Reconstruction of Maxwell's Equations in the Light String Field——Based on the First-Principle Unified Theory of Light Strings

The classical Maxwell's equations unify the macroscopic laws of electricity, magnetism and light with an extremely high mathematical form, and are the core cornerstone of modern electromagnetism. However, this system of equations has three layers of underlying deficiencies in physical ontology: First, it relies on "electric charge" as a primitive fundamental entity and cannot trace the origin of electric charge; Second, the vacuum permittivity and permeability are phenomenological empirical constants without underlying physical mechanism support; Third, it only mathematically derives that the speed of electromagnetic waves equals the speed of light, but cannot explain the essential reason for their homology.Based strictly on the established axiom system of the first-principle unified theory of light strings, this paper completes the full reconstruction of the original form of Maxwell's equations in the light string field without introducing new physical assumptions, additional free parameters, or logical jumps. Taking the core viewpoints that electric field = steady-state density gradient potential difference of the light string field and magnetic field = directional vortex perturbation of the light string field, this paper completely eliminates the independent entity concepts of electric charge and electric current, reduces all phenomenological constants of electromagnetism to derived quantities of the light string field's ground-state density, field rigidity, anti-elastic modulus, and elastic coupling constant. It rigorously derives the origin of the speed of light in the light string field, proving that the propagation speed of electromagnetic waves is the inherent perturbation conduction speed of the light string field. Meanwhile, it completes the self-consistent verification of the degradation of classical Maxwell's equations under the light string field framework, realizing the underlying homologous closed loop between classical electrodynamics and the unified field theory of light strings.