Schiller C. Motion Mountain. The Adventure of Physics. Volume VI. The Strand Model - a Speculation on Unification

28th edition. — Christoph Schiller, 2015. — 455 p.From millennium physics to unification
Against a final theory
What went wrong in the past
An encouraging argument
Summary: how to find the final theory of motion
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
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
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
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
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
The basis of the strand model
Requirements for a final 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 of the strand model — and on continuity
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, path integrals and interference
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
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
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 on millennium issues about gauge interactions
Prediction about the number of interactions
Unification of interactions
No divergences
Predictions about grand unification and supersymmetry
No new observable gravity effects in particle physics
The status of our quest
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 is dark matter?
The topology of the universe
Predictions of the strand model about cosmology
Summary on millennium issues about relativity and cosmology
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
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 the vacuum
The omnipresent number 3
Predictions about dark matter, the LHC and the vacuum
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 knot model)
Higgs/Z boson mass ratio
A first approximation for elementary boson mass values
Quark mass ratios
Lepton mass ratios
Predictionsabout absolute mass values
Open issues about mass calculations
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
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 (2013 version)
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
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
Knot geometry