CiNii Books - Scale relativity and fractal space-time : a new approach to unifying relativity and quantum mechanics

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.

Table of Contents

General Introduction
Theory: Structure of the Theory
Nondifferentiable Fractal Space-Time
Laws of Scale Transformation
Non-Relativistic Quantum Mechanics
Relativistic Quantum Mechanics
Geometric Theory of Gauge Fields
Quantum-Like Mechanics in Scale Space
Applications: Applications to Physics
Applications to Elementary Particles
Applications to Cosmology
Applications to Gravitational Structuring
Applications to Life and Other Sciences.

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Scale relativity and fractal space-time : a new approach to unifying relativity and quantum mechanics

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