Motion Mountain - vol. 6 - The Adventure of Physics: The Strand Model - A Speculation on Unification

Preface Using this book Feedback and support Contents A Speculation on Unification Chapter1 From millennium physics to unification Against a final theory What went wrong in the past Summary: how to find the final theory of motion Chapter2 Physics in limit statements Simplifying physics as much as possible Everyday, or Galilean, physics in one statement Special relativity in one statement Quantum theory in one statement Thermodynamics 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 Planck limits for all physical observables Physics, mathematics and simplicity Limits to space, time and size Mass and energy limits Virtual particles -- a new definition Curiosities and fun challenges about Planck limits Cosmological limits for all physical observables Size and energy dependence Angular momentum and action Speed Force, power and luminosity The strange charm of the entropy bound Curiosities and fun challenges about system-dependent limits to observables Cosmology in one statement The cosmological limits to observables Limits to measurement precision and their challenge to thought No real numbers Vacuum and mass: two sides of the same coin Measurement precision and the existence of sets Summary on limits in nature Chapter3 General relativity versus quantum theory The contradictions The origin of the contradictions The domain of contradictions: Planck scales Resolving the contradictions The origin of points Summary on the clash between the two theories Chapter4 Does matter differ from vacuum? Farewell to instants of time Farewell to points in space The generalized indeterminacy relation Farewell to space-time continuity Farewell to dimensionality Farewell to the space-time manifold Farewell to observables, symmetries and measurements Can space-time be a lattice? A glimpse of quantum geometry Farewell to point particles Farewell to particle properties A mass limit for elementary particles Farewell to massive particles -- and to massless vacuum Matter and vacuum are indistinguishable Curiosities and fun challenges on Planck scales Common constituents Experimental predictions Summary on particles and vacuum Chapter5 What is the difference between the universe and nothing? Cosmological scales Maximum time Does the universe have a definite age? How precise can age measurements be? 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 -- 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 about the universe Hilbert's sixth problem settled The perfect physics book Does the universe make sense? Abandoning sets and discreteness eliminates contradictions Extremal scales and open questions in physics Is extremal identity a principle of nature? Summary on the universe A physical aphorism Chapter6 The shape of points -- extension in nature The size and shape of elementary particles Do boxes exist? Can the Greeks help? -- The limitations of knives Are cross sections finite? Can we take a photograph of a point? What is the shape of an electron? Is the shape of an electron fixed? Summary of the first argument for extension The shape of points in vacuum Measuring the void What is the maximum number of particles that fit inside a piece of vacuum? Summary of the second argument for extension The large, the small and their connection Is small large? Unification and total symmetry Summary of the third argument for extension Does nature have parts? Does the universe contain anything? An amoeba Summary of the fourth argument for extension The entropy of black holes Summary of the fifth argument for extension Exchanging space points or particles at Planck scales Summary of the sixth argument for extension The meaning of spin Summary of the seventh argument for extension Curiosities and fun challenges about extension Gender preferences in physics Checks of extension Current research based on extended constituents Superstrings -- extension and a web of dualities Why superstrings and supermembranes are so appealing Why the mathematics of superstrings is so difficult Testing superstrings: couplings and masses The status of the superstring conjecture Summary on extension in nature Chapter7 The basis of the strand model Requirements for a final theory Introducing strands From strands to modern physics Vacuum Observables and limits Particles and fields Curiosities and fun challenges about strands Do strands unify? -- The millennium list of open issues Are strands final? -- On generalizations and modifications Why strands? -- Simplicity Why strands? -- The fundamental circularity of physics Funnels -- an equivalent alternative to strands Summary on the fundamental principle of the strand model -- and on continuity Chapter8 Quantum theory of matter deduced from strands Strands, vacuum and particles Rotation, spin 1/2 and the belt trick The belt trick is not unique An aside: the belt trick saves lives Fermions and spin Bosons and spin Spin and statistics Tangle functions: blurred tangles Details on fluctuations and averages Tangle functions are wave functions Deducing the Schrödinger equation from tangles Mass from tangles Potentials Quantum interference from tangles Deducing the Pauli equation from tangles Rotating arrows, interference and path integrals Measurements and wave function collapse Hidden variables and the Kochen--Specker theorem Many-particle states and entanglement Mixed states The dimensionality of space-time Operators and the Heisenberg picture Lagrangians and the principle of least action Special relativity: the vacuum Special relativity: the invariant limit speed Dirac's equation deduced from tangles Visualizing spinors and Dirac's equation using tangles Quantum mechanics vs. quantum field theory A flashback: settling three paradoxes of Galilean physics Fun challenges about quantum theory Summary on quantum theory of matter: millennium issues and experimental predictions Chapter9 Gauge interactions deduced from strands Interactions and phase change Tail deformations versus core deformations Electrodynamics and the first Reidemeister move Strands and the twist, the first Reidemeister move Can photons decay, disappear or break up? Electric