Scale relativity and fractal space-time: a new approach to unifying relativity and quantum mechanics

Description

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.  Read more... Note continued: 13.2.2.Generalized theory of gravitation -- 13.3.Theoretical Predictions -- 13.3.1.Kepler potential -- 13.3.2.Constant density: harmonic oscillator potential -- 13.3.3.Matching of potentials -- 13.3.4.Application to gravitational structuring in cosmology -- 13.3.5.Ejection process -- 13.3.6.Theoretical expectation of the gravitational coupling -- 13.4.Solar System -- 13.4.1.Planetary system formation -- 13.4.2.Planetary distances -- 13.4.3.Satellites and rings -- 13.4.4.Planetary mass distribution according to distance -- 13.4.5.Intramercurial structures -- 13.4.6.Trans-Neptunian structures: Kuiper belt -- 13.4.7.Sedna and the very distant Kuiper belt -- 13.4.8.Obliquities and inclinations of planets and satellites -- 13.4.9.Space debris around the Earth -- 13.5.Extrasolar Planetary Systems -- 13.5.1.Semi-major axis -- 13.5.2.Eccentricity -- 13.5.3.Planetary system around the pulsar PSR 1257+12 -- 13.6.Galactic Structures -- 13.6.1.Star formation -- 13.6.2.Binary stars -- 13.6.3.High-velocity clouds -- 13.6.4.Proper motion near the Galactic center -- 13.7.Planetary Nebulae -- 13.7.1.Elementary morphologies -- 13.7.2.Quantized shapes -- 13.7.3.Comparison with observations -- 13.8.Extragalactic Structures -- 13.8.1."Dark matter" problem -- 13.8.2.Flat rotation curves of spiral galaxies -- 13.8.3.Compact groups -- 13.8.4.Galaxy pairs -- 13.8.5.Local group of galaxies -- 13.8.6.Clusters of galaxies -- 13.8.7.Local Supercluster -- 13.8.8.Very large scale structures -- 14.Applications to Life Sciences and Other Sciences -- 14.1.Fractals in Biology -- 14.2.Applications of Log-Periodic Laws -- 14.2.1.Species evolution -- 14.2.2.Embryogenesis and human development -- 14.2.3.Evolution of societies -- 14.2.4.History and geography -- 14.2.5.Geosciences -- 14.2.6.Predictivity -- 14.3.Applications of Scale Relativity to Biology -- 14.3.1.Confinement -- 14.3.2.Morphogenesis -- 14.3.3.Origin of life: a new approach? -- 14.3.4.Duplication -- 14.3.5.Bifurcation, branching process -- 14.3.6.Nature of first evolutionary leaps -- 14.3.7.Origin of the genetic code: possible new hints -- 14.3.8.Systems biology and multiscale integration -- 15.General Conclusion