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.
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