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Implications of scale relativity in gravitational and electromagnetic field theory. (English) Zbl 1231.83028

Summary: A non-differentiable mechanical model (an alternative to Nottale’s Scale Relativity Theory) considering that the particles movements takes place on Peano fractal curves is built. A Navier-Stokes type equation with an imaginary viscosity coefficient for a complex speed field, a Schrödinger-type equation and a hydrodynamic version of the non-differentiable mechanical model are obtained. The one body problem and the red-shift quantization in binary galaxies are investigated as an application.

MSC:

83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
81Q50 Quantum chaos