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Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B

A closed-loop-controlled stochastic process in the dynamics of a mass point in wave mechanics

D. Wickers

Published Dec 1, 1983• 0 citations
Publisher
DOI
10.1007/bf02721097

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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.
The dynamics induced while controlling quantum systems by optimally shaped laser pulses have often been difficult to understand in detail. A method is presented for quantifying the importance of specific sequences of quantum transitions involved in the control process. The method is based on a ``beable'' formulation of quantum mechanics due to John Bell that rigorously maps the quantum evolution onto an ensemble of stochastic trajectories over a classical state space. Detailed mechanism identification is illustrated with a model seven-level system. A general procedure is presented to extract mechanism information directly from closed-loop control experiments. Application to simulated experimental data for the model system proves robust with up to 25% noise.
We develop a real-variable mechanics in which complex quantum dynamics is not postulated at the microscopic starting point. The central observation is that integration by parts does more than generate formal boundary terms: in a medium with defects, interfaces, punctures, grains, or excised sets, those boundary terms encode the admissible transport law. Dirichlet, Neumann, and Robin boundary conditions therefore become dynamical selectors for absorption, reflection, and partial reflection-reaction. Robin structure is especially important because the same boundary parameter controls boundary local time in diffusion and a momentum-dependent reflection phase in wave mechanics. We combine this with an Eulerian--Lagrangian description of transport, a symmetric/antisymmetric tensor decomposition, and a compatible antisymmetric two-form. On an oriented two-plane the normalized antisymmetric transport operator satisfies J^2=-I, furnishing a real complex structure without inserting the scalar 'i' by hand. Nelson-type forward/backward stochastic kinematics then produces the continuity equation, quantum potential, and Schrodinger form, while closed defect loops yield Berry-like holonomy. A Glauber master-equation route supplies a discrete stochastic precursor. Bell correlations are treated as an endpoint test of globally prepared nonseparable transport: Bell's theorem is retained in full, so the construction is not a Bell-local hidden-variable model. Rather, it proposes that local propagation can coexist with a globally prepared holonomy/correlation state whose measurement statistics need not factorize. Finally, we connect the symmetric transport sector to emergent 3-geometry, entanglement-area structure, and loop-quantum-gravity-style geometric observables. The paper separates established mathematics from the proposed synthesis and lists numerical and experimental falsification tests.