We present a unified energy-ontological interpretation of non-relativistic quantum mechanics within the framework of Energy-Efficiency Theory (EET). Starting from three physically grounded axioms, we define the constrained potential U(r,t) as the spatial density of localized bound-state energy, and derive the continuity equation for the normalized constrained potential ρ(r,t)=U(r,t)/E_c. We prove that ρ(r,t) satisfies the quantum probability continuity equation, establishing the exact correspondence ρ(r,t)=|ψ|^2. We introduce the dimensionless energy ratio η = Ė_resp / Ė_main, which quantifies the balance between energy allocated to spatial exploration (response) and constraint maintenance. From first principles, we derive a modified Schrödinger equation with a real effective potential that preserves probability conservation for all values of η. Using an exact analytical solution for Gaussian wave packets, we derive the scaling relations Δx ∝ η^{-1/2} and Δp ∝ η^{1/2}, which imply the Heisenberg uncertainty principle ΔxΔp ≥ ħ/2 independent of η. Wave-particle duality is interpreted as the continuous sliding of η between exploration-dominated (wave-like, η>1) and maintenance-dominated (particle-like, η<1) regimes. We extend the framework to quantum measurement, deriving the scaling of η from first-principles system-apparatus energy coupling, and unify projective measurements, weak measurements, the quantum eraser, and decoherence within a single framework. We present four experimentally falsifiable predictions with strict statistical criteria, along with a protocol for independent experimental control of η. This work provides a self-consistent energy-ontological foundation for non-relativistic quantum mechanics, unifying probability density, wave-particle duality, the uncertainty principle, and quantum measurement under a single energy allocation framework.
We present a unified energy-ontological interpretation of non-relativistic quantum mechanics within the framework of Energy-Efficiency Theory (EET). Starting from three physically grounded axioms, we define the constrained potential U(r,t) as the spatial density of localized bound-state energy, and derive the continuity equation for the normalized constrained potential ρ(r,t)=U(r,t)/E_c. We prove that ρ(r,t) satisfies the quantum probability continuity equation, establishing the exact correspondence ρ(r,t)=|ψ|^2. We introduce the dimensionless energy ratio η = Ė_resp / Ė_main, which quantifies the balance between energy allocated to spatial exploration (response) and constraint maintenance. From first principles, we derive a modified Schrödinger equation with a real effective potential that preserves probability conservation for all values of η. Using an exact analytical solution for Gaussian wave packets, we derive the scaling relations Δx ∝ η^{-1/2} and Δp ∝ η^{1/2}, which imply the Heisenberg uncertainty principle ΔxΔp ≥ ħ/2 independent of η. Wave-particle duality is interpreted as the continuous sliding of η between exploration-dominated (wave-like, η>1) and maintenance-dominated (particle-like, η<1) regimes. We extend the framework to quantum measurement, deriving the scaling of η from first-principles system-apparatus energy coupling, and unify projective measurements, weak measurements, the quantum eraser, and decoherence within a single framework. We present four experimentally falsifiable predictions with strict statistical criteria, along with a protocol for independent experimental control of η. This work provides a self-consistent energy-ontological foundation for non-relativistic quantum mechanics, unifying probability density, wave-particle duality, the uncertainty principle, and quantum measurement under a single energy allocation framework.
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
The wave-particle duality of the electron is reinterpreted within Energy-Efficiency Theory (EET) as a continuous sliding of the energy ratio η = E˙ resp/E˙ main. In an atomic orbital, the electron is maintenance-dominated (η ≪ 1), exhibiting particle like localization. As a free wave packet, it is response-dominated (η ≫ 1), exhibiting wave-like delocalization. We derive the scaling relation ∆x ∝ η −1/2 from the exact solution of the modified Schr¨odinger equation and show that the Heisenberg uncertainty principle is preserved for all η. We propose an experimental protocol to continuously tune η using external microwave fields, thereby continuously controlling the electron’s interference visibility. Three falsifiable predictions are presented with explicit experimental designs, statistical criteria, and falsification conditions.
