Motion Mountain: The Adventure of Physics - Vol. VI: The Strand Model - A Speculation on Unification

New 2021 edition. What determines colours? What is motion? All colours in nature derive from the fine structure constant 1/137.035 999 1..., the most famous unexplained number in nature. What determines its value? All motion in nature is described either by quantum theory or by Einstein's general relativity, two theories that contradict each other. How can they be unified in a final theory?If you enjoy exploring ideas and checking them against the real world, you will like this volume. It first explains why the past proposals for a final, unified theory of physics – the so-called 'theory of everything' – have failed. Then, the text presents a better proposal: a final theory called the strand model. This model agrees with all experimental data known so far and makes clear, falsifiable predictions. They are being tested in experiments around the world. The strand model– predicts the standard model of particle physics – and allows no alternative or extension, – is based on one simple fundamental principle – and thus is 'beautiful', – predicts general relativity – and allows no alternative or extension, – predicts quantum theory – and allows no alternative or extension, – and solves the open issues of the standard model, gravitation and cosmology, including the explanation of all fundamental constants.These results follow naturally from one simple principle. Prepare yourself for a roller coaster ride trough modern physics, and for the excitement of solving one of the oldest physics puzzles known. This is an adventure that leads beyond space and time – right to the limits of human thought. For example, the adventure shows that the term 'theory of everything' is wrong, whereas 'final theory' is correct. The text presents an approach to the final, unified theory of physics with a simple basis but intriguing implications. The model is based on featureless strands that form space, particles and horizons; the model sums up textbook physics in a single fundamental principle: events and Planck units are crossing switches of strands. Surprisingly, this fundamental principle, which works in three dimensions only, allows to deduce Dirac's equation (from the belt trick), the principles of thermodynamics and Einstein's field equations (from the thermodynamics of strand crossing switches). Quantum theory and general relativity are thus found to be low-energy approximations of processes at the Planck scale. In particular, strands explain the entropy of black holes.As a further surprise, in the same approximation, the fundamental principle yields the three gauge groups and the Lagrangians of quantum electrodynamics, of the strong and of the weak interaction, including maximal parity violation and SU(2) breaking. The three Lagrangians appear as a natural consequence of the three Reidemeister moves of knot theory. The strand model does not permit any further interaction, gauge group or symmetry group. The strand model might even be the first unified model predicting the three gauge interactions – and the lack of other ones.In QED, the strand model proposes a simple understanding of Feynman diagrams and of Schwinger's formula for the anomalous magnetic moment of the electron and the muon. As a final surprise, the fundamental principle predicts three fermion generations, the Higgs boson, and the lack of any unknown elementary particles. The strand model thus predicts that the standard model is the final description of particle physics. The quark model and the construction of all mesons and baryons are shown to follow from strands. In other words, tangles of strands and their crossing switches explain all known elementary particles, all their quantum numbers, and the lack of any other elementary particles. The strand model might be the first unified model predicting the elementary particle spectrum.Finally, a natural method for the calculation of coupling constants, particle masses and mixing angles appears. Cover Preface Contents A Speculation on Unification 1 - From millennium physics to unification How to name the result of the quest Against a complete theory What went wrong in the past An encouraging argument Summary: how to find the complete theory of motion 2 - 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 Simplified cosmology in one statement The cosmological limits to observables Minimum force Summary on cosmological limits Limits to measurement precision No real numbers Vacuum and mass: two sides of the same coin No points Measurement precision and the existence of sets Summary on limits in nature 3 - 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 4 - 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 or 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 5 - 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 have mass? 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 6 - 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 plus a web of dualities Why superstrings and supermembranes are so appealing Why the mathematics of superstrings is difficult Testing superstrings: couplings and masses The status of the superstring conjecture Summary on extension in nature 7 - The basis of the strand conjecture Requirements for a unified theory Introducing strands Events, processes, interactions and colours From strands to modern physics Vacuum Observable values 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 Knots and the ends of strands Summary on the fundamental principle – and on continuity 8 - 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 and path integrals Interference and double slits 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: experimental predictions 9 - 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 topological 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 Open issue: are the W and Z tangles correct? 