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Christoph Schiller DUMMY TEXT TEXT TEXT TEXT TEXT TEXT TEXT TEXT TEXT TEXT TEXT TEXT TEXT TEXT TEXT TEXT TEX Motion Mountain The Adventure of Physics www.motionmountain.net Christoph Schiller Motion Mountain The Adventure of Physics available at www.motionmountain.net Editio decima octava Proprietas scriptoris Christophori Schiller secundo anno Olympiadis vicesimae sextae secundo anno Olympiadis vicesimae octavae 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 Eighteenth revision, September  Copyright ©  –  by Christoph Schiller, between the second year of the th olympiad and the second year of the th olympiad All rights reserved Commercial reproduction, distribution or use, in whole or in part, is not allowed without the written consent of the copyright owner You are not allowed to charge money for anything containing any part of this text; it was and remains free for everybody About the cover photograph, see page  To T τῷ ἐµοὶ δαὶµονι Die Menschen stärken, die Sachen klären Contents Preface 20 An appetizer First Part : 23 Cl assical Physics – How Do Things and Images Move? Chapter II Special R el ativity Maximum speed, observers at rest, and motion of light 249 249 Chapter III Gravitation and R el ativity Maximum force: general relativity in one statement The new ideas on space, time and gravity Motion in general relativity – bent light and wobbling vacuum 10 Why can we see the stars? – Motion in the universe 11 Black holes – falling forever 12 Does space differ from time? 13 General relativity in ten points – a summary for the layman 319 319 344 362 402 440 454 460 Chapter IV Cl assical Electrodynamics 14 Liquid electricity, invisible fields and maximum speed 15 What is light? 16 Charges are discrete – the limits of classical electrodynamics 17 Electromagnetic effects and challenges 18 Classical physics in a nutshell – one and a half steps out of three 478 478 516 545 547 568 Intermezzo The Brain, L anguage and the Human Condition 584 Second Part : tions? Quantum Theory – What Is Matter? What Are Interac- 656 656 668 685 702 Chapter VI Permu tation of Particles 23 Are particles like gloves? 24 Rotations and statistics – visualizing spin 719 719 727 Chapter VII Details of Quantum Theory and Electromagnetism 25 Superpositions and probabilities – quantum theory without ideology 26 Applied quantum mechanics – life, pleasure and the means to achieve them 27 Quantum electrodynamics – the origin of virtual reality 739 739 761 796 Copyright © Christoph Schiller November 1997–September 2005 Chapter V Quanta of Light and Matter 19 Minimum action – quantum theory for poets and lawyers 20 Light – the strange consequences of the quantum of action 21 Motion of matter – beyond classical physics 22 Colours and other interactions between light and matter www.motionmountain.net 28 28 40 158 239 Motion Mountain Chapter I Galilean Motion Why should we care about motion? Galilean physicsmotion in everyday life Global descriptions of motion: the simplicity of complexity From the limitations of physics to the limits of motion 28 Quantum mechanics with gravitation – the first approach 809 Chapter VIII Inside the Nucleus 29 The structure of the nucleus – the densest clouds 30 The strong nuclear interaction and the birth of matter 31 The weak nuclear interaction and the handedness of nature 32 The standard model of elementary particle physics – as seen on television 33 Grand unification – a simple dream 836 836 857 868 872 873 Chapter IX Advanced Quantum Theory (Not yet Avail able) 879 Chapter X Quantum Physics in a Nu tshell 880 Intermezzo Bacteria, Flies and Knots 896 Third Part : Particles? Motion Withou t Motion – What Are Space, Time and 918 920 952 975 985 1016 Chapter Extension and Unification (Not yet Avail able) 1046 Chapter XIII The Top of the Mountain (Not yet Avail able) 1047 Fourth Part : Appendices Appendix A Notation and Conventions 1049 Appendix B Units, Measurements and Constants 1060 Appendix C Particle Properties 1078 Appendix D Numbers and Spaces 1098 Appendix E Information Sources on Motion 1128 Appendix F Challenge Hints & Solu tions 1134 Appendix G List of Illustrations 1178 Appendix H List of Tables 1190 Appendix I Name Index 1193 Appendix J Subject Index 1216 XII Motion Mountain Chapter XI General R el ativity Versus Quantum Mechanics 34 Does matter differ from vacuum? 35 Nature at large scales – is the universe something or nothing? 36 The physics of love – a summary of the first two and a half parts 37 Maximum force and minimum distance: physics in limit statements 38 The shape of points – extension in nature www.motionmountain.net Copyright © Christoph Schiller November 1997–September 2005 Detailed Contents Preface 20 An appetizer 23 First Part : Cl assical Physics How Do Things and Images Move? 28 28 40 61 70 145 158 161 173 Copyright © Christoph Schiller November 1997–September 2005 133 www.motionmountain.net 108 Motion Mountain Chapter I Galilean Motion Why should we care about motion? Does motion exist? 29 • How should we talk about motion? 31 • What are the types of motion? 32 • Perception, permanence and change 36 • Does the world need states? 38 • Curiosities and fun challenges about motion 39 • Galilean physicsmotion in everyday life What is velocity? 41 • What is time? 42 • Why clocks go clockwise? 