Electromagnetism from relativistic fluid dynamics

Abstract: We present a matter-space framework characterizing particles and establish its compatibility with electromagnetism. In this approach, matter, such as photons, is considered to reside in a three-dimensional matter space, with the electromagnetic fields observed in four-dimensional spacetime interpreted as projections from this space. By imposing gauge symmetry through constraint equations, we derive the relationship between the vector field $A_a$ and the antisymmetric tensor $F_{ab}$, forming part of Maxwell's equations. The remaining Maxwell equation is obtained through the action principle in relativistic fluid dynamics. Notably, we demonstrate that this imposition of the gauge symmetry and constraints develop the dynamics. This framework offers a fresh perspective on particle-field interactions and deepens the theoretical foundation of relativistic fluid dynamics.