Quantum Mechanics as Energy-State Transitions: An Energy-Efficiency Interpretation

Quantum mechanics describes microscopic phenomena with extraordinary precision, yet its ontological foundations remain contested. This paper develops a complementary interpretation within Energy-Efficiency Theory (EET). Starting from the three axioms, we introduce the energy ratio η as a functional of the quantum state via a decomposition of the Hamiltonian into free and constrained parts: η(ψ) = ⟨ψ|Ĥ_free|ψ⟩ / ⟨ψ|Ĥ_bound|ψ⟩ (with η→∞ when the denominator vanishes, corresponding to a pure free state). This parameter quantifies the balance between wave-like (free) and particle-like (bound) behavior. We derive explicit relations connecting η to standard quantum observables: η ∝ Ω/Γ for driven two-level systems, and η_eq ∼ ħ/(τ_coh k_B T) for thermal decoherence. The measurement process is formulated as an energy-constrained transition using projection-valued measures, recovering the Born rule from the assumption that the probability is proportional to the energy transfer rate. We derive the uncertainty principle from the energy cost of localization, entanglement entropy from correlated constraint barriers, and decoherence rates from environmental relaxation of η. Three testable predictions are given with explicit mappings to experimental parameters (coherence time, measurement time, entanglement entropy) and statistical power analysis. This interpretation is fully compatible with standard quantum formalism while providing a first‑principles energy ontology that unifies quantum phenomena with the broader EET framework.