The Minimal Configuration Interpretation of Quantum Mechanics (MCI)

The Minimal Configuration Interpretation (MCI) of Quantum Mechanics (goes hand-in-hand with my UFGTG paper):

AXIOMS OF MCI

  1. 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)
  2. 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
  3. 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
  4. 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
  5. 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

  1. 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
  2. No-Cloning Theorem Configuration transitions preserve field uniqueness: ∄Û: Û(Ψ₁⊗Ψ₀) → Ψ₁⊗Ψ₁ For arbitrary states Ψ₁,Ψ₀
  3. Information Conservation Theorem Field information is preserved: I[Ψ(n)] = I[Ψ(n+1)] Where I is a suitable information measure
  4. Uncertainty Principle Field configurations satisfy: ΔxΔp ≥ ħ/2 Due to field mode structure
  5. 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

  1. Configuration Space C = {Ψ: X → C | E[Ψ] < ∞} With metric d defined above
  2. Transition Operator T̂: C → C T̂Ψ(n) = Ψ(n+1) Satisfying unitarity: T̂†T̂ = 1
  3. Observable Operators Â: C → C ⟨Â⟩ = ∫Ψ*(x,n)ÂΨ(x,n)dx
  4. Entropy Functional S[Ψ] = -k∫|Ψ|²ln|Ψ|²dx
  5. Energy Functional E[Ψ] = ∫(|∇Ψ|² + V(|Ψ|²))dx

PHYSICAL IMPLICATIONS

  1. Quantum Behavior
    • Superposition exists within single configurations
    • Measurement resolves via energy-entropy optimization
    • No infinite branching or collapse required
  2. Classical Emergence
    • Classical behavior emerges for high-entropy configurations
    • Decoherence is a natural consequence of entropy maximization
    • Clear quantum-to-classical transition
  3. Causality
    • Configuration transitions respect light-cone structure
    • No faster-than-light signaling despite non-locality
    • Clear arrow of time from entropy increase
  4. Computational Resources
    • Finite number of configurations
    • Polynomial computational complexity
    • Physically realizable evolution