Theory of sounds in He II

Abstract

A dynamical model for Landau’s original approach to superfluid helium is presented, with two velocities but only one mass density. The second sound is an adiabatic perturbation that involves the temperature and the roton, aka the notoph. The action incorporates all the conservation laws, including the equation of continuity. With only 4 canonical variables it has a higher power of prediction than Landau’s later, more complicated model, with its 8 degrees of freedom. The roton is identified with the massless notoph. This theory gives a very satisfactory account of second and fourth sounds. Second sound is an adiabatic oscillation of the temperature and both vector fields, with no net material motion. Fourth sound involves the roton, the temperature, and the density. With the experimental confirmation of gravitational waves, the relations between Hydrodynamics and Relativity and particle physics have become more clear, and urgent. The appearance of the Newtonian potential in irrotational hydrodynamics comes directly from Einstein’s equations for the metric. The density factor ρ is essential; it is time to acknowledge the role that it plays in particle theory. To complete the 2-vector theory we include the massless roton mode. Although this mode too is affected by the mass density, it turns out that the wave function of the unique notoph propagating mode N satisfies the normal massless wave equation N=0; the roton propagates as a free particle in the bulk of the superfluid without meeting resistance. In this circumstance, we may have discovered the mechanism that lies behind the flow of He II through very thin pores.