The Minimal Configuration Interpretation (MCI) of Quantum Mechanics (goes hand-in-hand with my UFGTG paper):
AXIOMS OF MCI
- Universal Field Axiom There exists a single universal field Ψ(x,n) where:
- x represents points in a discrete spatial set X with adjacency structure
- n represents discrete configuration index
- Ψ contains all physical information of the universe including gauge and matter components
- Ψ evolves through discrete configurations via the Configuration Transition Operator: Ψ(n+1) = T̂Ψ(n), where T̂ = exp(-iĤε/ℏ)
- Configuration Space Axiom The space of possible configurations C is:
- Discrete and countable
- Constrained by total energy E_total = constant
- Characterized by metric: d(Ψ₁,Ψ₂) = ∫|Ψ₁(x) – Ψ₂(x)|²dx
- Equipped with appropriate gauge structure and boundary conditions
- State Evolution Axiom Transitions between configurations follow path integral:
- Z⁻¹exp(iS[Ψ]/ℏ) for quantum evolution
- P(Ψn+1|Ψn) = Z⁻¹exp[-(ΔE – TΔS)/k] for thermal/measurement processes Where:
- Z is the partition function ensuring normalization
- S[Ψ] is the appropriate action
- ΔE is energy difference between configurations
- ΔS is entropy difference
- T is temperature
- k is Boltzmann’s constant
- Measurement Axiom Quantum measurements correspond to configuration transitions where:
- Initial configuration contains superposed field modes
- Interaction couples system to environment
- Transition probability follows the State Evolution Axiom
- Final configuration contains resolved state
- No “collapse”—just energy-entropy optimization through actual physical interactions
- Entanglement Axiom Entangled states share unified field patterns such that: Ψentangled(x₁,x₂,n) ≠ Ψ₁(x₁,n)⊗Ψ₂(x₂,n) For any separable states Ψ₁,Ψ₂
FORMAL THEOREMS
- Born Rule Theorem The Born rule emerges from the State Evolution Axiom: P(outcome) = |⟨outcome|Ψ⟩|² = Z⁻¹exp(-ΔE/kT) For energy-degenerate states
- No-Cloning Theorem Configuration transitions preserve field uniqueness: ∄Û: Û(Ψ₁⊗Ψ₀) → Ψ₁⊗Ψ₁ For arbitrary states Ψ₁,Ψ₀
- Information Conservation Theorem Field information is preserved: I[Ψ(n)] = I[Ψ(n+1)] Where I is a suitable information measure
- Uncertainty Principle Field configurations satisfy: ΔxΔp ≥ ħ/2 Due to field mode structure
- Bell’s Theorem Non-local correlations emerge from a unified field: ⟨AB⟩ ≠ ∫ρ(λ)A(a,λ)B(b,λ)dλ For any local hidden variables λ
MATHEMATICAL FRAMEWORK
- Configuration Space C = {Ψ: X → C | E[Ψ] < ∞} With metric d defined above
- Transition Operator T̂: C → C T̂Ψ(n) = Ψ(n+1) Satisfying unitarity: T̂†T̂ = 1
- Observable Operators Â: C → C ⟨Â⟩ = ∫Ψ*(x,n)ÂΨ(x,n)dx
- Entropy Functional S[Ψ] = -k∫|Ψ|²ln|Ψ|²dx
- Energy Functional E[Ψ] = ∫(|∇Ψ|² + V(|Ψ|²))dx
PHYSICAL IMPLICATIONS
- Quantum Behavior
- Superposition exists within single configurations
- Measurement resolves via energy-entropy optimization
- No infinite branching or collapse required
- Classical Emergence
- Classical behavior emerges for high-entropy configurations
- Decoherence is a natural consequence of entropy maximization
- Clear quantum-to-classical transition
- Causality
- Configuration transitions respect light-cone structure
- No faster-than-light signaling despite non-locality
- Clear arrow of time from entropy increase
- Computational Resources
- Finite number of configurations
- Polynomial computational complexity
- Physically realizable evolution