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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. Contents:General IntroductionTheory:IntroductionStructure of the TheoryNondifferentiable Geometry and Fractal Space-TimeLaws of Scale TransformationsFrom Fractal Space to Non-Relativistic Quantum MechanicsFrom Fractal Space-Time to Relativistic Quantum MechanicsGeometric Theory of Gauge Fields in Scale RelativityQuantum-type Mechanics in Scale SpaceApplications:IntroductionApplications to Laboratory and Earth Scale PhysicsApplications to Elementary Particle and High Energy PhysicsApplications to CosmologyApplications to Gravitational Structuring in AstrophysicsApplications to Life Sciences and Other Sciences Readership: Academics, post-graduates and professionals interested in astrophysics and cosmology. Keywords:Scale Relativity;Fractals;Quantum Mechanics;Space-Time GeometryKey Features:No competing title: it describes the state-of-the art of the theory of scale relativity and of its applications to various sciences by its founderApplications of the theory to various branches of physical science, including elementary particle physics, cosmology, and life sciences, are presented in detail in individual chaptersReviews:“The sweep of this book is enormous. It has implications for every aspect of physics. But it also has important implications for biological science. Systems Biology is multi-scale since integration of function can occur at many different levels from genes to whole organisms and populations in what some of us have called a principle of biological relativity. Could scale relativity provide the framework for systematizing that principle? Models at different levels could be seen to be working with different scale resolutions, or even scale dimensions. The prospect is tantalising and forms a major challenge to mathematical systems biologists. Those who would welcome that challenge will need to read this book.”Denis Noble, FRS Oxford University author of The Music of Life “Scale Relativity seeks to refine our understanding of the nature of space itself. Extended to its natural limits, it has the potential to unify the description of phenomena one associates with Quantum Mechanics, Biology and even Astrophysics and Cosmology.”Jean-Patrick Connerade Emeritus Professor and Distinguished Research Fellow Imperial College London President of the European Academy of Science, Arts and Literature “This is a rich and lovely book. The elegant approach to unifying many concepts in physics provides new ways of seeing things — some things we know in new ways and some very new ideas. It is also exciting to see some conceptual tools for thinking about problems as complex as those we face in understanding biological systems.”David J Galas Professor and Senior Vice President Institute for Systems Biology “Nottale's new book, from the first paragraph to the last section, is a bold, courageous and thoughtful work that addresses this problem directly through the paradigm of scale relativity. The book contains a wealth of insight to accompany an astonishing collection of numerical data from many scales of observation. Nottale has succeeded in going beyond the limitations inherent in conventional differential approaches to produce a convincing picture of scale-dependent physics. The book is a must-read for any scientist contemplating bridging the gap between the large and small-scale approximations of modern physics.”Garnet Ord Ryerson University
