Contents -- Preface -- 1. Zero -- 1.1 An Origin for Everything -- 1.2 The Genesis of Number -- 1.3 The Genesis of Algebra -- 1.4 Group Representations -- 1.5 Rewriting Nature -- 1.6 Quaternions and Vectors -- 2. Why Does Physics Work? -- 2.1 A Foundational Level -- 2.2 The Origin of Abstraction -- 2.3 Symmetry -- 2.4 The Meaning of the Conservation Laws -- 2.5 The Mathematical Structure of Physical Quantities -- 2.6 Where Does Dimensionality Come From? -- 2.7 A Group of Order 4 -- 2.8 Noether's Theorem Revisited -- 2.9 Analytic Versus Synthetic -- 2.10 The Power of Analogy -- 2.11 The Nature of Reality -- 3. The Emergence of Physics -- 3.1 The Mathematical Character of Physics -- 3.2 The Algebra of Space, Time, Mass and Charge -- 3.3 The Dirac Algebra -- 3.4 The Creation of the Dirac State -- 3.5 The Nilpotent Dirac Equation -- 3.6 Uniqueness, Qubits and Quantum Computing -- 3.7 The Completeness of Mathematical Physics -- 3.8 Theoretical Computation -- 4. Groups and Representations -- 4.1 The Dirac Equation and Quantum Field Theory -- 4.2 Reversals of Properties -- 4.3 The Dual Group and Higher Symmetries -- 4.4 A Broken Octonion -- 4.5 A Hierarchy of Dualities -- 4.6 Dimensionality -- 4.7 Symmetry Hierarchy -- 4.8 Colour Representation -- 4.9 3-D (Vector) Representation -- 4.10 Tetrahedral Representation -- 5. Breaking the Dirac Code -- 5.1 Singularities and Redundancy -- 5.2 Redundancy in the Dirac Equation -- 5.3 Defragmenting the Dirac Equation -- 5.4 The Dirac 4-Spinor -- 5.5 The 4-Component Differential Operator -- 5.6 C-Linear Maps and Lifts -- 5.7 The Quaternion Form Derived from a Matrix Representation -- 5.8 Bilinear Covariants and the Dirac Lagrangian -- 5.9 Removing Redundancies in Relativistic Quantum -- 5.10 Orthonormality of the Nilpotent Solutions of the Dirac Equation -- 6. The Dirac Nilpotent -- 6.1 Spin -- 6.2 Helicity.

6.3 Fermions and Bosons -- 6.4 Vacuum -- 6.5 CPT Symmetry -- 6.6 Baryons -- 6.7 Gluons and Exotic States -- 6.8 Parities of Bosons and Baryons -- 6.9 Supersymmetry and Renormalization -- 6.10 Annihilation and Creation Operators -- 6.11 The Quantum Field -- 6.12 The Nilpotent State -- 6.13 Nonlocality -- 6.14 BRST Quantization -- 7. Nonrelativistic Quantum Mechanics and the Classical Transition -- 7.1 The Bispinor Form of the Dirac Equation -- 7.2 The Schrödinger Approximation -- 7.3 The Heisenberg Formulation of Quantum Mechanics -- 7.4 Heisenberg v. Schrödinger -- 7.5 The Quantum-Classical Transition -- 7.6 The Classical Limit -- 7.7 The Dirac Nilpotent Using Discrete Differentiation -- 7.8 Idempotent and Nilpotent Versions of Quantum Mechanics -- 7.9 A Fundamental Quantum Mechanical Duality -- 8. The Classical and Special Relativistic Approximations -- 8.1 Linear Versus Orbital Dynamics -- 8.2 Scaling Relations -- 8.3 Special Relativity -- 8.4 The Significance of the Proper Time -- 8.5 The Nature of Classical Physics -- 8.6 Constructed Quantities -- 8.7 Classical Mechanics -- 8.8 Classical Electromagnetic Theory -- 9. The Resolution of Paradoxes -- 9.1 Paradoxes Relating to Conservation and Nonconservation -- 9.2 Paradoxes Relating to Continuity and Discontinuity -- 9.3 Irreversibility and Causality -- 9.4 The Mass Frame and Zero-Point Energy -- 9.5 Two Versions of Relativity -- 9.6 Thermodynamics and the Arrow of Time -- 10. Electric, Strong and Weak Interactions -- 10.1 The Dirac Equation in the Coulomb Field -- 10.2 Condensed Matter: The Kronig-Penney Model -- 10.3 The Helium Atom -- 10.4 SU(3) -- 10.5 The Quark-Antiquark and Three-Quark Interactions -- 10.6 Angular Momentum -- 10.7 The Weak Filled Vacuum -- 10.8 The Origin of the Higgs Mechanism -- 10.9 SU(2)L ¥ U(1) -- 10.10 The Weak Interaction and the Dirac Formalism.