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 An introduction to SU(3) From slides to SU(3) The strand model for gluons 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 and predictions about gauge interactions Predicting the number of interactions in nature Unification of interactions No divergences Grand unification, supersymmetry and other dimensions No new observable gravity effects in particle physics The status of our quest 10 - 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 The structure of horizons and black holes Is there something behind a horizon? Energy of black hole horizons The nature of black holes Entropy of vacuum and matter Entropy of black holes deduced from the strand model Temperature, radiation and evaporation of black holes Black hole limits Curvature around black holes The shape of non-rotating black holes The field equations of general relativity Equations from no equation The Hilbert action of general relativity Space-time foam Gravitons, gravitational waves and their detection Open challenge: Improve the argument for the graviton tangle Other defects in vacuum The gravity of superpositions Torsion, curiosities and challenges about quantum gravity Predictions of the strand model about gravity Cosmology The finiteness of the universe The big bang – without inflation The cosmological constant The value of the matter density Open challenge: What are the effects of dark matter? The topology of the universe Predictions of the strand model about cosmology Summary on millennium issues about relativity and cosmology 11 - The particle spectrum deduced from strands Particles and quantum numbers from tangles Particles made of one strand Unknotted curves Gauge bosons – and Reidemeister moves Open or long knots Closed tangles: knots Summary on tangles made of one strand Particles made of two strands Quarks Quark generations The graviton A puzzle Summary on two-stranded tangles Particles made of three strands Leptons Open issue: are the lepton tangles correct? 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 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 Glueballs The mass gap problem and the Clay Mathematics Institute Summary on tangles made of four or more strands Fun challenges and curiosities about particle tangles CPT invariance Motion through the vacuum – and the speed of light Summary on millennium issues about particles and the vacuum The omnipresent number 3 Predictions about dark matter and searches for new physics 12 - Particle properties deduced from strands The masses of the elementary particles General properties of particle mass values Boson masses W/Z boson mass ratio and mixing angle (in the 2016 - tangle model) The g-factor of the W boson The Higgs/Z boson mass ratio A first approximation for absolute boson mass values Quark mass ratios Lepton mass ratios On the absolute values of particle masses Analytical estimates for particle masses Open issues about mass calculations On fine-tuning and naturalness Summary on elementary particle masses and millennium issues Mixing angles Quark mixing – the experimental 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 Interaction strengths and strands Strands imply unification Calculating coupling constants First hint: the energy dependence of physical quantities Second hint: the running of the coupling constants at low energy Third hint: further predictions at low energy The running of the coupling constants up to Planck energy Limits for the fine structure constant do not provide explanations Charge quantization and topological writhe Charge quantization and linking number How to calculate coupling constants Coupling constants in the strand model Deducing alpha from precession Deducing the weak coupling Deducing the strong coupling Open challenge: calculate coupling constants with precision Electric dipole moments Five key challenges about coupling strengths Summary on coupling constants 13 - A pictorial summary of the strand model 14 - Experimental predictions of the strand model Final summary about the millennium issues 15 - 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 and vacuum 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 Appendix A - Knot and tangle geometry Challenge hints and solutions Bibliography Name index Subject index What is the origin of colours? Which problems in physics are unsolved since the year 2000 and what might be their solution?Why do motion and change exist?What is the origin of the principle of least action?What is the origin of gauge symmetries?What is the most fantastic voyage possible? Answering these and other questions, this book gives an entertaining and mind-twisting introduction to the search for the final theory of physics. The search leads to the strand model: Based on a simple principle, strands reproduce quantum theory, the standard model of particle physics and general relativity. Strands agree with all experimental data and allow estimating the fine structure constant, particle masses and all other constants of nature. Christoph Schiller, PhD Université Libre de Bruxelles, is a physicist and physics popularizer. This entertaining book is for students, teachers and anybody interested in modern research about fundamental physics.