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

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.