Scale relativity, fractal space-time and quantum mechanics

摘要: Abstract This paper describes the present state of an attempt at understanding quantum behaviour microphysics in terms a nondifferentiable space-time continuum having fractal (i.e. scale-dependent) properties. The fundamental principle upon which we rely is that scale relativity, generalizes Einstein's relativity to transformations. After related and renormalization group approaches, develop new version stochastic mechanics, correspondence Schrodinger equation are demonstrated by replacing classical time derivative ‘quantum-covariant’ derivative. Then recall leads one generalize standard ‘Galilean’ laws transformation into Lorentzian form, Planck length-scale becomes invariant under dilations, so plays for same role as played velocity light motion laws. We conclude application our framework problem mass spectrum elementary particles.