charge Challenge: What knot invariant is electric charge? Electric and magnetic fields and potentials The Lagrangian of the electromagnetic field U(1) gauge invariance induced by twists U(1) gauge interactions induced by twists The Lagrangian of QED Feynman diagrams and renormalization The anomalous magnetic moment Maxwell's equations Curiosities and fun challenges about QED Summary on QED and experimental predictions The weak nuclear interaction and the second Reidemeister move Strands, pokes and SU(2) Weak charge and parity violation Weak bosons The Lagrangian of the unbroken SU(2) gauge interaction SU(2) breaking The electroweak Lagrangian The weak Feynman diagrams Fun challenges and curiosities about the weak interaction Summary on the weak interaction and experimental predictions The strong nuclear interaction and the third Reidemeister move Strands and the slide, the third Reidemeister move From slides to SU(3) The gluon Lagrangian Colour charge Properties of the strong interaction The Lagrangian of QCD Renormalization of the strong interaction Curiosities and fun challenges about SU(3) Summary on the strong interaction and experimental predictions Summary on millennium issues about gauge interactions Prediction about the number of interactions Unification of interactions Predictions about grand unification and supersymmetry No new observable gravity effects in particle physics The status of our quest Chapter10 General relativity deduced from strands Flat space, special relativity and its limitations Classical gravitation Deducing universal gravitation from black hole properties Summary on universal gravitation from strands Curved space Horizons and black holes Is there something behind a horizon? Energy of black hole horizons The nature of black holes Entropy of vacuum Entropy of horizons Temperature, radiation and evaporation of black holes Black hole limits Curvature around black holes The shape of black holes The field equations of general relativity Equations from no equation The Hilbert action of general relativity Space-time foam Gravitons and gravitational waves Open challenge: Improve the argument for the graviton tangle Other defects in vacuum The gravity of superpositions Torsion, curiosities and challenges about general relativity Predictions of the strand model about general relativity Cosmology The finiteness of the universe The big bang The cosmological constant The value of the matter density Open challenge: Are the conventional energy and matter densities correct? The topology of the universe Predictions of the strand model about cosmology Summary on millennium issues about relativity and cosmology Chapter11 The particle spectrum deduced from strands Particles and quantum numbers from tangles Particles made of one strand Unknotted curves Gauge bosons Complicated open knots Closed tangles: knots Summary on tangles made of one strand Particles made of two strands Quarks Quark generations The graviton Glueballs The mass gap problem and the Clay Mathematics Institute A puzzle Summary on two-stranded tangles Particles made of three strands Leptons Open challenge: Find better arguments for the lepton tangles The Higgs boson -- the mistaken section from 2009 The Higgs boson -- the corrected section of 2012 2012 predictions about the Higgs Quark-antiquark mesons Meson form factors Meson masses, excited mesons and quark confinement CP violation in mesons Other three-stranded tangles and glueballs Spin and three-stranded particles Summary on three-stranded tangles Tangles of four and more strands Baryons Tetraquarks and exotic mesons Other tangles made of four or more strands Summary on tangles made of four or more strands Fun challenges and curiosities about particle tangles Motion through the vacuum -- and the speed of light Summary on millennium issues about particles and related predictions Predictions about dark matter, the LHC and the universe Chapter12 Particle properties deduced from strands The masses of the elementary particles General properties of particle mass values W/Z boson mass ratios and the weak mixing angle 2013: Higgs/Z boson and Higgs/W boson mass ratio Quark mass ratios Lepton mass ratios Mass ratios across particle families Predictions about absolute mass values and the full mass hierarchy Fine-tuning and naturalness Open issues about mass calculations Summary on elementary particle masses and millennium issues Mixing angles Quark mixing -- the data Quark mixing -- explanations A challenge CP-violation in quarks Neutrino mixing CP-violation in neutrinos Open challenge: Calculate mixing angles and phases ab initio Summary on mixing angles and the millennium list Coupling constants and unification Strands imply unification General expectations about coupling constants First hint: charge quantization and topological writhe Second hint: the energy dependence of physical quantities Third hint: the running of the coupling constants at low energy Fourth hint: predictions at low energy, independent of particle content The running of the coupling constants near Planck energy On estimating the fine structure constant from knot shapes Fifth hint: 3d-writhe Sixth hint: torsion Seventh hint: linking number Eighth hint: estimating coupling constants using random rotations Ninth hint: estimating the fine structure constant from deformation statistics Open challenge: Calculate coupling constants ab initio Electric dipole moments Summary on coupling constants and millennium issues Final summary about the millennium issues Experimental predictions of the strand model Chapter13 The top of Motion Mountain Our path to the top Everyday life: the rule of infinity Relativity and quantum theory: the absence of infinity Unification: the absence of finitude New sights The beauty of strands Can the strand model be generalized? What is nature? Quantum theory and the nature of matter Cosmology Musings about unification and strands The elimination of induction What is still hidden? A return path: je rêve, donc je suis What is the origin of colours? Summary: what is motion? Postface AppendixA Knot geometry Challenge hints and solutions Bibliography Credits Acknowledgments Film credits Image credits Name index Subject index