The Theory of Scale Relativity

This book provides a comprehensive survey of the state-of-the-art in the development of the relativity theory of scales. This theory suggests an original solution to the disunified nature of the classical-quantum transition in physical systems, enabling quantum mechanics to be based 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 scale transformations), the fundamental laws of physics may be given a general form that transcends and integrates the classical and the quantum regimes. A related concern of this book is the geometry of space-time, particularly at small scales.
By collecting and organizing developments and applications from diverse fields, it is hoped that this monograph will serve as a reference for graduate students and researchers interested in the foundations of physics, quantum mechanics, astronomy, cosmology, the life sciences, self-organization processes, and scale-dependent phenomena. Prerequisites are limited to a basic knowledge of classical and quantum mechanics, special and general relativity, and fluid mechanics.

Table of contents:

Preface.- Part I: Theory.- Introduction.- Structure of the Theory.- From Non-differentiability to Fractality.- Scale Laws.- Fractal Space and Induced Quantum Mechanics.- Fractal Space-time and Relativistic Quantum Mechanics.- Gauge Theories and Scale Relativity.- Quantum Mechanics in Scale-Space.- Part II: Applications to Physics.- Application to Elementary Particle and High Energy Physics.- Application to Gravitational Structuring.- Application to Cosmology.- Part III: Applications to Social and Life Sciences.- Application of Scale Laws to Sciences of Life.- Application of Generalized Quantum Laws to Sciences of Life.- Application of New Quantum Mechanics in Scale-Space.- Future Prospects.- Conclusion.- References.- Index.