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Author: Laurent Nottale Publisher: World Scientific ISBN: 9789810208783 Category : Science Languages : en Pages : 358
Book Description
This is the first detailed account of a new approach to microphysics based on two leading ideas: (i) the explicit dependence of physical laws on scale encountered in quantum physics, is the manifestation of a fundamental principle of nature, scale relativity. This generalizes Einstein's principle of (motion) relativity to scale transformations; (ii) the mathematical achievement of this principle needs the introduction of a nondifferentiable space-time varying with resolution, i.e. characterized by its fractal properties.The author discusses in detail reactualization of the principle of relativity and its application to scale transformations, physical laws which are explicitly scale dependent, and fractals as a new geometric description of space-time.
Author: Laurent Nottale Publisher: World Scientific ISBN: 9789810208783 Category : Science Languages : en Pages : 358
Book Description
This is the first detailed account of a new approach to microphysics based on two leading ideas: (i) the explicit dependence of physical laws on scale encountered in quantum physics, is the manifestation of a fundamental principle of nature, scale relativity. This generalizes Einstein's principle of (motion) relativity to scale transformations; (ii) the mathematical achievement of this principle needs the introduction of a nondifferentiable space-time varying with resolution, i.e. characterized by its fractal properties.The author discusses in detail reactualization of the principle of relativity and its application to scale transformations, physical laws which are explicitly scale dependent, and fractals as a new geometric description of space-time.
Author: Laurent Nottale Publisher: World Scientific ISBN: 9814520217 Category : Science Languages : en Pages : 349
Book Description
This is the first detailed account of a new approach to microphysics based on two leading ideas: (i) the explicit dependence of physical laws on scale encountered in quantum physics, is the manifestation of a fundamental principle of nature, scale relativity. This generalizes Einstein's principle of (motion) relativity to scale transformations; (ii) the mathematical achievement of this principle needs the introduction of a nondifferentiable space-time varying with resolution, i.e. characterized by its fractal properties.The author discusses in detail reactualization of the principle of relativity and its application to scale transformations, physical laws which are explicitly scale dependent, and fractals as a new geometric description of space-time.
Author: Laurent Nottale Publisher: World Scientific ISBN: 1848166508 Category : Science Languages : en Pages : 766
Book Description
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.
Author: B. Dubrulle Publisher: Springer Science & Business Media ISBN: 3662097990 Category : Science Languages : en Pages : 291
Book Description
This book is an excellent introduction to the concept of scale invariance, which is a growing field of research with wide applications. It describes where and how symmetry under scale transformation (and its various forms of partial breakdown) can be used to analyze solutions of a problem without the need to explicitly solve it. The first part gives descriptions of tools and concepts; the second is devoted to recent attempts to go beyond the invariance or symmetry breaking, to discuss causes and consequences, and to extract useful information about the system. Examples are carefully worked out in fields as diverse as condensed matter physics, population dynamics, earthquake physics, turbulence, cosmology and finance.
Author: P. J. E. Peebles Publisher: Princeton University Press ISBN: 0691209839 Category : Science Languages : en Pages : 439
Book Description
The classic account of the structure and evolution of the early universe from Nobel Prize–winning physicist P. J. E. Peebles An instant landmark on its publication, The Large-Scale Structure of the Universe remains the essential introduction to this vital area of research. Written by one of the world's most esteemed theoretical cosmologists, it provides an invaluable historical introduction to the subject, and an enduring overview of key methods, statistical measures, and techniques for dealing with cosmic evolution. With characteristic clarity and insight, P. J. E. Peebles focuses on the largest known structures—galaxy clusters—weighing the empirical evidence of the nature of clustering and the theories of how it evolves in an expanding universe. A must-have reference for students and researchers alike, this edition of The Large-Scale Structure of the Universe introduces a new generation of readers to a classic text in modern cosmology.
