A serendipity event in 1975 led to the discovery of a complex mapping that transformed the two dimensional time dependent Schroedinger equation for a charged particle in an electromagnetic field into a complex differential equation. When the imaginary component was separated, it was exactly of the form of the Navier-Stokes vorticity equation for a compressible VISCOUS (!) fluid. Click here

The transformation was not equivalent to the Magdelung transformation that leads to a non-viscous Eulerian fluid. At that time I was not conversant with the Bohm view of quantum mechanics, and the concept of a "pilot" wave that depended upon a gradient field (or potential function). However, the complex mapping mentioned above effectively extends the Bohm approach to pilot fields that are not represented by perfect differentials. Indeed, the absolute square of the wave function, through the Navier-Stokes construction, is not a position probability, but is precisely the square of the vorticity distribution in the Navier-Stokes fluid.

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