Cantorian ε(∞) space-time, a hydrodynamical model and unified superconductivity

We prove that the fractal space-time interpretation of Nelson’s stochastic quantum mechanics may be put into a one-to-one correspondence to the hydrodynamic model of quantum mechanics. Some implications of this correspondence are analyzed: Navier–Stokes type equations, uncertainty relation and type II superconductivity by means of a higher-dimensional fractal string. The two-dimensional (2D) projections of the higher fractal string corresponds to the anyons and 1D projections to the Cooper pair. The Cantorian-fractal structures occur, either by assimilating the Cooper pair with a two coupled oscillators (a simple mechanical model for ε(∞) theory), or by El Naschie’s filling factor ν≡φ3=0.23606 (Cantorian-fractal quantum Hall effect).