Irrotational solutions to Euler's equation for a compressible fluid

This talk is about the patterns of flow in a fluid such as the air if it had no viscosity. It is illustrated with animations and movies, and should be accessible to those without prior knowledge. We show that a compressible inviscid fluid supports structures which are similar to smoke rings, but are irrotational. They obey the same equations of motion and diffraction as natural particles, which is illustrated in movies of an experimental analogue in two dimensions, due to Couder, which show tunnelling, double-slit diffraction, and quantised energy levels. Some of the structures are chiral. Opposite chiralities attract and like chiralities repel with a force which obeys Maxwell's equations, whose strength is characterised by a fine structure constant less than approximately 1/45.