47 • Does time flow? 47 • What is space? 48 • Are space and time absolute or relative? 50 • Size: why area exists, but volume does not 51 • What is straight? 54 • A hollow Earth? 55 • Curiosities and fun challenges about everyday space and time 56 • How to describe motion: kinematics What is rest? 63 • Objects and point particles 66 • Legs and wheels 69 • Objects and images Motion and contact 72 • What is mass? 72 • Is motion eternal? 77 • More on conservation – energy 79 • Is velocity absolute? – The theory of everyday relativity 81 • Rotation 83 • Rolling wheels 87 • How we walk? 87 • Is the Earth rotating? 89 • How does the Earth rotate? 94 • Does the Earth move? 96 • Is rotation relative? 99 • Curiosities and fun challenges about everyday motion 100 • Legs or wheels? – Again 106 • Dynamics due to gravitation Properties of gravitation 111 • Dynamics: how things move in various dimensions? 115 • Gravitation in the sky 116 • The Moon 117 • Orbits 118 • Tides 120 • Can light fall? 123 • What is mass? – Again 124 • Curiosities and fun challenges about gravitation 125 • What is classical mechanics? Should one use force? 134 • Complete states: initial conditions 139 • Do surprises exist? Is the future determined? 141 • A strange summary about motion 144 • Bibliography Global descriptions of motion: the simplicity of complexity Measuring change with action The principle of least action 164 • Why is motion so often bounded? 168 • Curiosities and fun challenges about Lagrangians 170 • Motion and symmetry Why can we think and talk? 174 • Viewpoints 174 • Symmetries and groups 176 • Representations 177 • Symmetries, motion and Galilean  contents 201 212 214 232 239 242 249 249 www.motionmountain.net 269 282 Copyright © Christoph Schiller November 1997–September 2005 Chapter II Special Relativity Maximum speed, observers at rest, and motion of light Can one play tennis using a laser pulse as the ball and mirrors as rackets? 254 • Special relativity in a few lines 256 • Acceleration of light and the Doppler effect 257 • The difference between light and sound 260 • Can one shoot faster than one’s shadow? 261 • The addition of velocities 263 • Observers and the principle of special relativity 263 • What is space-time? 266 • Can we travel to the past? – Time and causality 268 • Curiosities of special relativity Faster than light: how far can we travel? 269 • Synchronization and aging: can a mother stay younger than her own daughter? – Time travel to the future 270 • Length contraction 272 • Relativistic movies – aberration and Doppler effect 275 • Which is the best seat in a bus? 277 • How fast can one walk? 278 • Is the speed of shadow greater than the speed of light? 278 • Parallel to parallel is not parallel – Thomas rotation 282 • A never-ending story: temperature and relativity 282 • Relativistic mechanics Mass in relativity 283 • Why relativistic snooker is more difficult 284 • Mass is concentrated energy 285 • Collisions, virtual objects and tachyons 287 • Systems of particles: no centre of mass 289 • Why is most motion so slow? 290 • The history of the mass–energy equivalence formula by de Pretto and Einstein 290 • Four-vectors 291 • Four-momentum 294 187 Motion Mountain physics 179 • Reproducibility, conservation and Noether’s theorem 182 • Curiosities and fun challenges about motion symmetry 187 • Simple motions of extended bodies – oscillations and waves Waves and their motion 189 • Why can we talk to each other? – Huygens’ principle 193 • Signals 194 • Solitary waves and solitons 195 • Curiosities and fun challenges about waves and extended bodies 197 • Do extended bodies exist? Mountains and fractals 201 • Can a chocolate bar last forever? 202 • How high can animals jump? 203 • Felling trees 204 • The sound of silence 205 • Little hard balls 205 • Curiosities and fun challenges about fluids and solids 208 • What can move in nature? Why are objects warm? Entropy 217 • Flow of entropy 218 • Do isolated systems exist? 219 • Why balloons take up space? – The end of continuity 220 • Brownian motion 221 • Entropy and particles 223 • The minimum entropy of nature: the quantum of information 224 • Why can’t we remember the future? 226 • Is everything made of particles? 226 • Why stones can be neither smooth nor fractal, nor made of little hard balls 227 • Curiosities and fun challenges about heat 228 • Self-organization and chaos Curiosities and fun challenges about self-organization 237 • From the limitations of physics to the limits of motion Research topics in classical dynamics 239 • What is contact? 240 • Precision and accuracy 240 • Can all of nature be described in a book? 241 • Why is measurement possible? 241 • Is motion unlimited? 242 • Bibliography ... particular between the various examples of motion This is a guide to the top of what I have called Motion Mountain The hike is one of the most beautiful adventures of the human mind Clearly, the first... fire, the warmth of a human body, the waves of the sea and the mood changes of people are all variations of motion of particles This story is told in more detail in the second part of the text,... limitations of physics to the limits of motion 28 Quantum mechanics with gravitation – the first approach 809 Chapter VIII Inside the Nucleus 29 The structure of the nucleus – the densest clouds 30 The