From the Ship of Theseus to Schrödinger's cat, from Zeno's arrow to Maxwell's demon, classical paradoxes have persistently challenged our understanding of identity, measurement, time, and information. Despite their diversity, these paradoxes share a common root: the implicit assumption that existence can be characterized by static snapshots (material constitution, geometric position, or information state) rather than by dynamical processes. Energy-Efficiency Theory (EET) offers a unified ontological framework based on three causal-functional postulates. We introduce the core concepts of constrained energy density U(r), Yang's energy ratio η = Ė_resp/Ė_main, inertial inheritance, and the real/observed space distinction. Using these tools, we provide systematic resolutions to: (i) identity paradoxes (Ship of Theseus, Replication, Swampman, Twin Earth) by grounding identity in the continuity of energy-allocation trajectories; (ii) quantum paradoxes (Schrödinger's cat, Maxwell's demon) by showing that macroscopic systems have η ≪ 1, suppressing coherence, and that information has an energetic cost; (iii) motion paradoxes (Zeno's arrow) by invoking a minimal time interval Δt_min = d_min/v_max. The framework not only resolves each paradox individually but also reveals their common underlying structure: each arises from conflating ontological energy processes with their rule-layer
What is quantum mechanics, constitutionally? This document provides the answer within the Energy-Efficiency Theory framework: quantum mechanics is not an independent set of physical laws, nor a "theory of particles," nor a "theory of measurement." Quantum mechanics is the dynamics of non-matter—the coherent propagation of free-state energy (E_f, E_c = 0) along Type II edges of the constraint network at the optimal cooperative capacity point η ≈ 1. Constraint Dynamics (CND v4.0) describes the dynamics of matter (Being, E_c > 0). Measurement is the constitutional interface between them: a Cut → Encapsulate event at the Type I/Type II boundary that terminates non-matter propagation and creates a persistent matter record. The QM ↔ Measurement Constitutional Duality is the constitutional expression of the Non-Matter/Matter distinction in dynamics. Version 3.1 is a comprehensive constitutional upgrade that preserves all v3.0 content while introducing five core refinements. (i) The Matter/Non-Matter constitutional framework (Particle v3.3) is implanted throughout: QM governs non-matter; measurement is the non-matter → matter constitutional transition; the wavefunction ψ = |ψ| e^{iS/A_EET} is the complex amplitude of non-matter propagation—physically real (ontic), not epistemic, not many-worlds. (ii) Barrier Asymmetry is conditionalized: E_b^melt ≫ E_b^form emerges from Γ(η) decay at η ≠ 1; at η = 1, E_b^form = E_b^melt = A_EET · ω (Inertia v3.4, CLOSED). Quantum coherence is protected by the three-engine architecture. (iii) The decoherence rate is corrected from a contradictory single-factor model to a two-channel additive model distinguishing encapsulation-driven decoherence (∝ f_enc(L)) from efficiency-imbalance-driven decoherence (∝ 1−Γ(η)). (iv) The quantum-to-classical transition is refined from a binary "L ≥ 3" threshold to a three-regime crossover governance (L ≤ 2 quantum, L = 3–4 crossover, L ≥ 5 effective classical), with the L_branch concept distinguishing whole-object coherence (excluded) from collective-coordinate coherence (experimentally observed). (v) The Schrödinger's cat paradox receives its constitutional resolution: the radioactive atom is non-matter (transient constraint events); the cat is matter (E ∈ {0,1} binary). The paradox arises from conflating these two constitutional domains. Ten core constitutional deepenings distinguish v3.1 from its predecessor. DEEPENING-1: The wavefunction's ontic status is systematically situated against all six major QM interpretations (Copenhagen, Many-Worlds, de Broglie–Bohm, QBism, GRW, EET), establishing EET's distinct constitutional position. DEEPENING-2: The five-channel complete constraint Second Law (CND v4.0, CLOSED) is integrated into the quantum measurement framework, unifying passive decoherence, environmental decoherence, and measurement-induced decoherence as three variants of meltdown channel activation. DEEPENING-3: The dual-channel decoherence model unifies elastic decoherence (reversible, ∝ 1−Γ(η)) and plastic decoherence (irreversible, ∝ C(t), measurement collapse) within a single constitutional framework, resolving the measurement problem. DEEPENING-4: The non-matter → matter constitutional transition is established as the three-step measurement dynamics (Difference Detection → Template Matching → Persistent Record Formation), constitutionally anchored in the constraint formation competition framework. DEEPENING-5: The line graph duality (Field v3.1 R4, Particle v3.3 Part VI) is registered as the graph-theoretic foundation of wave-particle duality—not a quantum mystery, but a universal graph-theoretic theorem. DEEPENING-6: QM and GR co-originate from the energy bifurcation at η = 1: QM is the dynamics of non-matter; GR is the geometry of matter. No "quantization of gravity" is required. DEEPENING-7: Emergent Minkowski spacetime (Space v3.3 §5, Time v3.2 §3.4) is constitutionally registered as QM's constitutional stage—not the background in which QM operates, but the symmetry that emerges at the optimal cooperative capacity point. DEEPENING-8: The quantum-to-classical crossover is governed by three independent constitutional mechanisms (decoherence via meltdown channel, force attenuation via encapsulation depth, and jamming via constraint density), of which decoherence and force attenuation are fully developed in v3.1. DEEPENING-9: Quantum information is constitutionally distinguished as transient information (non-matter, no constraint boundary, no maintenance power, no inertial mass), to be contrasted with constraint-grounded information (matter, persistent, E = mc² > 0). DEEPENING-10: The constitutional responses to twenty-six major problems in quantum mechanics are systematically registered, spanning CLOSED-in-EET (QM-GR co-origination, wave-particle duality, QM ↔ Measurement duality), STANDARD (measurement problem constitutionally located, two-channel decoherence, emergent Minkowski spacetime), WORKING HYPOTHESIS (mass as coarse coherence proxy, quantum Darwinism reformulated as blind pump), and CONJECTURE (AdS/CFT correspondence, CDT/MERA emergence). The document is organized as follows. Part I establishes the constitutional foundations, including the Matter/Non-Matter constitutional chain, Barrier Asymmetry conditionalized, and the QFT vs. EET ontological incommensurability. Part II defines QM as non-matter dynamics, establishes the wavefunction as the complex amplitude of non-matter propagation (with systematic comparison to all major QM interpretations), and delineates the constitutional domain boundaries. Part III provides the complete companion ontology interface system, synchronized through June 2026. Part IV-A presents the mathematical foundations, including the Schrödinger equation dual-path derivation and the constraint network path integral. Part IV-B develops quantum states and dynamics, with entanglement re-expressed as shared constraint boundary topology. Part IV-C provides the measurement framework—the non-matter → matter constitutional transition, five-channel measurement, and responses to Frauchiger-Renner, Leggett-Garg, and indefinite causal order. Part IV-D presents the unified two-channel decoherence model and the quantum-to-classical crossover governance with the L_branch concept. Part IV-E treats the vacuum as the N=0 ground state. Part V covers cross-scale instantiation. Part VI provides nine falsifiable predictions. Part VII lists eleven constitutional open problems. Part VIII systematically registers EET constitutional responses to twenty-six major problems in quantum mechanics. Part IX registers the academic priority of forty-eight constitutional claims. Quantum mechanics is the dynamics of the non-material substrate at its optimal operating point. Measurement is the constitutional transition from non-matter to matter. The Schrödinger equation is the deterministic law of non-matter propagation. The Born rule is the statistical law of the non-matter/matter interface. Together, they constitute the complete constitutional framework of quantum mechanics in EET. Keywords: Non-matter dynamics; matter/non-matter distinction; constraint network; coherent free-state propagation; measurement as constitutional transition; two-channel decoherence; quantum-to-classical crossover; encapsulation-depth refinement; Born rule as interface statistics; η-generalized Lindblad equation; emergent Minkowski spacetime; line graph duality; constitutional ontology of quantum mechanics; Energy-Efficiency Theory.
