Hydrodynamic Electromagnetism: Maxwell's Equations in the Superfluid Vacuum

This paper presents a comprehensive reformulation of classical electromagnetism within the framework of Superfluid Vacuum Theory. By treating the vacuum as empty space exhibiting dynamic properties mathematically identical to those of a chiral superfluid belonging to the ³He-A universality class, electromagnetic phenomena emerge naturally as the acoustics and vorticity of the vacuum. A critical clarification: this framework does not propose that space contains a substance. Space is genuinely empty. However, empty space has properties—it permits movement, carries energy, and supports wave propagation. The mathematics describing these properties is isomorphic to the mathematics of superfluid systems. The term "non-viscous ether" captures this precisely: space has dynamic properties but no drag, no resistance, no substance. Core Identifications: Electric field (E) as pressure gradient (∇P) Magnetic field (B) as vorticity (∇×v) Electric charge as topological defect (oscillon) with quantised winding number Speed of light (c) as the limiting velocity emerging from Fermi point topology Gauge invariance as phase symmetry of the condensate wavefunction Critical Objections Resolved: The paper addresses four historical objections to ether theories: (1) transverse polarisation in a fluid medium, resolved via the internal degrees of freedom of the chiral superfluid order parameter, which supports transverse modes experimentally confirmed through the Acoustic Faraday Effect in superfluid ³He-B (Avenel et al., 1995); (2) the fine structure constant α ≈ 1/137, derived from vortex wave closure conditions (Meucci, 2024—awaiting peer review and independent verification); (3) QED's 12-digit precision, reframed as effective field theory of superfluid fluctuations; (4) gauge invariance, emerging from phase symmetry of the condensate. Fundamental Mysteries Addressed: Why charge is quantised (topological necessity: circulation Γ = nh/m) Why magnetic monopoles do not exist (∇·(∇×v) ≡ 0 geometrically) Why proton and electron charges are exactly equal (same winding number, opposite phase) The electron's infinite self-energy paradox (resolved: electron is extended vortex structure) Practical Applications: The framework suggests testable engineering applications including pressure-based lightning prediction, static electricity control via separation rate, antenna efficiency beyond the Chu limit, and earthquake early warning through atmospheric field monitoring. Companion Papers: This document completes a three-paper series presenting a unified hydrodynamic framework: Harrison's Theorem of Anti-gravity — Experimental predictions and falsification criteria Hydrodynamic Quantum Gravity: Theoretical Foundations — Gravitational derivation from superfluid dynamics Hydrodynamic Electromagnetism (this paper) — Electromagnetic derivation and unification The framework does not claim to replace Quantum Electrodynamics, which remains the most precisely verified calculation scheme in physics. Rather, it proposes the physical substrate that QED describes—what electromagnetic fields actually are, not merely how they behave. Discussion and feedback: https://github.com/Gptham123456/Hydrodynamic-Quantum-Gravity/discussions