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  • Preface

  • 1. An appetizer

  • First Classical PhysicsHow Do Things and Images Move?

    • ChapterI Galilean Motion

      • 2. Why should we care about motion?

        • Does motion exist?

          • How should we talk about motion?

          • What are the types of motion?

          • Perception, permanence and change

          • Does the world need states?

          • Curiosities and fun challenges about motion

      • 3. Galilean physics -- motion in everyday life

        • What is velocity?

          • What is time?

          • Why do clocks go clockwise?

          • Does time flow?

          • What is space?

          • Are space and time absolute or relative?

          • Size: why area exists, but volume does not

          • What is straight?

          • A hollow Earth?

          • Curiosities and fun challenges about everyday space and time

        • How to describe motion: kinematics

          • What is rest?

          • Objects and point particles

          • Legs and wheels

        • Objects and images

          • Motion and contact

          • What is mass?

          • Is motion eternal?

          • More on conservation -- energy

          • Is velocity absolute? -- The theory of everyday relativity

          • Rotation

          • Rolling wheels

          • How do we walk?

          • Is the Earth rotating?

          • How does the Earth rotate?

          • Does the Earth move?

          • Is rotation relative?

          • Curiosities and fun challenges about everyday motion

          • Legs or wheels? -- Again

        • Dynamics due to gravitation

          • Properties of gravitation

          • Dynamics: how do things move in various dimensions?

          • Gravitation in the sky

          • The Moon

          • Orbits

          • Tides

          • Can light fall?

          • What is mass? -- Again

          • Curiosities and fun challenges about gravitation

        • What is classical mechanics?

          • Should one use force?

          • Complete states: initial conditions

          • Do surprises exist? Is the future determined?

          • A strange summary about motion

        • Bibliography

      • 4. Global descriptions of motion: the simplicity of complexity

        • Measuring change with action

          • The principle of least action

          • Why is motion so often bounded?

          • Curiosities and fun challenges about Lagrangians

        • Motion and symmetry

          • Why can we think and talk?

          • Viewpoints

          • Symmetries and groups

          • Representations

          • Symmetries, motion and Galilean physics

          • Reproducibility, conservation and Noether's theorem

          • Curiosities and fun challenges about motion symmetry

        • Simple motions of extended bodies -- oscillations and waves

          • Waves and their motion

          • Why can we talk to each other? -- Huygens' principle

          • Signals

          • Solitary waves and solitons

          • Curiosities and fun challenges about waves and extended bodies

        • Do extended bodies exist?

          • Mountains and fractals

          • Can a chocolate bar last forever?

          • How high can animals jump?

          • Felling trees

          • The sound of silence

          • Little hard balls

          • Curiosities and fun challenges about fluids and solids

        • What can move in nature?

        • Why are objects warm?

          • Entropy

          • Flow of entropy

          • Do isolated systems exist?

          • Why do balloons take up space? -- The end of continuity

          • Brownian motion

          • Entropy and particles

          • The minimum entropy of nature: the quantum of information

          • Why can't we remember the future?

          • Is everything made of particles?

          • Why stones can be neither smooth nor fractal, nor made of little hard balls

          • Curiosities and fun challenges about heat

        • Self-organization and chaos

          • Curiosities and fun challenges about self-organization

      • 5. From the limitations of physics to the limits of motion

        • Research topics in classical dynamics

          • What is contact?

