An Analog Model of Electromagnetism and Gravity from a Quaternionic Spin Fluid

This is a working draft with various problems, now uploaded so Sean Cleary and other colleagues can take a look. This paper constructs an analogue model in which the physical vacuum is a dense fluid ofgyrons with quaternionic orientation. The fluid-moment dictionary reproduces the homogeneousMaxwell equations and the electric force exactly, and the inhomogeneous Maxwell equations atleading order in the incompressible transverse regime. The orientation-velocity conservationlaw is derived from the Boltzmann equation, and the Jeffery back-reaction is shown to havethe same third-derivative structure as the Bohm potential; the reduction to a Schrödinger formfollows on a surface in parameter space, with the spherical-harmonic structure of bound statesand the photoelectric effect as consequences. The orientation-pressure wave is identified asthe model’s neutrino sector, with reconnection as the production mechanism; the Goldhaberhelicity is addressed and the oscillation data are acknowledged as a failure. A speculativeextension assigns the observed particles to knotted and linked configurations of the orientationfield, with the charge assignments, the stability hierarchy, and the mass tuning stated as aresearch program. The gravitational sector reproduces the Newtonian limit; the relativisticextension is open. Cosmology is out of scope. The paper states throughout what is derived,what is assumed, what is speculated, and what is open.