nal description of all motion. e wish to describe all motion is a large endeavour. Fortunately, this large endeavour canbestructuredinthesimplediagramshowninFigure .enal and unied descrip- tion of motion, the topic of this book, corresponds to the highest point in the diagram. Searching for this nal and unied description is an old quest. In the following, I briey summarize its history and then present an intriguing, though speculative solution to the riddle. e search for the nal, unied description of motion is a story of many surprises. For example, twentieth-century research has shown that there is a smallest distance in nature. Research has also shown that matter cannot be distinguished from empty space at those small distances. A last surprise dates from this century: particles and space are best described as made of strands, instead of little spheres or points. e present text explains how to reach these unexpected conclusions. In particular, quantum eld theory, the standard model of particle physics, general relativity and cosmology are shown to follow from strands. e three gauge interactions, the three particle generations and the three dimensions of space turn out to be due to strands. In fact, all the open questions of twentieth-century physics about the foundations of motion, all the millennium issues, can be solved with the help of strands. e strand model, as presented in this text, is an unexpected result from a threefold aim that I have pursued since , in the ve previous volumes of this series: to present the basics of motion in a way that is up to date, captivating and simple. In retrospect, the aim for maximum simplicity has been central in deducing this speculation. While the previous volumes introduced, in an entertaining way, the established parts of physics, this volume presents, in the same entertaining and playful way, a speculation about uni- cation. Nothing in this volume is established knowledge – yet. e text is the original presentation of the topic. e search for a nal theory is one of the great adventures of life: it leads to the limits of thought. e search overthrows our thinking habits about nature. A change in think- ing habits can produce fear, oen hidden by anger. But by overcoming our fears we gain strength and serenity. Changing thinking habits thus requires courage, but it also pro- duces intense and beautiful emotions. Enjoy them! Munich, December . Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Copyright © Christoph Schiller June 1990–December 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. 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 for which no solution has yet been included in the book are marked (ny). is sixth volume of the Motion Mountain series has been typeset in a way that print- ing the le in black and white gives the smallest possible reduction in reading pleasure. Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Copyright © Christoph Schiller June 1990–December 2012 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 missing or hard to follow and should be claried? Challenge 1 s 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–December 2012 C F Against a nal theory •Whatwentwronginthepast • How to nd the nal theory of motion P 24 Simplifying physics as much as possible Everyday, or Galilean, physics in one statement • Special relativity in one state- ment • Quantum theory in one statement • ermodynamics in one state- ment • General relativity in one statement • Deducing general relativity • Deducing universal gravitation • e size of physical systems in general rela- tivity • A mechanical analogy for the maximum force 33 Planck limits for all physical observables Physics, mathematics and simplicity • Limits to space, time and size •Mass and energy limits • Virtual particles – a new denition • Curiosities and fun challenges about Planck limits 41 Cosmological limits for all physical observables Size and energy dependence • Angular momentum and action • Speed • Force, power and luminosity • e strange charm of the entropy bound • Curiosities and fun challenges about system-dependent limits to observables • Cosmology in one statement • e cosmological limits to observables • Limits to measurement precision and their challenge to thought •Noreal numbers • Vacuum and mass: two sides of the same coin •Measurement precision and the existence of sets 50 Summary on limits in nature G e contradictions •eoriginofthecontradictions •edomainofcon- tradictions: Planck scales • Resolving the contradictions •eoriginof points • Summary on the clash between the two theories D ? Farewell to instants of time •Farewelltopointsinspace • e generalized indeterminacy principle •Farewelltospace-timecontinuity •Farewell to dimensionality • Farewell to the space-time manifold •Farewelltoob- servables, symmetries and measurements • Can space-time be a lattice? • Aglimpseofquantumgeometry •Farewelltopointparticles •Farewell to particle properties • A mass limit for elementary particles •Farewellto massive particles – and to massless vacuum • Matter and vacuum are indistin- guishable • Curiosities and fun challenges on Planck scales • Common constituents • Experimental predictions • Summary on particles and vacuum W ? Cosmological scales •Maximumtime • Does the universe have a denite age? • How precise can age measurements be? •Doestimeexist? • What is the error in the measurement of the age of the universe? •Maxi- mum length • Is the universe really a big place? •eboundaryofspace – is the sky a surface? • Does the universe have initial conditions? •Does the universe contain particles and stars? • Does the universe contain masses Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Copyright © Christoph Schiller June 1990–December 2012 [...]... processes, as is observed Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net L ook at what happens around us A child who smiles, a nightingale that sings, a ily that opens: all move Every shadow, even an immobile one, is due to moving ight Every mountain is kept in place by moving electrons Every star owes its formation and its shine to motion of matter and... of general relativity 261 • Equations from no equation 262 • The Hilbert action of general relativity 263 • Space-time foam 263 • Gravitons and gravitational waves 263 • Open challenge: Improve the argument for the graviton tangle 264 • Other defects in vacuum 264 • Torsion, curiosities and challenges about general relativity 265 • Predictions of the strand model about general relativity 268 Cosmology... grand unification and supersymmetry 247 • No new observable gravity effects in particle physics 247 • The status of our quest 248 10 General rel ativit y deduced from strands Flat space, special relativity and its limitations 249 • Classical gravitation 250 • Deducing universal gravitation from black hole properties 251 • Summary on universal gravitation from strands 252 • Curved space 253 • Horizons and... the search is a reductionist endeavour, as will become Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net The millennium list contains everything that particle physics and general relativity cannot explain In other words, the list contains everything that was unexplained in the domain of fundamental motion in the year 2000 The list is short, but it is... limit Whether elementary particles fulfil or even match this limit remains open at this point More about this issue below General relativity also implies an ‘indeterminacy relation’ for the size l and the energy E of systems: c4 ΔE ⩽ (21) Δl 4G Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Challenge 8 e Universal gravitation follows from the... four or more strands 307 Fun challenges and curiosities about particle tangles Motion through the vacuum – and the speed of light 309 Summary on millennium issues and predictions about particles Predictions about dark matter and the LHC 314 12 Particle properties deduced from strands The masses of the elementary particles General properties of particle mass values 316 • Boson mass ratios and the weak mixing... example of motion Combining quantum theory and general relativity, we discover that at the Planck limits, the universe, space and particles are not described by points We find that as long as we use points to describe particles and space, and as long as we use sets and elements to describe nature, a unified description of motion is impossible The combination of quantum theory and general relativity teaches... difference between kinetic energy T and potential energy U In other words, motion obeys the so-called least action principle, written as δW = 0 , where W = (T − U) dt (1) Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net T wentieth century physics deduced several invariant properties of motion hese invariants, such as the speed of light or the quantum of... spinning particle or a system showing the quantum Zeno effect, finding this minimum change is tricky Enjoy the challenge Copyright © Christoph Schiller June 1990–December 2012 Ref 13 (5) Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net W ⩾ ħ = 1.1 ⋅ 10−34 Js simplifying physics as much as possible Ref 14 Vol IV, page 23 existence of elementary particle... of the maximum force, as well as being the mass–energy of a black hole divided by its diameter, is also the surface gravity of a black hole times its mass Thus Copyright © Christoph Schiller June 1990–December 2012 Ref 17 c4 = 3.0 ⋅ 1043 N 4G Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net F⩽ simplifying physics as much as possible Challenge 5 e Challenge . you can provide feedback on www.motionmountain.net/ wiki.Helponthespecicpointslistedonthewww.motionmountain.net/help.html web page would be particularly. 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