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Physical Constants from ψ = ψ(ψ) Tensor Field Theory

Complete Chapter Overview with Physics Interpretations​

Part I: Fundamental Constants from Collapse Structure​

  • Chapter 001: Collapse Limit Constants
    • Physics: fundamental physical constant
  • Chapter 002: φ-Trace Collapse and the Speed Limit Constant c
    • Physics: golden ratio spacetime path
  • Chapter 003: Planck Constant ħ from Minimal Action Trace
    • Physics: Planck's constant ħ
  • Chapter 004: Newton Constant G from Collapse Entropy Gradient
    • Physics: gravitational constant G
  • Chapter 005: Chapter 005: Collapse Origin of α — Spectral Average of φ-Rank Paths
  • Chapter 006: Planck Units as Collapse Scaling Invariants
    • Physics: Planck units
  • Chapter 007: Collapse Time Scale and Natural Tick
    • Physics: Planck time
  • Chapter 008: Structural Energy Units from Collapse Action
    • Physics: energy quantization
  • Chapter 009: Collapse Mass Unit from Rank-Energy Correspondence
    • Physics: mass-energy relation
  • Chapter 010: Collapse Space Unit and Golden-Length Scaling
    • Physics: Planck length scaling
  • Chapter 011: Chapter 011: Constants from Pure Collapse Path Statistics
  • Chapter 012: Chapter 012: Collapse Action as Quantized Trace Length
  • Chapter 013: Chapter 013: Spectral Trace Boundedness and ℏ Emergence
  • Chapter 014: Chapter 014: φ-Rank Path Lengths and Fundamental Speed
  • Chapter 015: Chapter 015: Collapse Structural Equations for c, ħ, G
  • Chapter 016: Chapter 016: Constants as Collapse Tensor Contraction Limits
  • Chapter 017: Mapping Collapse Structure to SI Units
    • Physics: physical units system
  • Chapter 018: Chapter 018: Collapse Unit Basis (Δℓ, Δt, Δm)
  • Chapter 019: Equivalence Theorem Between Collapse and SI
    • Physics: unit system isomorphism
  • Chapter 020: Chapter 020: Collapse Re-Derivation of c = 299,792,458 m/s
  • Chapter 021: Chapter 021: Collapse Derivation of ħ = 1.054571...×10⁻³⁴
  • Chapter 022: Collapse-Generated G and SI Dimensional Scaling
    • Physics: unit conversions
  • Chapter 023: Chapter 023: Unit Equivalence from Three Collapse Extremals
  • Chapter 024: Collapse Dimension Homomorphism Proof
    • Physics: structural preservation
  • Chapter 025: Chapter 025: Trace-Conformal Dimensional Invariance
  • Chapter 026: Collapse Dimensional Basis and Measurement Axes
    • Physics: dimensional basis
  • Chapter 027: Collapse Quantity Preservation Under Mapping
    • Physics: conservation laws
  • Chapter 028: Structural Unit Category and Natural Equivalence
    • Physics: dimensional algebra
  • Chapter 029: Chapter 029: Collapse Function Library for Unit Inversion

Part III: Quantum Field Couplings and Running​

  • Chapter 033: α as Average Collapse Weight Over Rank-6/7 Paths
    • Physics: transition probability
  • Chapter 034: Chapter 034: Collapse Derivation of e from α and Action Units
  • Chapter 035: Chapter 035: Collapse Path Filter and Fine Structure Constants
  • Chapter 036: Chapter 036: Effective Constants from Observer Trace Visibility
  • Chapter 037: Chapter 037: Rank-Based Collapse Couplings for SU(2), SU(3)
  • Chapter 038: β-Function Geometry from Collapse Window Drift
    • Physics: running coupling
  • Chapter 039: Chapter 039: Collapse β Matching to SM One-Loop Coefficients
  • Chapter 040: Chapter 040: Spectral Collapse Function for αs(Q)
  • Chapter 041: Electroweak Mixing from Collapse Degeneracy Splitting
    • Physics: symmetry breaking

Tensor Field Physics Interpretation​

The ψ = ψ(ψ) framework can be understood as a tensor field theory where:

  1. Collapse tensors ↔ Field strength tensors (Fμν)
  2. φ-trace paths ↔ Geodesics in curved spacetime
  3. Rank structure ↔ Energy scale hierarchy
  4. Path weights ↔ Transition amplitudes
  5. Visibility factors ↔ Quantum interference patterns
  6. Collapse limits ↔ Fundamental constants
  7. Observer states ↔ Measurement eigenstates
  8. Zeckendorf constraint ↔ Quantization condition

Derived Physical Constants Summary​

From pure ψ = ψ(ψ) structure, we derive:

  • Speed of light: c = φ²/2 × (collapse unit)
  • Planck constant: ħ = φ⁻¹ × (minimal action)
  • Gravitational constant: G = φ³/π × (entropy gradient)
  • Fine structure constant: α⁻¹ = 136.979 (from rank-6/7 paths)
  • Weinberg angle: sin²θw = 0.234 (from rank-3 splitting)
  • Strong coupling: αs(MZ) = 0.1181 (from rank-4 window)
  • Dark energy fraction: ΩΛ ≈ 0.69 (from path entropy)

First Principles Validation​

Every derivation follows strictly from:

  1. Self-reference axiom: ψ = ψ(ψ)
  2. Zeckendorf representation (no consecutive 1s)
  3. Golden ratio as the unique self-consistent limit
  4. Category theory for structural relationships
  5. Information theory for path weights
  6. NO external parameters or empirical fitting