          • Precision and accuracy

          • Can all of nature be described in a book?

          • Why is measurement possible?

          • Is motion unlimited?

        • Bibliography

    • ChapterII Special Relativity

      • 6. Maximum speed, observers at rest, and motion of light

        • Can one play tennis using a laser pulse as the ball and mirrors as rackets?

          • Special relativity in a few lines

          • Acceleration of light and the Doppler effect

          • The difference between light and sound

          • Can one shoot faster than one's shadow?

          • The addition of velocities

          • Observers and the principle of special relativity

          • What is space-time?

          • Can we travel to the past? -- Time and causality

        • Curiosities of special relativity

          • Faster than light: how far can we travel?

          • Synchronization and aging: can a mother stay younger than her own daughter? -- Time travel to the future

          • Length contraction

          • Relativistic movies -- aberration and Doppler effect

          • Which is the best seat in a bus?

          • How fast can one walk?

          • Is the speed of shadow greater than the speed of light?

          • Parallel to parallel is not parallel -- Thomas rotation

          • A never-ending story: temperature and relativity

        • Relativistic mechanics

          • Mass in relativity

          • Why relativistic snooker is more difficult

          • Mass is concentrated energy

          • Collisions, virtual objects and tachyons

          • Systems of particles: no centre of mass

          • Why is most motion so slow?

          • The history of the mass--energy equivalence formula by de Pretto and Einstein

          • Four-vectors

          • Four-momentum

          • Four-force

          • Rotation in relativity

          • Wave motion

          • The action of a free particle -- how do things move?

          • Conformal transformations: Why is the speed of light constant?

        • Accelerating observers

          • Acceleration for inertial observers

          • Accelerating frames of reference

          • Event horizons

          • Acceleration changes colours

          • Can light move faster than c?

          • What is the speed of light?

          • Limits on the length of solid bodies

        • Special relativity in four sentences

          • Could the speed of light vary?

          • What happens near the speed of light?

        • Bibliography

    • ChapterIII Gravitation and Relativity

      • 7. Maximum force: general relativity in one statement

        • The maximum force and power limits

          • The 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 flow limit

          • Hide and seek

          • An intuitive understanding of general relativity

          • An intuitive understanding of cosmology

          • Experimental challenges for the third millennium

          • A summary of general relativity

          • Bibliography

      • 8. The new ideas on space, time and gravity

        • Rest and free fall

          • What is gravity? -- A second answer

          • What tides tell us about gravity

          • Bent space and mattresses

          • Curved space-time

          • The speed of light and the constant of gravitation

          • Why does a stone thrown into the air fall back to Earth? -- Geodesics

          • Can light fall?

        • Curiosities about gravitation

          • What is weight?

          • Why do apples fall?

      • 9. Motion in general relativity -- bent light and wobbling vacuum

        • Weak fields

          • The Thirring effects

          • Gravitomagnetism

          • Gravitational waves

          • Bending of light and radio waves

          • Time delay

          • Effects on orbits

          • The geodesic effect

          • Curiosities about weak fields

        • How is curvature measured?

          • Curvature and space-time

          • Curvature and motion in general relativity

          • Universal gravity

          • The Schwarzschild metric

          • Curiosities and fun challenges about curvature

        • All observers: heavier mathematics

          • The curvature of space-time

          • The description of momentum, mass and energy

          • Hilbert's action -- how do things fall

          • The symmetries of general relativity

          • Einstein's field equations

          • More on the force limit

          • Deducing universal gravity

          • Deducing linearized general relativity

          • How to calculate the shape of geodesics

          • Mass in general relativity

          • Is gravity an interaction?

          • The essence of general relativity

          • Riemann gymnastics

      • 10. Why can we see the stars? -- Motion in the universe

        • Which stars do we see?

          • What do we see at night?

          • What is the universe?

          • The colour and the motion of the stars

          • Do stars shine every night?

          • A short history of the universe

          • The history of space-time

          • Why is the sky dark at night?

          • Is the universe open, closed or marginal?

          • Why is the universe transparent?

          • The big bang and its consequences

          • Was the big bang a big bang?

          • Was the big bang an event?

          • Was the big bang a beginning?

          • Does the big bang imply creation?

          • Why can we see the Sun?

          • Why are the colours of the stars different?

          • Are there dark stars?

          • Are all stars different? -- Gravitational lenses

          • What is the shape of the universe?

          • What is behind the horizon?

          • Why are there stars all over the place? -- Inflation

          • Why are there so few stars? -- The energy and entropy content of the universe

          • Why is matter lumped?

