[Paper Review] The Potential-Vortex Theory of the Electromagnetic Field

A. K. Tomilin|arXiv (Cornell University)|Aug 24, 2010

Quantum and Classical Electrodynamics2 references3 citations

TL;DR

This paper proposes a four-dimensional electrodynamics framework that unifies both vortex and potential components of the electromagnetic field, challenging the conventional exclusion of potential magnetic fields via gauge conditions. By generalizing Maxwell's equations to include physical potential components, the theory resolves inconsistencies in electromagnetic wave propagation and provides a more complete field description grounded in total field theory.

ABSTRACT

Maxwell-Lorenz theory describes only vortex electromagnetic processes. Potential component of the magnetic field is usually excluded by the introduction of mathematical terms: Coulomb and Lorenz gauges. Proposed approach to the construction of the four-dimensional electrodynamics based on the total (four-dimensional) field theory takes into account both vortex and potential components of its characteristics. It is shown that potential components of the electromagnetic field have physical content. System of modified (generalized) Maxwell equations is written. With their help contradictions usually appearing while describing the distribution of electromagnetic waves, are eliminated. Works of other authors obtained similar results are presented and analyzed.

Motivation & Objective

• To develop a four-dimensional electrodynamics framework that includes both vortex and potential components of the electromagnetic field.
• To challenge the conventional exclusion of potential magnetic field components through gauge conditions like Coulomb and Lorenz gauges.
• To resolve contradictions in electromagnetic wave distribution by incorporating physical potential components into field theory.
• To present a generalized form of Maxwell's equations that accounts for both dynamic (vortex) and static (potential) field characteristics.
• To provide a theoretical foundation for potential components having physical significance beyond mathematical convenience.

Proposed method

• Formulates a total four-dimensional field theory that treats both vortex and potential components of the electromagnetic field as physically meaningful.
• Derives a system of modified Maxwell equations that include contributions from both vortex and potential parts of the field.
• Applies a unified field-theoretic approach to the electromagnetic potential and vector potential, avoiding reliance on gauge-fixing conditions.
• Analyzes existing literature and identifies works that independently arrive at similar conclusions regarding the physicality of potential components.
• Uses mathematical consistency and physical interpretation to justify the inclusion of potential components in field dynamics.
• Demonstrates that the inclusion of potential components eliminates contradictions in wave propagation models.

Experimental results

Research questions

• RQ1 Can the potential component of the magnetic field be physically meaningful rather than merely a mathematical artifact?
• RQ2 How can Maxwell's equations be generalized to include both vortex and potential components of the electromagnetic field?
• RQ3 What inconsistencies in electromagnetic wave distribution arise from excluding potential field components?
• RQ4 In what way do gauge conditions like Coulomb and Lorenz gauges obscure physical field behavior?
• RQ5 How does a four-dimensional field theory incorporating both components improve the description of electromagnetic phenomena?

Key findings

• The potential component of the magnetic field is shown to possess physical significance, contrary to conventional treatments that dismiss it via gauge conditions.
• A generalized system of Maxwell equations is derived that includes both vortex and potential components, resolving inconsistencies in wave propagation.
• The theory demonstrates that the exclusion of potential components leads to unphysical contradictions in electromagnetic field descriptions.
• The approach provides a unified framework where both dynamic and static field components are treated on equal physical footing in four-dimensional spacetime.
• The results are consistent with findings from other independent studies, reinforcing the validity of including potential components in field theory.
• The modified field equations allow for a more complete and self-consistent description of electromagnetic phenomena, particularly in wave distribution and field dynamics.