Nottale L. Scale Relativity And Fractal Space-Time: A New Approach to Unifying Relativity and Quantum Mechanics

Imperial College Press, 2011. — 742 p. — ISBN10: 1848166508.This book provides a comprehensive survey of the development of the theory of scale relativity and fractal space-time. It suggests an original solution to the disunified nature of the classical-quantum transition in physical systems, enabling the basis of quantum mechanics on the principle of relativity, provided this principle is extended to scale transformations of the reference system. In the framework of such a newly generalized relativity theory (including position, orientation, motion and now scale transformations), the fundamental laws of physics may be given a general form that unifies and thus goes beyond the classical and quantum regimes taken separately. A related concern of this book is the geometry of space-time, which is described as being fractal and nondifferentiable. It collects and organizes theoretical developments and applications in many fields, including physics, mathematics, astrophysics, cosmology and life sciences.General IntroductionTheoryStructure of the Theory
Nondifferentiable Geometry and Fractal Space-Time
Laws of Scale Transformations
From Fractal Space to Non-Relativistic Quantum Mechanics
From Fractal Space-Time to Relativistic Quantum Mechanics
Geometric Theory of Gauge Fields in Scale Relativity
Quantum-type Mechanics in Scale SpaceApplicationsApplications to Laboratory and Earth Scale Physics
Applications to Elementary Particle and High Energy Physics
Applications to Cosmology
Applications to Gravitational Structuring in Astrophysics
Applications to Life Sciences and Other Sciences
General Conclusion