          • Why are stars so small compared with the universe?

          • Are stars and galaxies moving apart or is the universe expanding?

          • Is there more than one universe?

          • Why are the stars fixed? -- Arms, stars and Mach's principle

          • At rest in the universe

          • Does light attract light?

          • Does light decay?

      • 11. Black holes -- falling forever

        • Why study black holes?

          • Horizons

          • Orbits

          • Hair and entropy

          • Black holes as energy sources

          • Paradoxes, curiosities and challenges

          • Formation of and search for black holes

          • Singularities

          • A quiz: is the universe a black hole?

      • 12. Does space differ from time?

        • Can space and time be measured?

          • Are space and time necessary?

          • Do closed timelike curves exist?

          • Is general relativity local? -- The hole argument

          • Is the Earth hollow?

          • Are space, time and mass independent?

      • 13. General relativity in ten points -- a summary for the layman

        • The accuracy of the description

          • Research in general relativity and cosmology

          • Could general relativity be different?

          • The limits of general relativity

        • Bibliography

    • ChapterIV Classical Electrodynamics

      • 14. Liquid electricity, invisible fields and maximum speed

        • Amber, lodestone and mobile phones

          • How can one make lightning?

          • Electric charge and electric fields

          • Can we detect the inertia of electricity?

          • Feeling electric fields

          • Magnets

          • Can humans feel magnetic fields?

          • How can one make a motor?

          • Magnetic fields

          • How motors prove relativity to be right

          • Curiosities and fun challenges about things electric and magnetic

        • The description of electromagnetic field evolution

          • Colliding charged particles

          • The gauge field: the electromagnetic vector potential

          • Energy, linear and angular momentum of the electromagnetic field

          • The Lagrangian of electromagnetism

          • Symmetries: the energy--momentum tensor

          • What is a mirror?

          • What is the difference between electric and magnetic fields?

        • Electrodynamic challenges and curiosities

          • Could electrodynamics be different?

          • The toughest challenge for electrodynamics

      • 15. What is light?

        • The slowness of progress in physics

          • Does light travel in a straight line?

          • The concentration of light

          • Can one touch light?

          • War, light and lies

          • What is colour?

          • What is the speed of light? -- Again

          • 200 years too late: negative refraction indices

          • Signals and predictions

          • How does the world look when riding on a light beam?

          • Does the aether exist?

        • Challenges and curiosities about light

          • How to prove you're holy

          • Do we see what exists?

          • How does one make pictures of the inside of the eye?

          • How does one make holograms and other 3-d images?

          • Imaging

      • 16. Charges are discrete -- the limits of classical electrodynamics

        • How fast do charges move?

          • Challenges and curiosities about charge discreteness

      • 17. Electromagnetic effects and challenges

        • Is lightning a discharge? -- Electricity in the atmosphere

          • Does gravity make charges radiate?

          • Research questions

          • Levitation

          • Matter, levitation and electromagnetic effects

          • Why can we see each other?

          • A summary of classical electrodynamics and of its limits

      • 18. Classical physics in a nutshell -- one and a half steps out of three

        • The future of planet Earth

          • The essence of classical physics: the infinitely small implies the lack of surprises

          • Why have we not yet reached the top of the mountain?

        • Bibliography

    • IntermezzoThe Brain, Language and the Human Condition

      • Evolution

        • Children and physics

          • Why a brain?

          • What is information?

          • What is memory?

          • The capacity of the brain

        • What is language?

          • What is a concept?

          • What are sets? What are relations?

          • Infinity

          • Functions and structures

          • Numbers

          • Why use mathematics?

          • Is mathematics a language?

          • Curiosities and fun challenges

        • Physical concepts, lies and patterns of nature

          • Are physical concepts discovered or created?

          • How do we find physical patterns and rules?

          • What is a lie?

          • Is this statement true?

          • Challenges about lies

        • Observations

          • Have enough observations been recorded?

          • Are all physical observables known?

          • Do observations take time?

          • Is induction a problem in physics?

        • The quest for precision and its implications

          • What are interactions? -- No emergence

          • What is existence?

          • Do things exist?

          • Does the void exist?

          • Is nature infinite?

          • Is the universe a set?

          • Does the universe exist?

          • What is creation?

          • Is nature designed?

          • What is a description?

          • Reason, purpose and explanation

          • Unification and demarcation

          • Pigs, apes and the anthropic principle

          • Does one need cause and effect in explanations?

          • Is consciousness required?

