The scale-relativity program

DOI10.1016/S0960-0779(98)00195-7zbMath0997.81526MaRDI QIDQ1610022

Laurent Nottale

Publication date: 18 August 2002

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

zbMATH Keywords

Schrödinger equationfractalprinciple of relativitymethod of entropy maximizationmetric formsspace-time differentiability

Mathematics Subject Classification ID

Foundations, quantum information and its processing, quantum axioms, and philosophy (81P99) Relativistic gravitational theories other than Einstein's, including asymmetric field theories (83D05) Fractals (28A80)

Related Items (17)

Quantum derivatives and the Schrödinger equation ⋮ Analysis of the equilibrium positions of nonlinear dynamical systems in the presence of coarse-graining disturbance in space ⋮ The Minkowski's space-time is consistent with differential geometry of fractional order ⋮ From Lagrangian mechanics fractal in space to space fractal Schrödinger's equation via fractional Taylor's series ⋮ Fractional-moment capital asset pricing model ⋮ Scale-relativistic cosmology. ⋮ Fractional partial differential equations and modified Riemann-Liouville derivative new methods for solution ⋮ Lagrangian mechanics of fractional order, Hamilton-Jacobi fractional PDE and Taylor's series of nondifferentiable functions ⋮ On the quantum potential ⋮ Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable. functions. Further results ⋮ Chaotic motion in classical fluids with scale relativistic methods ⋮ Scale relativity and fractal space-time: theory and applications ⋮ Non-differentiable embedding of Lagrangian systems and partial differential equations ⋮ Generalized Euler-Lagrange equations for variational problems with scale derivatives ⋮ Nondifferentiable variational principles in terms of a quantum operator ⋮ On the unification of the fundamental forces and complex time in the \(\mathcal E^{(\infty)}\) space. ⋮ A non-differentiable Noether's theorem

Cites Work

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• Scale relativity and fractal space-time: applications to quantum physics, cosmology and chaotic systems.
• Schrödinger's equation and discrete random walks in a potential field
• Penrose universe and Cantorian spacetime as a model for noncommutative quantum geometry
• Scale relativity and quantization of planet obliquities
• ``Scale covariant representation of quantum mechanics. Energy in scale-relativity theory.
• Numerical simulation of a quantum particle in a box
• THE THEORY OF SCALE RELATIVITY

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