Scale Relativity And Fractal Space-time: A New Approach To Unifying Relativity And Quantum Mechanics A New Approach to Unifying Relativity and Quantum Mechanics

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 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. Pt. I. General Introduction -- Pt. Ii. Theory. 1. Introduction. 2. Structure Of The Theory. 3. Nondifferentiable Geometry And Fractal Space-time. 4. Laws Of Scale Transformations. 5. From Fractal Space To Non-relativistic Quantum Mechanics. 6. From Fractal Space-time To Relativistic Quantum Mechanics. 7. Geometric Theory Of Gauge Fields In Scale Relativity. 8. Quantum-type Mechanics In Scale Space -- Pt. Iii. Applications. 9. Introductions. 10. Applications To Laboratory And Earth Scale Physics. 11. Applications To Elementary Particle And High Energy Physics. 12. Applications To Cosmology. 13. Applications To Gravitational Structuring In Astrophysics. 14. Applications To Life Sciences And Other Sciences. 15. General Conclusion. Laurent Nottale. 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... Abstract: Presents a comprehensive survey of the development of the theory of scale relativity and fractal space-time. Read more... 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. Nottale (Paris-Meudon Observatory) discusses the current status in the development of the theory of the relativity of scales, which he first presented in his 1993 Fractal Space-Time and Microphysics: Towards a Theory of Scale Relativity. The theory has been developed and extended, he says, and applications have been proposed in various sciences. In many cases, theoretical predictions have now been put to the test with positive results on new experimental and development results. Among the topics are the structure of the theory, the geometric theory of gauge fields in scale relativity, and applications in gravitational structuring in astrophysics. Distributed in the US by World Scientific. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com) Content: General Introduction Theory: Structure of the Theory Nondifferentiable Fractal Space-Time Laws of Scale Transformation Non-Relativistic Quantum Mechanics Relativistic Quantum Mechanics Geometric Theory of Gauge Fields Quantum-Like Mechanics in Scale Space Applications: Applications to Physics Applications to Elementary Particles Applications to Cosmology Applications to Gravitational Structuring Applications to Life and Other Sciences.