          • Curiosity

          • Courage

        • Bibliography

  • Second Quantum TheoryWhat Is Matter? What Are Interactions?

    • ChapterV Quanta of Light and Matter

      • 19. Minimum action -- quantum theory for poets and lawyers

        • Gedanken experiments and challenges

      • 20. Light -- the strange consequences of the quantum of action

        • What is colour?

          • What is light? -- Again

          • The size of photons

          • Are photons countable? -- Squeezed light

          • The position of photons

          • Are photons necessary?

          • How can a wave be made up of particles?

          • Can light move faster than light? -- Virtual photons

          • Indeterminacy of electric fields

          • Curiosities and fun challenges about photons

      • 21. Motion of matter -- beyond classical physics

        • Wine glasses and pencils

          • Cool gas

          • No rest

          • Flows and the quantization of matter

          • Quantons

          • The motion of quantons -- matter as waves

          • Rotation and the lack of North Poles

          • Silver, Stern and Gerlach

          • The language of quantum theory and its description of motion

          • The evolution of operators

          • The state -- or wave function -- and its evolution

          • Why are atoms not flat? Why do shapes exist?

          • Rest: spread and the quantum Zeno effect

          • Tunnelling, hills and limits on memory

          • Spin and motion

          • Relativistic wave equations

          • Maximum acceleration

          • Curiosities and fun challenges about quantum theory

      • 22. Colours and other interactions between light and matter

        • What are stars made of?

          • What determines the colour of atoms?

          • Relativistic hydrogen

          • Relativistic wave equations -- again

          • Antimatter

          • Virtual particles and QED diagrams

          • Compositeness

          • Curiosities and fun challenges about colour

          • The strength of electromagnetism

        • Bibliography

    • ChapterVI Permutation of Particles

      • 23. Are particles like gloves?

        • Why does indistinguishability appear in nature?

          • Can particles be counted?

          • What is permutation symmetry?

          • Indistinguishability and symmetry

          • The behaviour of photons

          • The energy dependence of permutation symmetry

          • Indistinguishability in quantum field theory

          • How accurately is permutation symmetry verified?

          • Copies, clones and gloves

      • 24. Rotations and statistics -- visualizing spin

        • The belt trick

          • The Pauli exclusion principle and the hardness of matter

          • Integer spin

          • Is spin a rotation about an axis?

          • Why is fencing with laser beams impossible?

          • Rotation requires antiparticles

          • Limits and open questions of quantum statistics

        • Bibliography

    • ChapterVII Details of Quantum Theory and Electromagnetism

      • 25. Superpositions and probabilities -- quantum theory without ideology

        • Why are people either dead or alive?

          • Conclusions on decoherence, life and death

        • What is a system? What is an object?

          • Is quantum theory non-local? -- A bit about Einstein-Podolsky-Rosen

          • Curiosities

        • What is all the fuss about measurements in quantum theory?

          • Hidden variables

        • Conclusions on probabilities and determinism

          • What is the difference between space and time?

          • Are we good observers?

          • What connects information theory, cryptology and quantum theory?

          • Does the universe have a wave function? And initial conditions?

      • 26. Applied quantum mechanics -- life, pleasure and the means to achieve them

        • Biology

          • Reproduction

          • Quantum machines

          • How do we move? -- Molecular motors

          • Curiosities and fun challenges about biology

        • The physics of pleasure

          • The nerves and the brain

          • Clocks in quantum mechanics

          • Do clocks exist?

          • Living clocks

          • Metre sticks

          • Why are predictions so difficult, especially of the future?

          • Decay and the golden rule

          • Zeno and the present in quantum theory

          • What is motion?

          • Consciousness: a result of the quantum of action

          • Why can we observe motion?

          • Curiosities and fun challenges about quantum experience

        • Chemistry -- from atoms to DNA

          • Ribonucleic acid and Deoxyribonucleic acid

          • Chemical challenges and curiosities

        • Materials science

          • Why does the floor not fall?

          • Rocks and stones

          • How can one look through matter?

          • What is necessary to make matter invisible?

          • How does matter behave at lowest temperatures?

          • Curiosities and fun challenges about materials science

        • Quantum technology

          • Motion without friction -- superconductivity and superfluidity

          • Quantized conductivity

          • The fractional quantum Hall effect

          • Lasers and other spin-one vector boson launchers

          • Can two photons interfere?

          • Can two electron beams interfere?

