Physics
- The Search for the Grande Algorithm and the Chained Super Organism
- 6D Mathematics: Laws of Physics, Chemistry, Biology and Social Sciences
- 1 Introduction, Approach and 6D Physics
- 1.1 Introduction and the Universal Law of Homeostasis: Considerations
of Approach
- 1.1.1 Overview
- 1.2 Approaches
- 1.2.1 The split-6D method
- 1. 1.3 The Theory of Everything (ToE) and new 6D and 12D approaches
- 1. 1.4 Outline of the book
- 2 Our Universal Math and Predictive Power to Physics
- 2.1 Introduction to 6D geometry and physics
- 2.1.1 SO(3)
- 2.1.2 SO(3,3)
- 2.1.3 Mechanics and dynamics of SO(3,3)
- 2.1.4 Further consideration of three time dimensions and causality
- 2.1.5 Geometric Algebra and Calculus and Predictive Power
- 2.2 Geometric calculus and the unified laws of physics
- 3 Universal math II: Conformal projective geometric algebra and calculus
- 3. 1 Twistor spaces, cohomology, R3,3, SL4(C), and symmetries
- 3. 2 Geometric Twistor Correspondence
- 3.2.1 Cohomological Constructions
- 3.2.2 Correspondence Space Bundles
- 3.2.3 Six-Dimensional Penrose Transforms
- 3.2.4 Split Signature Ξ-Transform
- 3.2.5 Conformally Invariant Differential Operators
- 3.2.6 Conformal Laplacians and the Existence of Q-curvatures
- 3.2.7 ConstructionofLocalConformalInvariants
- 3.2.8 GJMS Operators and Uniqueness of Q-Curvatures
- 3.2.9 Twistors and why time is three dimensional
- 3.3 Quaternions, 6D Lorentz category, and three time dimensions
- 3.3.1 Supersymmetry from division algebras
- 3.4 Projections of 6D into 3D gauge theory and duality
- 3.5 Embedding 4D into 6D: Topological Gravity and the Cosmological
Constant Problem
- 3.5.1 Embedding General Relativity in R3,3 and other spacetimes
- 3.5.2 Embedding black hole spacetimes in flat 6D and R3,3
- 3.6 Lorentz Transformations, Hyperbolic Parametrizations and Lorentz Factors of 6D Spacetime
- 3.6.1 System of Equations for 6D Lorentz Transformations
- 3.6.2 Transformations Preserving Quadratic Forms
- 3.6.3 Algebraic Solution Obtaining the Lorentz Transformations
- 3.6.4 The special case of a ’boost’ along a single space coordinate in 6D space
- 3.7 Quasicrystals – a new state of matter from 6D!
- 3.7.1 More on the projection of 6D onto spacetime from the quasicrystal approach
- 3.7.2 Quasicrystals and biology to modelling plant growth from 6D
- 3.8 Conformal Geometric Algebra and representation theory on split- signature spacetimes
- 3.8.1 Conformal geometric algebra and spacetime algebras
- 3.8.2 The case of R3,3 and projective conformal geometric algebras
- 3.9 L-systems and turtles for geometric rendering and plant growth
- 3.9.1 L-systems for plant and fractal generation
- 3.9.2 A universal 6D ’plant’ to generate them all!
- 3.9.3 Using Geometric Algebra
- 3.10 Non-Euclidean Geometries in Modelling Biology and Plant Growth from 6D
- 3.10.1 Ultrametricity: From knots to leaves and phyllotaxis
- 3.10.2 Geometric optics approach to plant formation and the eikonal approximation
- 3.10.3 Modular geometry and spectral statistics of plants
- 3.11 Models of Hyperbolic Geometry
- 3.11.1 6d hyperbolic model of information searches and networks
- 3.12 Towards a Notion of an Objective Reality
- 3.12.1 Conservation of Static Geometry
- 3.12.2 Onion-Object in 6D
- 3.12.3 ’Combining’ 2 Onions
- 3.12.4 On Reality as the 24D Metaverse
- 3.13 Other experimental tests of 6D relativity
- 3.13.1 6D Gedankenexperiments and Gravity
- 3.13.2 Blackholes in 6D gravity and light deflection in GR limit
- 3.13.3 Experiment: Deflection of light across the Sun in 6D
- 3.13.4 Experiment: Variable speed of light electrodynamics, optics and cosmology
- 4 Revelations from 6D to physics and the Universe
- 4.1 Electrodynamics and beyond in R3,3, and solutions to the wave equation in 6D
- 4.1.1 Maxwell in 6D: Electrodynamics over SO(3,3) where electric and magnetic matter in 4D are free fields in 6D!