10.11 The Higgs Mechanism for U(1) and SU(2)L -- 10.12 The Spherical Harmonic Oscillator -- 10.13 The Weak Interaction as a Harmonic Oscillator -- 10.14 A Strong-Electroweak Solution of the Dirac Equation -- 11. QED and its Analogues -- 11.1 A Perturbation Expansion of the Dirac Equation for QED -- 11.2 Integral Solutions of the Dirac Equation -- 11.3 Renormalization -- 11.4 Green's Function Solution -- 11.5 The Propagator Method in Lowest Order -- 11.6 Electron Scattering -- 11.7 Strong and Weak Analogues -- 11.8 QFD Using Nilpotents -- 11.9 The Success of the Nilpotent Method -- 12. Vacuum -- 12.1 Physics and Observables -- 12.2 Zero-Point Energy -- 12.3 The Weak Vacuum -- 12.4 The Strong Vacuum -- 12.5 The Electric Vacuum -- 12.6 The Gravitational Vacuum -- 12.7 The Casimir Effect -- 12.8 Berry's Geometric Phase -- 13. Fermion and Boson Structures -- 13.1 The Charge Structures of Quarks and Leptons -- 13.2 A Unified Representation for Quarks / Leptons -- 13.3 Conservation of Charge Type and Conservation of Angular Momentum -- 13.4 Phase Diagrams for Charge Conservation -- 13.5 Quark and Lepton Charge Structures in Tabular Form -- 13.6 Mesons and Baryons -- 13.7 The Standard Model -- 13.8 A Pentad Structure for Charges and their Transitions -- 13.9 Lepton-Like Quarks -- 14. A Representation of Strong and Weak Interactions -- 14.1 Charge Occupancy -- 14.2 Symmetries in a Matrix Representation -- 14.3 Constructing a Baryon -- 14.4 Constructing a Meson -- 14.5 Lepton Structures -- 14.6 The Electroweak Interaction Mechanism -- 14.7 The Production of Leptons -- 14.8 Electroweak Mixing -- 14.9 SU(2) Transitions -- 14.10 The Higgs Coupling -- 14.11 The Mass Gap for Any Gauge Group -- 15. Grand Unification and Particle Masses -- 15.1 A Dirac Equation for Charge -- 15.2 SU(5) Symmetry -- 15.3 The Grand Unification Group Generators.

