First Principles: From Unitary Computation to Physical Reality

This book builds a physical theoretical framework based on discrete information ontology from first principles.

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Foreword

• Foreword: Occam’s Ultimate Razor

Book Structure

Part I: The Birth of Axioms

Chapter 1: The Necessity of Discrete Ontology

• 1.1 Zeno’s Paradox and the Ghost of Continuum
• 1.2 Black Hole Entropy and Bekenstein Bound: The Universe as a Finite-Capacity Hard Drive
• 1.3 Information Realism: Bits and Qubits as the Atoms of Matter

Chapter 2: The Ultimate Axiom $\Omega$

• 2.1 Axiom Statement: The Universe is a Quantum Cellular Automaton (QCA) Operating on Discrete Lattice Points Following Local Unitary Evolution Rules
• 2.2 Why Unitarity? — Conservation of Probability and Logical Consistency
• 2.3 Why Locality? — Avoiding “God’s Eye View” and Action at a Distance
• 2.4 Formal Definition: Graph $\Lambda$, Hilbert Space $\mathcal{H}$, and Update Operator $\hat{U}$

Part II: The Emergence of Spacetime

Chapter 3: Causality and the Speed of Light

• 3.1 The Discrete Origin of Light Cones: Deriving the Maximum Signal Velocity $c$ from Lattice Hopping
• 3.2 Light Path Conservation Theorem: Proving $v_{ext}^2+v_{int}^2=c^2$ from Unitarity
• 3.3 Derivation of Lorentz Transformation: No Geometry, Only Statistics of Resource Allocation

Chapter 4: Gravity as Statistical Necessity

• 4.1 Entanglement and Geometry: Spacetime Distance as Quantum Mutual Information
• 4.2 Local Information Volume Conservation: Why Must Space Expand When Information Compresses Time?
• 4.3 Entropic Derivation of Einstein Field Equations: Proof of the IGVP Principle
• 4.4 Black Holes: Entanglement Knots in QCA Networks and Holographic Screens

Part III: The Emergence of Matter

Chapter 5: The Topological Origin of Mass

• 5.1 Why Do Photons Have No Mass? — Pure Translation Modes
• 5.2 Matter as Topological Knots: Self-Referential Loops and Winding Numbers
• 5.3 Mass as Impedance: Information Refresh Rate Required to Maintain Internal Oscillation ($v_{int}$)
• 5.4 Origin of Fermion Statistics: Riccati Square Root and ${\mathbb{Z}}_2$ Phase

Chapter 6: Interactions and Gauge Fields

• 6.1 Independence of Local Reference Frames: Why Does Each Cell Need “Translation”?
• 6.2 Necessity of Link Variables: Derivation of Maxwell and Yang-Mills Equations
• 6.3 Geometric Meaning of Coupling Constants: Network Connectivity and Information Leakage Rate

Part IV: The Emergence of Observation

Chapter 7: Quantum Measurement and Objectivity

• 7.1 The Discrete Solution to Schrödinger’s Cat: Entanglement and Branching under Unitary Evolution
• 7.2 Combinatorial Proof of Born Rule: Based on Zurek Rotation and Microstate Counting
• 7.3 The Achievement of Objective Reality: Nash Equilibrium and Consensus Geometry in Multi-Agent Systems

Chapter 8: The Physics Definition of Consciousness

• 8.1 Observer Model: Computational Structure (Agent) as Self-Referential Subsystem
• 8.2 Information Mass $M_I$ and Free Energy Minimization
• 8.3 Red Queen Effect and Thermodynamics: Why Does the Universe Not Have Heat Death?

Part V: Verification and Inference

Chapter 9: Experimental Predictions

• 9.1 Entanglement Gravity Detection Scheme in Microwave Cavities
• 9.2 Lorentz Violation Effects in Ultra-High-Energy Cosmic Rays
• 9.3 Cosmological Drift of Fine Structure Constant

Chapter 10: Ultimate Questions of the Computational Universe

• 10.1 The Universe’s Source Code: How Was Rule $\hat{U}$ Selected? (Criticality Hypothesis)
• 10.2 Physical Projection of Gödel’s Incompleteness: The Boundary of Agnosticism
• 10.3 Are We Players or NPCs? — On the Status of Free Will in Deterministic QCA

Conclusion

• Book Conclusion: From Observer to Builder

Afterword

• Afterword: The Unfinished Symphony

Appendices

• Appendix A: Mathematical Foundations
• Appendix B: QCA Simulation Guide
• Appendix C: Core Theorem Proof Collection
• Appendix D: Key Terminology Glossary