- 4.1.2 Lie algebras so(p,q) and representations of so(3,3)
- 4.1.3 Laplacians and differential equations on split-signature space-times and M3,3
- 4.2 Dirac equation in 6D and Clifford Algebra
- 4.2.1 Further applications of the Dirac equation on R3,3
- 4.3 Applications of 6D to Outstanding Problems in Physics
- 4.3.1 Neutrino masses from 6D orbifold compactifications
- 4.3.2 HBT interferometry at the RHIC and LHC as a test for geometry preserving 6D geometry
- 4.3.3 Standard Models of Particle Physics from 6D and Testing 6D at the LHC
- 4.3.4 6D Clifford Algebra Model of the Standard Model and Beyond
- 4.4 Grand Unified Theories without supersymmetry from three time dimensions
- 4.5 Embedding Quantum Mechanics into 6D, time-like Kaluza-Klein theory and beyond
- 4.5.1 Wavefunction collapse from six dimensions and wave-particle duality ex- plained with extra time like dimensions
- 4.5.2 Analyzing high energy collisions from a 6D perspective
- 4.5.3 Predicting the Electron and the Muon from 6D
- 4.5.4 Proton Decay Problem Solved with 6D
- 4.5.5 Fermion Families from Six Dimensions
- 4.5.6 Dark Matter Candidates from R3,3
- 4.5.7 SO(10) GUTs from 6D
- 4.5.8 New Heavy Higgs from 6D compactifications and tests at LHC
- 4.6 Nuclear Physics and the Liquid Drop Model in 6D
- 4.7 Geometric calculus and gravity
- 4.7.1 Electromagnetism from a gravitational perspective in 6D
- 4.7.2 6D multi-timing magnetic monopoles in gravity theories
- 4.8 Six dimensional cosmology and the cosmological constant problem
- 4.9 Emergent gravity and spacetime, and new quantum interpretations
- 4.9.1 Emergent gravity and cosmology without need of dark matter
- 4.10 Aspects of 6D gravity and the six dimensional Schwarzschild metric
- 4.11 Statistical mechanics of six dimensions
- 4.11.1 d-dimensional Fermi gases
- 4.11.2 d-dimensional Bose gases
- 4.11.3 Statistical mechanics of multiple time dimensions on R3,3
- 4.12 6D quantum field theory on R3,3
- 4.12.1 Renormalization and coordinate invariance in quantum field theories using extra time dimensions
- 4.13 Multi-time dimensional Brownian motion on R3,3
- 4.13.1 Relativistic covariant Brownian motion on R3,3 and gravity
- 4.14 6D Finance: Stochastic calculus on the fractional Brownian mountains
- 4.15 Ising models and other critical phenomena on R3,3
- 4.15.1 Percolation
- 4.15.2 Ising models and Mean Field Theory
- 4.15.3 Universality and critical exponents
- 4.15.4 Lattice animals, spin-glasses and other models of the same universality class
- 4.15.5 Random walks and power laws: Evolutionary applications
- 4.15.6 Neurophysics and psychophysics from a 6D perspective
- 4.16 Sandpiles and self-organized criticality: Nature on all scales
- 4.16.1 Universality of sand piles and duality to long-range Ising models in external fields
- 4.16.2 Sandpiles in higher dimensions and relations to other universality classes 231
- 4.16.3 Sandpiles, growth phenomena, material deposition, and the Kardar-Parisi-Zhang (KPZ) equation
- 4.17 Fractal renormalization and quantum computing of quantum field theories
- 4.18 Circuits and Networks, fractals and 6D
- 4.19 Physical constants from a 6D unification
- 5 Applications of 6D algebra and physics to biology
- 5.1 Newton’s Laws of Biology I: the genetic code and evolution
- 5.2 Newton’s Laws of Biology II: scaling laws, fractals, chaos and allometry
- 5.2.1 Extensions and 6D biophysics
- 6 The Superorganism: Politics, Psychology and Social Sciences
- 6.1 Social Networks and the 6D small world
- 6.1.1 Small-world percolation: From friendships to disease propagation
- 6.1.2 Rumours, swarms, ants and bees…
- 6.2 Ising Models and Politics and Beyond
- 6.2.1 Opinion dynamics and Voter models
- 6.2.2 Languages,and evolutionary linguistics
- 6.3 Psychology from 6D: Power laws and beyond quantifying mental anguish
- 6.3.1 Psychology of Reward: Discounting Delays to Gambling
- 6.3.2 Psychology and Quantifying Mental Anguish
- 7 Restatement of Predictive Power and Conclusion
- 8 Appendix
- 8.1 Philosophy of 6D and the Homeostasis model
- 8.1.1 Reasons to Refute
- 8.1.2 Alternative Approaches
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