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The Local Matter-Wave Threshold Model

Andrew Hollis

Published Oct 14, 2026• 0 citations
Publisher

Abstract

This paper presents a strictly local, realist interpretation of quantum statistics using independent, continuous, standard sine matter waves. By introducing a frequency-dependent photoelectric threshold type mechanism alongside geometric projection interactions at macroscopic detectors, I demonstrate that non-linear correlation profiles arise naturally without requiring non-local wavefunction collapse. This localized field framework is tested to show full analytical correspondence with both two-particle and three-particle Greenberger-Horne-Zeilinger (GHZ) state profiles. Evaluated via the Bell-Dzhafarov-Kujala (BDK) contextuality framework, the model proves that quantum statistics can be completely replicated by local realist boundaries that flex dynamically across non-Euclidean parameter spaces.

DOI
10.5281/zenodo.23376985

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This paper presents a strictly local, realist interpretation of quantum statistics using independent, continuous, standard sine matter waves. By introducing a frequency-dependent photoelectric threshold type mechanism alongside geometric projection interactions at macroscopic detectors, I demonstrate that non-linear correlation profiles arise naturally without requiring non-local wavefunction collapse. This localized field framework is tested to show full analytical correspondence with both two-particle and three-particle Greenberger-Horne-Zeilinger (GHZ) state profiles. Evaluated via the Bell-Dzhafarov-Kujala (BDK) contextuality framework, the model proves that quantum statistics can be completely replicated by local realist boundaries that flex dynamically across non-Euclidean parameter spaces.
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The Greenberger–Horne–Zeilinger (GHZ) puzzle has been used to study quantum nonlocality and provide an all-or-nothing, no-go theorem for local hidden-variable models. Recent experiments using coincident-detected entangled photons prepared in a three-particle GHZ state have been used to test quantum nonlocality, but fail to rule out local realism due to a reliance on the fair-sampling hypothesis and insufficient detection efficiency. This paper describes a physically motivated local hidden-variable model based on amplitude-threshold detection that is capable of producing similar results. Detection efficiencies for the model are within the bounds permitted for local realism and, interestingly, exhibit statistical correlations between detectors, even when the detection events are spacelike separated. Increasing the detection threshold improves agreement with the ideal quantum predictions at the cost of decreased detection efficiency. A curious emergent feature of the model is that detection efficiencies may depend upon which observables are chosen for measurement.
I propose a local, realist interpretation of quantum mechanics based on a physical scalar wave field in ordinary three-dimensional space. Each fundamental particle (electron, photon, proton, etc.) possesses its own wave field. The field is fundamental — it is not emitted by the particle, nor does it draw energy from the particle’s motion. The particle is guided by the phase gradient of its own wave via a Bohmian guidance law. The wave evolves according to a linear Klein-Gordon equation. For a single particle this reproduces the full empirical success of quantum mechanics, including the hydrogen spectrum and the double-slit interference pattern. For multiple particles, each particle retains its own local 3D wave; no configuration space is needed. Entanglement is rejected as a fundamental physical phenomenon: the correlations observed in Bell-type experiments are interpreted as ordinary statistical correlations arising from common past interactions, not as evidence of non-locality or of a non-separable quantum state. The quantum mechanical wave function in configuration space is regarded as a mathematical tool, not a physical field. The theory is local, realist, and fully three-dimensional.
A sequence of Bell inequalities for NNN-particle systems, which involve three settings of each of the local measuring apparatuses, is derived. For Greenberger-Horne-Zellinger states, quantum mechanics violates these inequalities by factors exponentially growing with NNN. The threshold visibilities of the multiparticle sinusoidal interference fringes, for which local realistic theories are ruled out, decrease as (2/3)N{(2/3)}^{N}(2/3)N.
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