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.
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.
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.
The double-slit experiment is the quintessential demonstration of wave-particle duality. In standard quantum mechanics, interference visibility v = (Imax − Imin)/(Imax + Imin) is unity for a perfectly coherent, isolated source. Any reduction is attributed to decoherence caused by environmental coupling. Here we propose an additional, intrinsic mechanism for visibility reduction that originates from the internal energy allocation of the quantum system itself, without requiring any loss of coherence. Energy-efficiency theory (EET) posits that any persistent localized system continuously allocates incoming energy between two competing channels: maintenance (E˙ main) that sustains the existing localized structure, and response (E˙ resp) that explores configuration space. Their ratio η = E˙ resp/E˙ main defines a dynamical regime. Standard quantum mechanics corresponds to the balanced equilibrium case η = 1. By externally driving the system, η can be tuned away from unity, leading to modified wavepacket spreading and, consequently, a reduced interference visibility even in the absence of decoherence. This paper presents a precise quantitative prediction for v(η), a feasible experimental realization using ultracold atoms in optical lattices, and a rigorous statistical protocol for falsification. The prediction is independent of any free parameters and can be tested with existing technology.
Bohr’s atomic model, though superseded by quantum mechanics, retains pedagogical value for its intuitive picture of quantized orbits. This paper reinterprets Bohr’s model within Energy-Efficiency Theory (EET), revealing its deep connection to the energy ratio η = E˙ resp/E˙ main. We show that the principal quantum numbern corresponds to the inverse square of η: ηn ∝ 1/n2 . In the ground state (n = 1), η ≪ 1, and the electron is particle-like; in highly excited states (n ≫ 1), η approaches 1, and the electron becomes wave-like. This provides a continuous picture of the transition from quantum to classical behavior, and offers a pedagogical bridge from Bohr’s model to modern quantum theory.
Wave-particle duality remains one of the most striking and conceptually unresolved features of quantum mechanics. Here I present a dynamical mechanism for wave-particle duality based on spontaneous stochastic mass-energy interconversion at subatomic scales. By promoting particle mass to a fluctuating quantity consistent with Einstein’s mass-energy equivalence, I derive a Schrödinger equation with an additional stochastic kinetic-phase term. Applied to the canonical double-slit experiment, the framework shows that quantum interference arises from coherent, path-dependent phase accumulation driven by mass-energy fluctuations, while particle-like localization emerges naturally at detection. The formalism yields closed-form expressions for interference visibility, predicts a momentum- and mass-dependent decoherence rate, admits a path-integral interpretation, and enables direct experimental bounds using neutron, electron, and atom interferometry. The results provide a physically grounded account of wave-particle duality without modifying the axioms of quantum mechanics.
Within the path integral Feynman formulation of quantum mechanics, the fundamental Heisenberg Uncertainty Relationship (HUR) is analyzed in terms of the quantum fluctuation influence on coordinate and momentum estimations. While introducing specific particle and wave representations, as well as their ratio, in quantifying the wave-to-particle quantum information, the basic HUR is recovered in a close analytical manner for a large range of observable particle-wave Copenhagen duality, although with the dominant wave manifestation, while registering its progressive modification with the factor 1-n2, in terms of magnitude n∈[0,1]. of the quantum fluctuation, for the free quantum evolution around the exact wave-particle equivalence. The practical implications of the present particle-to-wave ratio as well as of the free-evolution quantum picture are discussed for experimental implementation, broken symmetry and the electronic localization function.
Wave-particle duality and the superposition of quantum mechanical states furnish quantum mechanics with unique features which distinguishes it from classical mechanics and give it the apparently counter-intuition interpretation. The two principles are responsible for the observation of the interference effects of quantum particles such as electrons, atoms and molecules. Visibility is a measure of the wave nature and can be though of as a "normalized" coherence quantifier. Reduction in the visibility arises from dephasing (decoherence): a process in which the relative phases get partially or totally destroyed leading to domination of the particle nature. We calculate the coherence and visibility of an ensemble of a single electron and two electrons on two sites using the density matrix formulation. For such a system of electrons, visibility and predictability (a particle nature measure) follow an oscillatory-complementary temporal evolution and neither of them depends on the single particle energy.