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Wave-Particle Duality through a Hydrodynamic Model of the Fractal Space-Time Theory

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Agop M., Nica P., Harabagiu A.

Acta Physica Polonica A

2008

vol. 113

issue 6

1571-1588

Considering that the microparticle movements take place on fractal curves, the wave-particle duality is studied in the fractal space-time theory (scale relativity theory). The Nottale model was extended by assuming arbitrary fractal dimension, D_F, of the fractal curves and third-order terms in the equation of motion of a complex speed field. It results that, in a fractal fluid, the convection, dissipation, and dispersion are reciprocally compensating at any scale (differentiable or non-differentiable), whereas a generalized Schrödinger equation is obtained for an irrotational movement of the fractal fluid. The absence of the dispersion implies a generalized Navier-Stokes type equation and the usual Schrödinger equation results for the irrotational movement in D_F=2 of the fractal fluid. The absence of dissipation implies a generalized Korteweg-de Vries type equation. In such conjecture, the duality is analyzed through a hydrodynamic formulation. At the differentiable scale, the duality is achieved by the flowing regimes of the fractal fluid, while at the non-differentiable scale, a fractal potential controls, through the coherence, the duality.

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1 Acta Physica Polonica A

1 2008

1 Agop M.

1 Harabagiu A.

1 Nica P.

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Wave-Particle Duality through a Hydrodynamic Model of the Fractal Space-Time Theory