This paper mentions that vortices in a 2d system of phases end up acting like particles that obey a 1/r force law, which is so cool to me. Instead of thinking 'vortices act like particles' I prefer 'whoa, particles act like vortices'. Electrons and positrons annihilate when they meet in much the same way that a vortex plus an antivortex do (except they give off photons, so maybe they're just 'more complicated' vortices in some way?).
A version of this viewpoint is basically standard in modern particle physics, where quantum field theory is used to describe electrons and positrons as excitations of the electron field. (However, nothing in the QFT description treats electrons & positrons as vortex-like, so don't get too excited about the swirling..)
In fact, treating particles like vortices and vice versa is a good analogy that can be made more precise with an idea called particle-vortex duality. The basic idea is that you make a change of variables so that the vortices of the old variables become the particles of the new variables and vice-versa.
there's some crank out there with a "vortex theory of the universe". But from you description it seems like vortex is a subset of particles (but not the other way) because there are plenty of particles that don't obey 1/r force laws. Moreover, extending vortices to three dimensions is tricky, due to the hairy ball theorem.
The 1/r thing is just emergent from it being a 2d space, since the surface area of a 2d ball goes as 'r', a divergenceless field goes as 1/r (since the flux through any contour around the particle ought to be constant). In 3d this would correspond to 1/r^2.
The hairy ball theorem is an interesting point. Maybe to equate particles with vortices we have to work in 4d spacetime, since that theorem only applies to even-dimensional spheres?
