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 |