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Dynamical Localized Wave Packet Theory (DLWPT): Many-Body Coherence, Bell Correlations, and No-Signaling

Eric Aboagye Amankwah

Published Jun 13, 2026• 0 citations
Publisher

Abstract

DLWPT: Many-Body Coherence, Bell Correlations, and No-Signaling extends the Dynamical Localized Wave Packet Theory (DLWPT) to many-body quantum systems and investigates its implications for Bell correlations, quantum nonlocality, contextuality, and the measurement problem. The paper develops a deterministic, collapse-free framework in which the fundamental ontic entity is a conserved coherence field defined on configuration space rather than a probabilistic wavefunction interpretation. The work demonstrates how local detector interactions arise through marginal coupling to the coherence density while the global non-separable structure of the many-body field naturally generates Bell-inequality violations. Operational no-signaling is preserved despite ontic nonlocality, thereby providing a deterministic account of quantum correlations without invoking wavefunction collapse, hidden particle trajectories, superdeterminism, or retrocausality. A concrete Stern–Gerlach detector model is developed to show how discrete measurement outcomes emerge through spatial sorting and temporal coarse-graining of the coherence density. The paper further establishes the contextual nature of DLWPT in accordance with the Kochen–Specker theorem and proposes experimentally testable deviations from standard quantum mechanics in ultrafast and high-energy Bell experiments. Overall, this work positions DLWPT as a coherence-based reconstruction of quantum foundations in which the Born rule, Bell correlations, and operational no-signaling emerge from a unified dynamical principle based on the conservation and evolution of coherence density.

DOI
10.5281/zenodo.20674019

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Dynamical Localized Wave Packet Theory (DLWPT) is a theoretical framework that extends conventional quantum mechanics by interpreting the wavefunction as a physically real coherence field rather than a purely probabilistic object. In this approach, quantum particles correspond to dynamically stable, localized wave packets whose evolution is governed by modified dynamical equations incorporating a fundamental coherence scale. In its relativistic formulation, DLWPT modifies the standard Dirac dynamics by introducing a nonlocal coherence operator. This operator captures the finite spacetime coherence region associated with localized fermionic wave packets. As a result, the theory naturally describes fermions as extended but localized structures with Planck-scale coherence tails, rather than strictly pointlike particles. The DLWPT framework provides a deterministic description of wave packet evolution while maintaining compatibility with relativistic covariance. At energies far below the Planck scale, the modified dynamics reduce smoothly to the standard Dirac equation, ensuring consistency with established quantum field theory. However, at ultra-high energies the coherence operator introduces Planck-suppressed corrections to the dispersion relation and particle propagation. Several conceptual implications follow from this formulation. The nonlocal structure of the coherence operator provides a natural interpretation of quantum non-separability through overlapping coherence regions. Localized fermions arise as stable eigenmodes of the coherence operator, and the theory suggests that internal orientation degrees of freedom of these coherence packets may underlie the emergence of gauge symmetries. Within this framework, gravity can be interpreted as an emergent phenomenon associated with gradients in the coherence energy density of localized wave packets. The Planck scale therefore appears not merely as a parameter of quantum gravity but as the fundamental coherence scale governing the structure of matter fields. DLWPT thus proposes a unified conceptual picture in which particles are self-coherent spacetime wave packets, interactions arise from coherence structures and their orientation modes, and spacetime geometry reflects the collective behavior of coherence energy at the Planck scale. The present work develops the relativistic fermionic sector of the theory, deriving the modified Dirac equation, associated dispersion relations, and propagator structure. Potential observational signatures include Planck-suppressed deviations in high-energy particle propagation and coherence-induced modifications to scattering processes.
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This paper presents the foundational formulation of the Dynamical Localized Wave Packet Theory (DLWPT), a proposed extension of non-relativistic quantum mechanics in which the wavefunction is reinterpreted as a physically real dynamical coherence field possessing intrinsic temporal inertia. The manuscript develops a mathematically consistent second-order generalization of Schrödinger dynamics derived from a local U(1)-symmetric Lagrangian framework. Unlike standard quantum mechanics, where temporal evolution is governed by a first-order equation, DLWPT introduces a second-order temporal coherence term characterized by a coherence inertia parameter Γ. This modification produces richer dynamical structure while recovering the conventional Schrödinger equation in the low-inertia limit. The paper argues that standard quantum mechanics may represent an emergent effective regime of a deeper coherence-based dynamics rather than the most fundamental layer of physical reality.
The standard interpretation of quantum measurement on entangled systems holds that measuring one particle nonlocally collapses the wavefunction of its spacelike-separated partner. We argue that this conclusion rests on a false presupposition: that subsystems of entangled systems possess independent ontic states. If the global wavefunction is the sole ontic object (ψ-ontic holism), then for entangled systems there is no “state of B” to be affected by measurement at A. The reduced density matrix of a subsystem, while operationally useful, is not ontologically real for non-factorizable states. Measurement is a local dynamical process — concretely modeled by continuous spontaneous localization (CSL) — that destroys one local wavefunction component at the measurement site. The global state factorizes as a consequence, and subsystem ontology emerges for the first time. The transition of the distant particle’s reduced density matrix from mixed to pure reflects this emergence of separability, not a physical change at the distant location. We show that this framework is consistent with no-signaling, with the contextuality required by the Kochen–Specker and GHZ theorems, and with the local measurement axiom (Postulate M) proposed in a companion paper. Bell’s theorem does not force nonlocality upon our framework because it presupposes outcome determinism — the assignment of definite values to observables prior to measurement — which several quantum mechanical theorems and our ψ-ontic ontology explicitly deny. Decoherence, which is ubiquitous in nature, provides the mechanism by which the global wavefunction factorizes and classical separability emerges. The apparent nonlocality of quantum mechanics is thus reinterpreted as nonseparability: the fundamental ontology is holistic, but the dynamics are local.