The world may be an illusion, a simple projection of our own consciousness. Like many ideas, it cannot be disproven. And yet most of us overlook this fact and embrace the potential illusion, taking the world for what it seems to be according to our senses. Naturally, then, we have spent the best part of our known history categorizing the world around us. Biologists have named the plants and animals around us. Linguists have come up with an international phonetic alphabet. In math, we have created languages, we have invented numbers, and systems in which we use numbers, in increasingly complicated ways, to describe the world around us.
However, we are actually finding that the math does not have overwhelming predictive power and that it seems not to synchronize with reality perfectly. We are so far along this road that it is difficult even to look back, let alone to return to our axioms for a reappraisal, audit, and maybe a fresh start. If our global understanding does have an error, is it one that we will find in the future or one that we will find by examining our biases and assumptions.
The so-called Theory of Everything is a theory of physics to unify all the forces of Nature into one physical and mathematical entity, both a formula and a source. This includes gravity (both geometric/general relativistic or gauge-quantum in nature), quantum mechanics, electricity, magnetism, strong and weak nuclear forces in nuclear physics and particle theory, and special and general relativity. There, along the way, must also be found an answer to unanswered problems in physics relating to the fate of the Universe, the Big Bang, its very early stages, the abundance of Dark Matter in the Universe and what it is, the existence or non-existence of supersymmetry, and extra dimensions, and how many there are, the size of the cosmological constant, the proton decay problem, quark confinement and mass gap, matter anti-matter asymmetry, and the list goes on and on,…,
We investigate a six dimensional spacetime with three time dimensions, with a split Minkowskian symmetry, R3;3, and its simplifying and predictive aspects to universal 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
