where ρ ρ is the mass density of the fluid and v is its velocity (also the group velocity of the wave). In the classical limit, we can associate the velocity with ∇ ∇ S m , which is the same as equating ∇ S with the classical momentum p = m v however, it does not represent a physical velocity or momentum at a point since simultaneous measurement of position and velocity violates uncertainty principle. This interpretation fits with Hamilton–Jacobi theory, in which p = ∇ ∇ S in Cartesian coordinates is given by ∇ S, where S is Hamilton's principal function.