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Physics

  • Anthropomorphic global warming and the `heat pump` thermodynamics physics model
  • Six Dimensional Space Time ‎
  • 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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