The Two Fundamental Forms of Energy: Free State and Constrained State A Physical Ontological Foundation of Energy-Efficiency Theory

Energy-Efficiency Theory (EET) takes the first axiom “energy is the sole ontology” as its starting point. This paper systematically expounds the two fundamental forms of energy: the free state (continuously distributed, propagating at the speed of light, such as waves and fields) and the constrained state (localized, stable, subluminal, such as particles and matter). We provide rigorous definitions, mathematical characterizations, and a quantitative model of state transitions. Based on this framework, we unify three fundamental physical phenomena: (1) wave particle duality as a dynamic sliding of energy between the two states (superposition |ψ⟩ = α|free⟩ + β|bound⟩), with quantitative compatibility demonstrated via the electron wavepacket example; (2) quantum measurement collapse as an irreversible transition from the free state to the constrained state, with transition time satisfying ∆tmin = dmin/c and energy dissipation obeying Landauer’s limit; (3) the mass-energy equivalence E = mc2 as a conversion formula between the two states, where mass is the spatial density of constrained-state energy, validated by experimental data from the carbon-12 nucleus. We further derive quantitative transition rate formulas and engage with contemporary structural realism. This work provides a unified energy-ontological interpretation of quantum mechanics and relativity, establishing the physical foundation of the EET framework. Keywords: free-state energy; constrained-state energy; wave-particle duality; quantum measurement; mass-energy equivalence; Energy-Efficiency Theory