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This book provides a comprehensive survey of the stateoftheart in the development of the theory of scale relativity and fractal spacetime. It suggests an original solution to the disunified nature of the classicalquantum 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 newlygeneralized relativity theory (including position, orientation, motion and now scale transformations), the fundamental laws of physics may be given a general form that goes beyond and integrates the classical and the quantum regimes. A related concern of this book is the geometry of spacetime, 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.
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