DESCRIPTION This work presents a complete, deterministic framework for quantum mechanics derived entirely from a single, testable postulate: the density of quantum space. The Core Problem For over a century, quantum mechanics has been interpreted as a theory of fundamental randomness, wave-particle duality, instantaneous jumps, and irreducible uncertainty. The standard Copenhagen interpretation treats the wave function as a probability amplitude, measurement as a "collapse" of that probability, and the Heisenberg uncertainty principle as a fundamental limit of nature. This work demonstrates that all these "mysteries" are not properties of nature—they are artifacts of our limited perception. We observe quantum phenomena through slow, macroscopic instruments that cannot resolve the actual continuous dynamics occurring in a space that is 6.54 trillion times denser than what we perceive as "empty space." The Fundamental Postulate The foundation of this work is a single, geometrically derived constant: ρ = (number of Planck lengths in 1 mm) / (number of millimeters in 1 light-year) = 6.54 × 10¹² Physical Meaning: One millimeter of physical space contains 6.54 trillion times more quantum spatial units than one light-year contains millimeters. What we perceive as "empty space" is actually a dense, discrete, information-rich medium. The entire observable universe (93 billion light-years in diameter) maps to only 0.014 light-years in quantum space—well within our Solar System. Consequence: The density inversion explains why quantum phenomena appear strange: we are observing a dense, fast, discrete reality through slow, coarse, macroscopic instruments. The apparent "weirdness" is not in nature—it is in our perception. The Comprehensive Law From the density postulate and classical physics (Newton, Coulomb, Maxwell, Einstein), a single comprehensive law is derived that contains all known physics as limit cases: E(t,v,n) = (m₀c²/ρ) · ‖n‖ · √(1 + (γv/c)²) · sin(2πt/T) This formula contains: Einstein's E = mc² as the limit ρ → 1, ‖n‖ → 1, sin → 1, v ≪ c Newtonian mechanics as the limit v ≪ c Special relativity as the limit ρ → 1, ‖n‖ → 1, sin → 1 Quantum mechanics as the discrete geometry n ∈ ℤ³ and resonance sin(2πt/T) Each term has a precise physical meaning: the rest mass energy (m₀c²) is scaled by the quantum space density (1/ρ), modified by the position relative to the absolute zero point Z₀ (‖n‖), adjusted for relativistic motion (√(1 + (γv/c)²)), and modulated by temporal resonance (sin(2πt/T)). Resolution of All Quantum Paradoxes Wave-Particle Duality = Optical Illusion The electron is always a localized particle with a definite trajectory. The "wave" is the charge density distribution—a standing wave in the dense quantum medium. From the standing wave condition 2πr = nλ, the Poynting vector in the far field is exactly zero (S = 0), meaning the electron does not radiate. The apparent "wave behavior" is an optical illusion caused by the density ρ smearing the point-like trajectory in our low-resolution projection. Wave Function = Energy Density, Not Probability The squared modulus of the wave function |Ψ|² is the energy density fraction, not a probability density. The particle itself follows a deterministic trajectory y(t) = v₀t - ½g₀t². Probability appears only because we cannot resolve the trajectory (due to t_total = 118 as ≪ Δt_instr) and we do not know the initial phase φ of the oscillation. Schrödinger Equation = Effective Approximation The Schrödinger equation is an effective, averaged description of how the energy density evolves. The fundamental law is classical motion in the dense quantum medium. The Schrödinger equation emerges when we average over the fast oscillation sin(2πt/T), ignore the density force F_ρ, and treat trajectories statistically. Quantization = Resonance, Not Arbitrary Jumps Energy levels are the resonant harmonics of the quantum space medium. The standing wave condition 2πr = nλ gives E_n = -13.6 eV/n²—exactly the same physics as a vibrating string. Only frequencies that satisfy the standing wave condition are stable. The transition between levels is not an instantaneous "jump" but a continuous trajectory y(t) = v₀t - ½g₀t² with total duration t_total = 118 as. The apparent "instantaneous jump" is an artifact of our slow instruments. Heisenberg Uncertainty = Collision, Not Fundamental Limit The uncertainty product depends on the measurement geometry: Δx·Δp = h·tan(θ/2), where θ is the scattering angle of the measurement photon. As θ → 0 (forward scattering with perfect detection), the product approaches zero. There is no fundamental lower bound. The uncertainty is a practical limitation of invasive measurement—we disturb the particle's trajectory when we hit it with a photon. Quantum Randomness = Ignorance Residual "quantum randomness" is simply unmodeled environmental force noise. The apparent randomness arises from three sources: temporal resolution (t_total = 118 as ≪ Δt_instr—we cannot resolve the trajectory), initial phase ignorance (we do not know the phase φ of sin(2πt/T)), and measurement perturbation (we do not know the exact collision parameters). If we could measure the outgoing photon completely and know the initial phase, the outcome would be fully deterministic. Randomness is in our ignorance, not in nature. Five Testable Predictions The theory makes five