          • Challenges and dreams about quantum technology

      • 27. Quantum electrodynamics -- the origin of virtual reality

        • Ships, mirrors and the Casimir effect

          • The Banach--Tarski paradox for vacuum

          • The Lamb shift

          • The QED Lagrangian

          • Interactions and virtual particles

          • Vacuum energy

          • Moving mirrors

          • Photon hitting photons

          • Is the vacuum a bath?

          • Renormalization -- why is an electron so light?

        • Curiosities and fun challenges of quantum electrodynamics

          • How can one move on perfect ice? -- The ultimate physics test

        • Summary of quantum electrodynamics

          • Open questions in QED

      • 28. Quantum mechanics with gravitation -- the first approach

        • Corrections to the Schrödinger equation

          • A rephrased large number hypothesis

          • Is quantum gravity necessary?

          • Limits to disorder

          • Measuring acceleration with a thermometer: Fulling--Davies--Unruh radiation

        • Black holes aren't black

          • Gamma ray bursts

          • Material properties of black holes

          • How do black holes evaporate?

          • The information paradox of black holes

          • More paradoxes

        • Quantum mechanics of gravitation

          • The gravitational Bohr atom

          • Decoherence of space-time

          • Do gravitons exist?

          • Space-time foam

          • No particles

          • No science fiction

          • Not cheating any longer

        • Bibliography

    • ChapterVIII Inside the Nucleus

      • 29. The structure of the nucleus -- the densest clouds

        • A physical wonder: magnetic resonance imaging

          • The size of nuclei

          • Nuclei are composed

          • Nuclei can move alone -- cosmic rays

          • Nuclei decay

          • Nuclei can form composites

          • Nuclei have colours and shapes

          • Motion in the nuclear domain -- four types of motion

          • Nuclei react

          • Bombs and nuclear reactors

          • The Sun

          • Curiosities and fun challenges on radioactivity

      • 30. The strong nuclear interaction and the birth of matter

        • Why do the stars shine?

          • Where do our atoms come from?

          • The weak side of the strong interaction

          • Bound motion, the particle zoo and the quark model

          • The mass, shape, and colour of protons

          • Experimental consequences of the quark model

          • The Lagrangian of quantum chromodynamics

          • The sizes and masses of quarks

          • Confinement and the future of the strong interaction

          • Curiosities about the strong interactions

      • 31. The weak nuclear interaction and the handedness of nature

        • Curiosities about the weak interactions

          • Mass, the Higgs boson and a ten thousand million dollar lie

          • Neutrinium and other curiosities about the electroweak interaction

      • 32. The standard model of elementary particle physics -- as seen on television

        • Conclusion and open questions about the standard model

      • 33. Grand unification -- a simple dream

        • Experimental consequences

          • The state of grand unification

        • Bibliography

    • ChapterIX Advanced Quantum Theory (Not yet Available)

    • ChapterX Quantum Physics in a Nutshell

      • Quantum theory's essence: the lack of the infinitely small

        • Achievements in precision

          • Physical results of quantum theory

          • Results of quantum field theory

          • Is quantum theory magic?

          • The dangers of buying a can of beans

        • The essence and the limits of quantum theory

          • What is unexplained by quantum theory and general relativity?

          • How to delude oneself that one has reached the top of the Motion Mountain

          • What awaits us?

        • Bibliography

    • IntermezzoBacteria, Flies and Knots

      • Bumble-bees and other miniature flying systems

        • Swimming

          • Falling cats and the theory of shape change

          • Turning a sphere inside out

          • Knots, links and braids

          • Knots in nature and on paper

          • Clouds

          • Fluid space-time

          • Solid space-time

          • Swimming in curved space

          • Curiosities and fun challenges

          • Outlook

        • Bibliography

  • Third Motion Without MotionWhat Are Space, Time and Particles?

    • ChapterXI General Relativity Versus Quantum Mechanics

      • The contradictions

      • 34. Does matter differ from vacuum?

        • Planck scales

          • Farewell to instants of time

          • Farewell to points in space

          • Farewell to the space-time manifold

          • Farewell to observables and measurements

          • Can space-time be a lattice? -- A glimpse of quantum geometry

          • Farewell to particles

          • Farewell to mass

          • Curiosities and fun challenges

          • Farewell to the big bang

          • The baggage left behind

        • Some experimental predictions

        • Bibliography

      • 35. Nature at large scales -- is the universe something or nothing?

        • Cosmological scales

          • Maximum time

          • Does the universe have a definite age?

          • How precisely can ages be measured?

          • Does time exist?

          • What is the error in the measurement of the age of the universe?

          • Maximum length

          • Is the universe really a big place?

          • The boundary of space-time -- is the sky a surface?

