Relativistic Dynamical Localized Wave Packet Theory: Planck-Scale Coherence and Emergent Fermionic Dynamics

Abstract

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.