15.4 The Dirac Algebra Operators and SU(5) Generators -- 15.5 Superspace and Higher Symmetries -- 15.6 Grand Unification and the Planck Mass -- 15.7 The Generation of Mass -- 15.8 The Higgs Model for Fermions -- 15.9 The Masses of Baryons and Bosons -- 15.10 The Masses of Fermions -- 15.11 The CKM Mixing -- 15.12 A Summary of the Mass Calculations -- 16. The Factor 2 and Duality -- 16.1 Duality and Physics -- 16.2 Kinematics and the Virial Theorem -- 16.3 Relativity -- 16.4 Spin and the Anomalous Magnetic Moment -- 16.5 The Linear Harmonic Oscillator -- 16.6 The Heisenberg Uncertainty Principle -- 16.7 Fermions and Bosons -- 16.8 Radiation Reaction -- 16.9 Supersymmetry and the Berry Phase -- 16.10 Physics and Duality -- 16.11 The Factor 2 and Electroweak Mixing -- 16.12 Alternative Dualities -- 16.13 Mathematical Doubling and the Self-Duality of the Dirac Nilpotent -- 17. Gravity and Inertia -- 17.1 The Continuity of Mass-Energy -- 17.2 The Speed of Gravity -- 17.3 What is General Relativity About? -- 17.4 General Relativity and Quantum Mechanics -- 17.5 The Schwarzschild Solution -- 17.6 Gravitational Redshift -- 17.7 The Gravitational Deflection of Electromagnetic Radiation -- 17.8 The Gravitational Time-Delay of Electromagnetic Radiation -- 17.9 Perihelion and Periastron Precession -- 17.10 The Inertial Correction -- 17.11 The Aberration of Space -- 17.12 Gravomagnetic Effects -- 17.13 A Linear Interpretation of the Gravitational Field -- 18. Dimensionality, Strings and Quantum Gravity -- 18.1 Discreteness and Dimensionality -- 18.2 Dimensionality and Chirality -- 18.3 '4-Dimensional' Space-Time -- 18.4 Proper Time and Causality -- 18.5 The Klein Bottle Analogy -- 18.6 A String Theory Without Strings -- 18.7 Twistor Representations -- 18.8 Quantum Gravitational Inertia -- 18.9 Calculation of Quantized Gravitational Inertia -- 19. Nature's Code.

19.1 The Dirac Nilpotent as the Origin of Symmetry-Breaking -- 19.2 The Significance of the Pseudoscalar Term -- 19.3 Spin and Aggregation of Matter -- 19.4 Self-Organization of Matter -- 19.5 The Filled Weak Vacuum and the One-Handed Bias in Nature -- 19.6 The Idea of 3-Dimensionality -- 19.7 Application to Biology: DNA and RNA Structure -- 19.8 Transcription -- 19.9 Translation and Triplet Codons -- 19.10 Triplet Codons and the Dirac Algebra -- 19.11 The Five Platonic Solids -- 19.12 Fibonacci Numbers -- 19.13 Application of Geometrical Structures to DNA and Genetic Coding -- 19.14 Pentagonal Symmetry Within DNA -- 19.15 The Cube and the Harmonic Oscillator -- 19.16 The Rewrite Process as Nature's Code -- 19.17 The Unification of Physics and Biology -- 20. Nature's Rules -- 20.1 A Semantic Model of Computation -- 20.2 Scientific Perspectives on Computation -- 20.3 The Nilpotent Structure of the Universal Grammar -- 20.4 General Relativity and NQM Semantic Description -- 20.5 Analysis over the Surreals -- 20.6 The Heaviside Operator -- 20.7 Wheeler's Meaning Circuit -- 20.8 Anticipatory Computation and Other Ideas Supporting the NUCRS -- 20.9 A Boundary Condition and the Holographic Principle -- 20.10 Quantum Holography -- 20.11 The Bra and Ket Notation -- 20.12 The Universe as a Quantum Thermodynamic Engine -- 20.13 The Riemann Zeta Function -- 20.14 Galactic Structure -- 20.15 Quantum Thermodynamics and Evolution -- 20.16 DNA as a Rewrite System -- 20.17 Brains as Quantum Carnot Engines -- 20.18 Language and Universal Grammar -- 20.19 Nature's Process -- 21. Infinity -- 21.1 A Version of Mach's Principle -- 21.2 Gravity and Inertia -- 21.3 Cosmology and Physics -- 21.4 Information Loss and Radiation -- 21.5 A Numerological Coincidence? -- 21.6 Vacuum Acceleration and Radiation -- 21.7 The Concept of Creation -- Appendix A Summary and Predictions.

A.1 Summary of the Main Argument.