An Extension of Bohm's Quantum Theory to include Non-gradient Potentials and the Production of Nanometer Vortices.

An exact complex mapping of the wave function has been found, which, when followed by a separation into real and imaginary parts, transforms the two dimen-sional Schroedinger equation for a charged particle interacting with an electro-magnetic field into two partial differential systems. The first partial differential system is exactly the evolutionary equation for the vorticity of a compressible, viscous two dimensional Navier-Stokes fluid. The second system is related to the Beltrami equation defining a minimal surface in terms of the kinetic and potential energy. The absolute square of the wave function is exactly the vorticity distribu-tion (including topological vorticity defects) in a fluid with a viscosity coefficient, º = h=2m0. Alternately, there is a minimum viscosity defined in terms of the mass of the electron, º0 = h=2m: This cohomological, but classical, interpre-tation of the wave function offers an alternative to the Copenhagen dogma. The vorticity distribution replaces the Bohm quantum potential. The velocity field of the viscous compressible fluid acts as the Bohmian guiding °ow to the "wave function". The second system of equations relates geometrical properties of the Bohmian Potential to energy densities in the fluid. The relationship of geometry to energy (in spirit equivalent to the Einstein ansatz,Gº = T º) comes out directly from the mapping and the separation into real and imaginary parts. In effect, the Bohmian Eulerian fluid has been mapped into a Bohmian Navier Stokes fluid, with dissipation, and the production of nanometer vortices