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 spatial coordinates
– n represents discrete configuration index
– Ψ contains all physical information of the universe
– Ψ evolves through discrete configurations via:
Ψ(x,n+1) = Ψ(x,n) + ε[−∇E(x,n) + γT∇S(x,n)]
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
3. State Evolution Axiom
Transitions between configurations follow:
P(Ψn+1|Ψn) = Z⁻¹exp[-(ΔE – TΔS)/k]
Where:
– Z is partition function ensuring normalization
– ΔE is energy difference between configurations
– ΔS is entropy difference
– T is temperature
– k is Boltzmann 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 State Evolution Axiom
– Final configuration contains resolved state
– No “collapse” – just energy-entropy optimization
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 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: R³ → 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 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