Scale relativity: From quantum mechanics to chaotic dynamics

Scale Relativity: From Quantum Mechanics to Chaotic Dynamics

Scale relativity is a new approach to the problem of the origin of fundamental scales and of scaling laws in physics, which consists in generalizing Einstein’s principle of relativity to the case of scale transformations of resolutions. We recall here how it leads one to the concept of fractal space-time, and to introduce a new complex time derivative operator which allows to recover the Schröd...

Quantum Mechanics and Relativity

In a framework of a stationary universe, time is de ned as a local and quantum-mechanical notion in the sense that it is de ned for each local and quantummechanical system consisting of a nite number of particles. In this context, the total universe consisting of an in nite number of particles has no time associated, and quantum mechanics and general theory of relativity are united consistently...

Scale Relativity, Fractal Space-Time, and Quantum Mechanics

This paper describes the present state of an attempt at understanding the quantum behaviour of microphysics in terms of a nondifferentiable space-time continuum having fractal (i.e., scale-dependent) properties. The fundamental principle upon which we rely is that of scale relativity, which generalizes to scale transformations Einstein’s principle of relativity. After having related the fractal...

Chaotic dynamics in billiards using Bohm’s quantum mechanics

Derivation of the postulates of quantum mechanics from the first principles of scale relativity

Quantum mechanics is based on a series of postulates which lead to a very good description of the microphysical realm but which have, up to now, not been derived from first principles. In the present work, we suggest such a derivation in the framework of the theory of scale relativity. After having analyzed the actual status of the various postulates, rules and principles that underlie the pres...