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Dynamical Localized Wave Packet Theory (DLWPT): Bounding and Deriving the Coherence Inertia Constant Γ

Eric Aboagye Amankwah

Published May 24, 2026• 0 citations
Publisher

Abstract

This paper investigates the coherence inertia constant (Γ), the sole new parameter introduced in the Dynamical Localized Wave Packet Theory (DLWPT). By combining experimental constraints from attosecond wavepacket physics and high-precision hydrogen spectroscopy with multiple independent theoretical derivations, the study demonstrates that Γ² converges naturally to the Planck-scale relation Γ² = ℏtₚ. The work establishes Γ not as a free adjustable parameter, but as a quantity fixed by the internal consistency of the DLWPT framework. The manuscript further explores the implications of this result for quantum coherence, wavepacket dynamics, Planck-scale phenomenology, and the foundations of quantum mechanics.

DOI
10.5281/zenodo.20361406

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This paper investigates the coherence inertia constant (Γ), the sole new parameter introduced in the Dynamical Localized Wave Packet Theory (DLWPT). By combining experimental constraints from attosecond wavepacket physics and high-precision hydrogen spectroscopy with multiple independent theoretical derivations, the study demonstrates that Γ² converges naturally to the Planck-scale relation Γ² = ℏtₚ. The work establishes Γ not as a free adjustable parameter, but as a quantity fixed by the internal consistency of the DLWPT framework. The manuscript further explores the implications of this result for quantum coherence, wavepacket dynamics, Planck-scale phenomenology, and the foundations of quantum mechanics.
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.
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.
This paper presents a theorem-driven resolution of the quantum measurement problem within the framework of the Dynamical Localized Wave Packet Theory (DLWPT). The theory treats the wavefunction as a real, physically evolving coherence field governed by second-order temporal dynamics and identifies the conserved coherence density, derived from a U(1) Noether current, as the fundamental measurable quantity. A sequence of logically connected results demonstrates that detector interactions necessarily couple to the conserved coherence density rather than the conventional probability density |Ψ|². Through temporal coarse-graining, the fast-mode structure of the coherence field becomes operationally inaccessible to realistic detectors, causing the standard Born rule to emerge as the leading-order approximation of a conserved dynamical quantity. The work establishes: A rigorous slow-fast mode decomposition of the DLWPT coherence field. Non-perturbative suppression of fast-mode detector contributions. Robust Born-rule emergence for realistic finite-bandwidth detectors. A uniqueness theorem identifying coherence density as the only physically admissible detector coupling observable. Detector universality as a testable prediction. A deterministic account of measurement without wavefunction collapse. Experimentally testable corrections to standard quantum mechanics at ultra-short timescales. The paper argues that probabilistic quantum outcomes arise from detector limitations rather than fundamental indeterminism, thereby dissolving rather than supplementing the measurement postulate of conventional quantum mechanics. This work forms Paper 3 in the DLWPT research series and develops the measurement-theoretic implications of the theory established in earlier foundational papers.
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.
This work establishes a Lorentz-invariant relativistic scalar extension of the Dynamical Localized Wave Packet Theory (DLWPT) by formulating a deterministic field ontology directly within spacetime. By utilizing a coherence-scaled Lagrangian density, the framework derives equations of motion and energy-momentum structures where physical attributes such as mass, localization, and inertial response emerge from the intrinsic coherence stiffness of the field rather than from independent postulates or point-like particle identities. A central feature of this construction is the natural emergence of preferred momentum and energy scales that act as a dynamical ultraviolet regulator, suppressing arbitrarily high-frequency excitations while strictly maintaining Lorentz covariance. The theory reinterprets the standard wave function as a representation of information density and field coherence conservation, effectively replacing the probabilistic Born rule with a symmetry-driven conservation law. Furthermore, the framework demonstrates a hierarchical structure where reality operates across nested coherence limits, ensuring that the equations reduce smoothly to both non-relativistic DLWPT and conventional Schrödinger dynamics in the appropriate low-energy limits. This formulation positions DLWPT not as a replacement for relativistic field theory, but as a fundamental reinterpretation that links localization stability and dispersion behavior to a deeper, coherence-based geometric substrate.