clear, quantitative predictions that distinguish it from standard quantum mechanics: Prediction 1 - Electron Transit Time: The electron transit time during the n=1 → n=2 transition in hydrogen is 118 ± 5 attoseconds. Standard quantum mechanics predicts zero duration (instantaneous jump). Testable with attosecond pump-probe spectroscopy. Prediction 2 - Heisenberg Product Can Approach Zero: With better detectors, the uncertainty product Δx·Δp can approach zero, not ħ/2. Standard quantum mechanics predicts Δx·Δp ≥ ħ/2 always. Testable with weak measurement experiments. Prediction 3 - Energy Oscillation at 116 kHz: The energy of gold-197 oscillates at 116 kHz with amplitude 1.252 × 10⁻²⁶ J. Standard quantum mechanics predicts constant energy for a given state. Testable with precision spectroscopy. Prediction 4 - Bell Inequality Violations Decrease with Measurement Strength: As measurement impulse strength decreases, Bell inequality violations decrease. Standard quantum mechanics predicts violations are independent of measurement strength. Testable with weak measurement entanglement experiments. Prediction 5 - Quantum Randomness is Environmental Noise: Residual "quantum randomness" equals unmodeled environmental force noise. Full force accounting restores classical determinism. Standard quantum mechanics predicts randomness is fundamental and irreducible. Testable with complete force reconstruction in closed quantum systems. The Absolute Zero Point Z₀ This work introduces Z₀ = (0,0,0) as a universal, absolute reference point in quantum space. Every point in space has a discrete address: n = (n_r, n_θ, n_φ), ‖n‖ = √(n_r² + n_θ² + n_φ²) Z₀ is physically grounded in the cosmic microwave background (CMB) rest frame, vacuum energy (the lowest possible energy state), and the geometric center of the quantum space lattice. This eliminates the relativity of reference frames—providing an absolute coordinate system that standard physics lacks. Mathematical Consistency The work provides rigorous derivations of: The density ρ from first principles (Planck length, electron mass, fine structure constant) The quantum coordinate norm ‖n‖ from the discrete metric of quantum space The oscillation period T from the de Broglie relation The coupling constant ε from fundamental constants The regularized metric eliminating all singularities The thermodynamic properties of quantum space (entropy, temperature, heat capacity) The covariant Einstein equation in quantum space The connection to quantum anomalies and topological invariants The Lamb shift from quantum space density oscillation Dark energy from quantum space density variation Comparison with Other Approaches String theory requires approximately 10⁵⁰⁰ free parameters and offers no testable predictions with current technology, while introducing new physics such as strings, extra dimensions, and supersymmetry. Loop quantum gravity requires approximately 10 parameters and also offers no testable predictions, introducing spin networks and loop quantization. Both approaches have difficulty connecting to the Standard Model. In contrast, this theory has only one parameter (ρ, which is derived from fundamental constants rather than being free), offers five testable predictions with current or near-future technology, requires no new physics beyond standard physics applied in a dense medium, and connects directly to the Standard Model through the energy-momentum tensor. The Core Message Quantum mechanics is not magic. It is not a new kind of physics. It is the same old physics—Newton, Maxwell, Coulomb—operating in a space that is 6.54 trillion times denser than we perceive. Three things to remember: Space is dense, not empty. What we call "empty space" is actually a dense, discrete medium. We are the ones who are sparse—not the universe. The particle has a trajectory. Every particle follows a precise, continuous path. We don't see it because our instruments are too slow. The path exists—we just can't resolve it. Energy breathes. Energy is not a static number. It oscillates in time, like a heartbeat. The universe is alive with resonance. Conclusion This work demonstrates that quantum mechanics is not a theory of fundamental randomness and irreducible uncertainty. It is the low-resolution, static-space approximation of a deeper, deterministic, dynamic reality. The deeper reality is quantum space—dense, discrete, resonant, and absolute. The final statement of this
In standard quantum mechanics, the visibility of double-slit interference is determined solely by coherence and decoherence. Here we introduce a dimensionless parameter η = Ė_resp / Ė_main that quantifies the internal energy allocation between response (exploration) and maintenance (localization) of a quantum system. We show that even in the absence of decoherence, the visibility becomes v(η) = 2√η/(1+η) when the system is prepared in a non-equilibrium steady state with η ≠ 1. The derivation is based on an effective mass renormalization m* = m/η that preserves the standard Schrödinger form while scaling the dispersion rate. A concrete experimental realization using ultracold atoms in an optical lattice with amplitude modulation is proposed, together with a full statistical protocol to falsify the prediction. This provides a clean, experimentally accessible test of energy-efficiency theory (EET) against standard quantum mechanics.