[Paper Review] On the Nature of the Electric Charge

Volodymyr Krasnoholovets|ArXiv.org|Jan 25, 2005

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TL;DR

This paper proposes a submicroscopic geometric model of the electric charge based on a discrete, fractal-like space structure called the 'tessellattice,' where the electric charge is localized on the surface of a particle. By analyzing scalar and vector potentials and deriving the Lagrangian, the authors show that Maxwell's equations emerge naturally from this framework, with photons and 'inerton' particles as fundamental excitations of the tessellattice, offering a unified geometric foundation for electromagnetism and quantum field theory at the Planck scale.

ABSTRACT

The geometry of the elementary charge is studied in the framework of the concept of space considered as a tessellation lattice ('tessellattice'), which has recently been developed by M. Bounias and the author. The descriptive-geometric sense of the electric and magnetic fields and their carriers - photons - is analyzed. The notion of the scalar and vector potentials of a charged particle and their behavior at the motion of the particle along a path is investigated in detail. Based on the potentials, the Lagrangian leading to the Maxwell equations is constructed. The distinctive properties of the inerton and the photon - two basic elementary excitations, or quasi-particles of the space tessellattice - are discussed. Summarizing, we may say that the work suggests the detailed interpretation of the Maxwell equations in terms of the submicroscopic approach to Nature.

Motivation & Objective

• To develop a geometric, submicroscopic interpretation of the electric charge based on a discrete space lattice (tessellattice).
• To explain the origin of electromagnetic fields and photons as excitations of the tessellattice structure.
• To derive the Maxwell equations from a Lagrangian constructed using scalar and vector potentials in this geometric framework.
• To clarify the physical nature of the inerton and photon as fundamental excitations of space, distinct from standard quantum field theory approaches.
• To reconcile the model with both modern physics and ancient Vedic cosmology, suggesting a deep consistency with fundamental physical principles.

Proposed method

• Models space as a topologically discrete tessellattice derived from set theory, topology, and fractal geometry, with primary cells representing the fundamental substrate.
• Introduces the concept of fractal deformation of cells to represent massive particles, where volume reduction corresponds to mass generation.
• Analyzes scalar and vector potentials of a charged particle and their evolution along a particle's trajectory to construct a Lagrangian.
• Derives the Maxwell equations from this Lagrangian, showing their geometric origin in the tessellattice dynamics.
• Introduces the inerton as a distinct quasi-particle excitation of the tessellattice, different from the photon, and analyzes their roles in field interactions.
• Uses mathematical analysis of surface defects in needle-shaped geometries to test stability and consistency of charge localization on particle surfaces.

Experimental results

Research questions

• RQ1 How can the electric charge be geometrically localized on the surface of a particle within a discrete space lattice?
• RQ2 What is the physical origin of the scalar and vector potentials in a submicroscopic, geometric model of space?
• RQ3 How do the Maxwell equations emerge from a Lagrangian derived in a tessellattice framework?
• RQ4 What distinguishes the inerton from the photon as fundamental excitations of the tessellattice?
• RQ5 Can the stability of charge localization be mathematically verified using geometric and topological constraints on surface defects?

Key findings

• The electric charge is localized on the surface of a particle, consistent with the geometric constraints of the tessellattice model.
• The Lagrangian derived from scalar and vector potentials leads to the Maxwell equations, confirming the consistency of the model with classical electrodynamics.
• The inerton and photon are identified as two distinct fundamental excitations of the tessellattice, with the inerton associated with mass and the photon with electromagnetic field propagation.
• The surface defect analysis for a needle-shaped geometry shows instability, indicating that such shapes cannot support a stable charge state, implying geometric constraints on charge localization.
• The solution to the stability condition yields a critical aspect ratio $\varkappa_0 \simeq 1.323311$, which determines the geometric limits of stable charge configurations.
• The determinant of the Hessian matrix for the surface defect is negative ($\text{Det} \simeq -2.82265$), confirming the absence of an extremum and thus instability of the needle shape, ruling it out as a viable charge carrier configuration.