Theory of Fundamental Physics: TFP to QFT Mapping

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Theory of Fundamental Physics: QFT Mapping

Theory of Fundamental Physics

Network Coherence → Standard Model + General Relativity
TFP Framework
Node Evolution: Ψᵢ(t + Δt) = Ψᵢ(t) + Δt[−dV/dΨᵢ + C₂∑ⱼ(Ψⱼ − Ψᵢ) + ηᵢ]
Cluster Coherence: C(l)² ≈ C₀²(l₀/l)ᵈ β(l) = 1 − C(l)²
Gauge Couplings: αₐ(l) ≈ C(l)² / (1 + β(l)) dαₐ/d(log l) = αₐ²∑ₖ[Gₐₖρₖ(l)] − Φ_δ
Standard Model Mapping
Gauge Fields: Aμₐ ↔ Coherent cluster synchronizations Gμνₐ ↔ Curvature in Ψᵢ phase space
Matter Fields: ψfermion ↔ Localized Ψᵢ excitations φboson ↔ Delocalized coherent modes
Spacetime Metric: gμν ≈ ⟨ΨᵢΨⱼ⟩ − ⟨Ψᵢ⟩⟨Ψⱼ⟩ Geff ∝ ∂²C(l)/∂x²

Fermions

Localized, Phase-Locked Excitations
• Constrained to small clusters
• Antisymmetric wavefunction → Pauli exclusion
• Discrete topological constraints

Bosons

Delocalized Cluster Synchronizations
• Spread across many nodes
• Symmetric statistics → Bose enhancement
• Propagating coherent modes

Key Insight: Statistics from Topology

Fermi-Dirac Statistics:
Emerge from discrete flow constraints in localized Ψᵢ clusters. Phase-locking creates topological barriers that prevent two excitations from occupying the same cluster state.
Bose-Einstein Statistics:
Delocalized synchronizations have no topological constraints. Multiple excitations can coherently superpose, leading to enhancement rather than exclusion.

TFP Predictions vs QFT Observables

Quantity TFP Definition Observable / QFT Analog Testable Prediction
β(l) 1 - C(l)² Residual misalignment → gauge hierarchy Scale-dependent β → coupling unification
αₐ(l) C(l)² / (1+β(l)) Running coupling constants Non-standard RG flow from coherence
Ψᵢ Node complex flow multiplet Gauge field / internal degrees Discrete spectrum, finite DoF per node
Fermions Localized phase-locked Ψᵢ Matter fields (quarks, leptons) Generation structure from cluster sizes
Bosons Delocalized cluster-sync Ψᵢ Force carriers (γ, W, Z, g, H) Mass gaps from coherence scales
Gₑff ∂²C(l)/∂x² Emergent Newton constant G varies with cosmic coherence evolution
mₖ, sₖ ℏc/l_min · β_cluster, Σ winding Particle mass and spin Mass ratios from β ratios, spin from topology
γₐsym(l) γ₀ exp[−γₛcₐₗₑ(log l − log l₀)] CPT violation, matter-antimatter Scale-dependent CP violation

Scale-Dependent Physics Explorer

Scale: Electroweak
Coherence C(l)
0.316
Misalignment β(l)
0.684
Strong α₃
0.118
EM α₁
0.010
1. Discrete Spectrum Signatures
Network discreteness should produce:
• Finite UV cutoff in loop calculations
• Specific ratios between coupling constants
• Oscillatory corrections to RG equations
2. Generation Structure
Fermion generations from cluster hierarchy:
• 3 generations ↔ 3 coherence scales
• Mass ratios me:mμ:mτ from β(l) ratios
• CKM/PMNS matrices from inter-cluster mixing
3. Cosmological Evolution
Time-varying "constants" from cosmic coherence:
• G varies as ∂²C(cosmic_scale)/∂t²
• α changes with universe coherence evolution
• CPT violation scales with cosmic expansion
4. Dark Sector
Hidden coherent sectors:
• Dark matter = incoherent Ψᵢ clusters
• Dark energy = large-scale coherence pressure
• Dark photon = isolated cluster synchronization
5. High-Energy Deviations
Beyond Standard Model at network scale:
• Modified dispersion relations
• Lorentz violation from preferred frame
• Maximum energy from finite node density
6. Quantum Gravity
Emergent spacetime signatures:
• Discrete area/volume eigenvalues
• Modified Newton potential at short scales
• Holographic entropy from cluster boundaries

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