ABSTRACT
After the fundamental works of Erwin Schrödinger, Erwin Madelung came up with a physical interpretation of the wave function, from the point of view of the classical fluids’ dynamics. This chapter is concerned with Madelung’s physical interpretation. The Madelung fluid is one case illustrating how “the forces detemine the velocities”, however at a different level of statistics. The “complex phase” of the wave function is the mark of the solution of nonstationary equation. However, his justification for the existence of the essentially complex wave function can be recognized only as anecdotal. The nonstationary Schrödinger equation admits, besides the classical Galilei group proper, an extra set of symmetries that can be taken in a form involving just one space dimension and time. The Maxwellian form of electrodynamics shows that, as long as the time is classically considered i.e. as just a parameter of continuity this concept of local does not require any further consideration beyond in a given space position.
