This is the first detailed account of a new approach to microphysics based on two leading ideas: that the explicit dependence of physical laws on scale encountered in quantum physics, is the manifestation of a fundamental principle of nature, namely, scale relativity (this generalizes Einstein's principle of (motion) relativity to scale transformations); and that the mathematical achievement of this principle needs the introduction of a nondifferentiable space-time varying with resolution, i.e. characterized by its fractal properties. The author discusses in detail reactualization of the principle of relativity and its application to scale transformations, physical laws which are explicitly scale dependent, and fractals as a new geometric description of space-time.
Author(s): Nottale, Laurent
Publisher: World Scientific
Year: 1993
Language: English
Pages: 333
City: River Edge, NJ, Singapore
Tags: Relativity Physics Quantum theory Scaling laws Statistical physics Fractals Relativité Physique Théorie quantique Lois d échelle statistique Fractales Quantenphysik Raum Zeit Fraktal
1. General introduction
2. Relativity and quantum physics
On the present state of fundamental physics
The need for a new extension of the principle of relativity
Relativity of scales
On the nature of quantum space-time
3. From fractal objects to fractal space-time
Basics of fractals
Where do fractals come from?
Fractal curves in a plane
Non-standard analysis and fractals
Fractal curves in space
Fractal surfaces
Fractal derivative
Fractal functions
Variable fractal dimension
Toward the definition of a fractal space-time
4. Fractal dimension of a quantum path
Introduction
Fractal dimension of a nonrelativistic quantum path
Fractal dimension of a quantum relativistic path
Fractal dimension of time
5. The fractal structure of quantum space-time
On quantum properties ofractals
Derivation of Heisenberg's relation in fractal space-time
Classical quantities as fractal structures
Emergence of spin from fractalization
Geodesical interpretation of wave-particle duality
Non-differentiable space and stochastic quantum mechanics
Classical-quantum transformation
Microscopic reversibility of fractal time
Fractals and quantum electrodynamics
Possible observable implications
Link to general relativity
6. Towards a special theory of scale relativity
Principle of scale relativity
Masses, charges and renormalization group
Galilean scale relativity
A new derivation of Lorentz transformation
Lorentzian scale transformation
Breaking of scale relativity
On the nature of the Planck scale
The new scale-relativistic transformation
Scale-relativistic mechanics
Implications for high-energy physics
On the nature of charges and masses