          • Does the universe have initial conditions?

          • Does the universe contain particles and stars?

          • Does the universe contain masses and objects?

          • Do symmetries exist in nature?

          • Does the universe have a boundary?

          • Is the universe a set?

          • Curiosities and fun challenges

          • Hilbert's sixth problem settled

          • Does the universe make sense?

          • A concept without a set eliminates contradictions

          • Extremal scales and open questions in physics

          • Is extremal identity a principle of nature?

        • Bibliography

      • 36. The physics of love -- a summary of the first two and a half parts

        • Bibliography

      • 37. Maximum force and minimum distance: physics in limit statements

        • Fundamental limits to all observables

          • Special relativity in one statement

          • Quantum theory in one statement

          • General relativity in one statement

          • Deducing general relativity

          • Deducing universal gravitation

          • The size of physical systems in general relativity

          • A mechanical analogy for the maximum force

        • Units and limit values for all physical observables

          • Limits to space and time

          • Mass and energy limits

          • Virtual particles -- a new definition

          • Limits in thermodynamics

          • Electromagnetic limits and units

          • Vacuum and mass-energy -- two sides of the same coin

          • Paradoxes and curiosities about Planck limits

        • Upper and lower limits to observables

          • Size and energy dependence

          • Angular momentum, action and speed

          • Force, power and luminosity

          • Acceleration

          • Momentum

          • Lifetime, distance and curvature

          • Mass change

          • Mass and density

          • The strange charm of the entropy bound

          • Temperature

          • Electromagnetic observables

          • Paradoxes and challenges around the limits

        • Limits to measurement precision and their challenge to thought

          • Measurement precision and the existence of sets

          • Why are observers needed?

          • A solution to Hilbert's sixth problem

          • Outlook

          • Bibliography

      • 38. The shape of points -- extension in nature

        • Introduction: vacuum and particles

          • How else can we show that matter and vacuum cannot be distinguished?

        • Argument 1: The size and shape of elementary particles

          • Do boxes exist?

          • Can the Greeks help? -- The limits of knifes

          • Are cross-sections finite?

          • Can one take a photograph of a point?

          • What is the shape of an electron?

          • Is the shape of an electron fixed?

        • Argument 2: The shape of points in vacuum

          • Measuring the void

          • What is the maximum number of particles that fits inside a piece of vacuum?

        • Argument 3: The large, the small and their connection

          • Small is large?

          • Unification and total symmetry

        • Argument 4: Does nature have parts?

          • Does the universe contain anything?

          • An amoeba

        • Argument 5: The entropy of black holes

        • Argument 6: Exchanging space points or particles at Planck scales

        • Argument 7: The meaning of spin

        • Present research

          • Conceptual checks of extension

          • Experimental falsification of models based on extended entities

          • Possibilities for confirmation of extension models

          • Curiosities and fun challenges

          • An intermediate status report

          • Sexual preferences in physics

          • A physical aphorism

        • Bibliography

    • ChapterXII Extension and Unification (Not yet Available)

    • ChapterXIII The Top of the Mountain (Not yet Available)

  • Fourth Appendices

    • AppendixA Notation and Conventions

      • The symbols used in the text

        • The Latin alphabet

          • The Greek alphabet

          • The Hebrew alphabet and other scripts

          • Digits and numbers

          • Calendars

          • Abbreviations and eponyms or concepts?

          • Bibliography

    • AppendixB Units, Measurements and Constants

      • Planck's natural units

        • Other unit systems

          • Curiosities

          • Precision and accuracy of measurements

          • Basic physical constants

          • Useful numbers

          • Bibliography

    • AppendixC Particle Properties

      • Bibliography

    • AppendixD Numbers and Spaces

      • Numbers as mathematical structures

        • Complex numbers

          • Quaternions

          • Octonions

          • Other types of numbers

          • Grassmann numbers

        • Vector spaces

        • Algebras

          • Lie algebras

          • Classification of Lie algebras

          • Lie superalgebras

          • The Virasoro algebra

          • Kac--Moody algebras

        • Topology -- what shapes exist?

          • Topological spaces

          • Manifolds

          • Holes, Homotopy and Homology

        • Types and classification of groups

          • Lie groups

          • Connectedness

          • Compactness

        • Mathematical curiosities and fun challenges

        • Bibliography

    • AppendixE Information Sources on Motion

    • AppendixF Challenge Hints & Solutions

    • AppendixG List of Illustrations

      • Picture credits

    • AppendixH List of Tables

    • AppendixI Name Index

    • AppendixJ Subject Index

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