Status: Preprint (not peer reviewed)
Author: Robert W. Harrison
Plain-English Summary
Maxwell’s equations are among the most successful in all of physics — yet after 150 years, we can calculate what electromagnetic fields do without understanding what they are. Maxwell himself believed fields were dynamics of a physical medium. The 20th century stripped that interpretation: relativity seemed to forbid a detectable medium, and quantum mechanics abstracted fields into probability amplitudes. What remained were extraordinarily effective equations with no physical ontology.
This paper restores Maxwell’s vision using modern condensed matter physics. It proposes an explicit mapping between hydrodynamic variables and electromagnetic quantities: the electric field E is identified as the pressure gradient in an effective inviscid medium, the magnetic field B is identified as the vorticity (rotational flow) of that medium, electric charge is a topological defect (quantised winding number) maintained by self-sustaining oscillation, and light is a transverse acoustic mode of a chiral superfluid vacuum.
The paper demonstrates that all four of Maxwell’s equations translate directly into standard fluid dynamics identities. Gauss’s law becomes the divergence of a pressure field around a source. Ampère’s law becomes Kelvin’s circulation theorem. Faraday’s law becomes the relationship between changing vorticity and induced pressure gradient. The absence of magnetic monopoles (∇·B = 0) becomes the geometric identity that the divergence of a curl is always zero — monopoles are not mysteriously absent but mathematically impossible in a vorticity field.
The framework addresses historical objections to medium-based models: transverse polarisation is permitted because the vacuum belongs to the ³He-A universality class (a chiral superfluid that supports transverse modes), and Lorentz invariance emerges from Fermi point topology rather than being violated by a detectable medium. The paper provides a complete translation table between hydrodynamic and electromagnetic quantities, with explicit open questions and proposed discriminating tests identified throughout.
What This Paper Claims (High Level)
- Maxwell’s equations can be explicitly mapped onto standard fluid dynamics: E = pressure gradient, B = vorticity, charge = topological winding number, current = defect transport, light = transverse acoustic mode.
- Coulomb’s law emerges from the Secondary Bjerknes Force — acoustic radiation pressure between oscillating structures in the medium — with the inverse-square law following geometrically from spherical wave spreading.
- Charge quantisation is a topological necessity: in a superfluid condensate with a single-valued phase, circulation (and thus winding number) must be integer-valued. Charge sign reflects the phase relationship of the oscillon to the background vacuum.
- Magnetic monopoles are geometrically impossible, not mysteriously absent: ∇·(∇×v) ≡ 0 is a mathematical identity for any vorticity field.
- Lorentz invariance is preserved as an emergent symmetry of quasiparticle excitations near Fermi points in the ³He-A universality class — the absolute frame exists ontologically but is operationally inaccessible to internal observers.
- The framework does not replace QED as a calculation tool but offers a candidate physical ontology: QED is reinterpreted as the effective field theory of superfluid vacuum fluctuations.
Why It Might Matter
If the mapping holds, it provides what Maxwell’s equations and QED currently lack: a physical account of what electromagnetic fields actually are. Several longstanding puzzles dissolve as geometric necessities rather than brute facts — charge quantisation from topology, monopole absence from vorticity mathematics, and the relationship between electricity and magnetism as pressure and rotation in the same medium. The paper also unifies the electromagnetic and gravitational interactions within a single hydrodynamic picture: both are Bjerknes-type forces between oscillating structures, distinguished only by phase constraints. This is a companion paper in the HQG series covering gravity, quantum mechanics, and electromagnetism as emergent phenomena of a single dynamic vacuum.
Links
PDF (this site):
DOI (Zenodo):
https://doi.org/10.5281/zenodo.18216884
Keywords / Topics
hydrodynamic electromagnetism, Maxwell’s equations, pressure gradient, vorticity, electric field, magnetic field, topological charge, winding number, charge quantisation, magnetic monopoles, Secondary Bjerknes Force, Coulomb’s law, superfluid vacuum, ³He-A universality class, Fermi point topology, emergent Lorentz invariance, non-viscous ether, gauge symmetry, phase coherence, transverse acoustic mode, QED effective theory, oscillon, zero-point field
Note: This is a technical preprint made available for discussion and critique. If you have relevant expertise and would like to comment, please reach out.