SCALE RELATIVITY AND FRACTAL SPACE-TIME: A NEW APPROACH TO UNIFYING RELATIVITY AND QUANTUM MECHANICS

by Laurent Nottale

This book provides a comprehensive survey of the state-of-the-art in 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 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 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 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.

750 pages, Hardcover

First published February 11, 2011

Reviews

[Erickson · Rating 3 out of 5]

Did not end up reading the full thing especially the applications part (too diverse, even including QED). However, the same impression I had with his other book titled Fractal Spacetime and Microphysics - it feels like a book written over-ambitiously. For a theory that is yet mainstream and written with "Exercises" for students to do, such confidence is a little odd unless the theorist has extremely high degree of confidence towards the proposal.

While it is remarkable that the motivation behind the theory is to revive geometrodynamics, the impression I have is that the proposals made here are slightly overdoing it. But perhaps being undergraduate, I cannot fully comprehend the radical features of the theory. But one way I can say is that this proposal is not quite convincing partly because in physics there is no real fundamental crisis that screams "we need fractals!", in the sense that the way fractals are introduced are a little too ill-motivated. Path integral fractal dimension is hardly, in my opinion, sufficient to suggest fractal spacetime (Brownian motion has fractal dimension too).

Overall, a main issue of the text is clarity and overly-diverse topics. If it is to be written like a textbook, concepts and motivations should be stronger.