A vortex atomic model based on classical fluid mechanics

Lord Kelvin's vortex atomic model is revived: A vortex ring is regarded as an 'atom,' solitons propagating on the vortex ring are as 'electrons,' and acoustic wave is as 'electromagnetic wave.' In order to theoretically investigate the behavior of a vortex atom in an external field, we attempt to utilize two kinds of analogies among three classical theories of fields; fluid mechanics, electrodynamics and thermodynamics. The first analogy, which connects fluid mechanics and electrodynamics under the concept of gauge invariance, leads to the electrodynamical description of a vortex atom. It is based on the postulation of 'wave function' which will interact with a fluid mechanical 'gauge field,' the same as the wave function of electrons interacting with an electrodynamical gauge field, but the identification of the wave function remains uncertain. On the other hand, the second analogy, which connects fluid mechanics and thermodynamics under the concept of an irreversible path integral, leads to the thermodynamical description of a vortex atom. It is derived directly from classical fluid mechanics and suggests that the transformations with respect to fluid mechanical 'entropy' and 'temperature' may respectively correspond to the gauge and Lorentz transformations in modern physics.