Author: Laurent Nottale Publisher: ISBN: 9780578456508 Category : Languages : en Pages : 372
Book Description
Translated into English for the first time, this brilliant French bestseller by eminent astrophysicist Laurent Nottale presents the theory of scale relativity, which offers a framework for the unification of quantum theory and relativity through fractal geometry. Updated and revised, with a new afterword by philosopher of science Charles Alunni, The Relativity of All Things is the first of Nottale's popularly accessible works available to English-language readers."To describe the ideas of relativity and quantum mechanics without a single mathematical formula is a veritable feat of magic. . . . With a philosophical audacity that only non-philosophers can possess, Nottale finds that the essence of the principle of relativity is in fact the affirmation of the existence of universal laws applied at every scale. . . . His task is enormous. He proposes that the theory of relativity and that of quantum mechanics, with the radical schism between their findings and methods of thinking, can be reconciled. . . . Nottale's methodological innovation is truly revolutionary. To bring it to fruition, he weds the mathematics of fractals with the theory of relativity. . . . Nottale's approach shows us that we are far from the 'end of science': we are perhaps only at its recommencement." Basarab Nicolescu, Business Digest"Einstein himself explicitly considered that a realistic approach to the quantum problem could go through the introduction of non-differentiability in physics. In 1948, he wrote in a letter to Wolfgang Pauli: 'Maybe someone will find out another possibility, provided he searches with enough perseverance.' Laurent Nottale is very precisely this 'someone'! Read and study this wonderful theory, let yourself be carried away by its beauty, its depth, and its major experimental implications, which are nothing less than fundamental for the future of science, and for philosophy." Charles Alunni, Director, Laboratoire Disciplinaire Pensée des Sciences at the École Normale Supérieure"Since the birth of quantum theory, physicists have been challenged with the development of a unified theory of quantum mechanics and relativity, with no general consensus on the best way forward. To progress further, we have to confront deep questions about space and time, quantum theory, and cosmology, which take theory back into contact with experiment. The theory of scale relativity offers a serious contribution to the debate on unification, offering an intuitive insight into how these theories could be fundamentally linked through space-time geometry." Philip Turner, Director, Centre for Plant Science and Biopolymer Research, Edinburgh Napier University"Laurent Nottale proposes that we look at the concept of fractals to make relativity, extended further yet, the fundamental principle on which to base quantum mechanics. After the relativity of time and space, he has tackled the relativity of scale, putting into question much of what we thought we knew." Pierre Bonnaure, Futuribles"Developments in geometry have often enabled progress in physics, especially when concerning relativity. Non-Euclidean geometry, geometrical systems where the plane is a sphere, made it possible for Einstein to devise his theory of curved space. Today, a new geometry, fractal geometry, allows us to propose a theory of fractal space." Idées clés, by Business Digest
Author: Viatcheslav Mukhanov Publisher: Cambridge University Press ISBN: 1139447114 Category : Science Languages : en Pages : 454
Book Description
Inflationary cosmology has been developed over the last twenty years to remedy serious shortcomings in the standard hot big bang model of the universe. This textbook, first published in 2005, explains the basis of modern cosmology and shows where the theoretical results come from. The book is divided into two parts; the first deals with the homogeneous and isotropic model of the Universe, the second part discusses how inhomogeneities can explain its structure. Established material such as the inflation and quantum cosmological perturbation are presented in great detail, however the reader is brought to the frontiers of current cosmological research by the discussion of more speculative ideas. An ideal textbook for both advanced students of physics and astrophysics, all of the necessary background material is included in every chapter and no prior knowledge of general relativity and quantum field theory is assumed.
Author: Patrice Abry Publisher: John Wiley & Sons ISBN: 1118622901 Category : Mathematics Languages : en Pages : 382
Book Description
Scaling is a mathematical transformation that enlarges or diminishes objects. The technique is used in a variety of areas, including finance and image processing. This book is organized around the notions of scaling phenomena and scale invariance. The various stochastic models commonly used to describe scaling — self-similarity, long-range dependence and multi-fractals — are introduced. These models are compared and related to one another. Next, fractional integration, a mathematical tool closely related to the notion of scale invariance, is discussed, and stochastic processes with prescribed scaling properties (self-similar processes, locally self-similar processes, fractionally filtered processes, iterated function systems) are defined. A number of applications where the scaling paradigm proved fruitful are detailed: image processing, financial and stock market fluctuations, geophysics, scale relativity, and fractal time-space.
Author: M.M. Novak Publisher: CRC Press ISBN: 9780412710209 Category : Mathematics Languages : en Pages : 414
Book Description
This book contains state of the art contributions to this rapidly growing research area. It will be of essential value to mathematicians, physicists and engineers working in the fields of fractals and related phenomena and to researchers working in medicine and the life sciences.
Author: Laurent Nottale
Author: Laurent Nottale
Author: Laurent Nottale
Author: Laurent Nottale
Author: Laurent Nottale
Author: B. Dubrulle
Author: P. J. E. Peebles
Author: Laurent Nottale
Author: Viatcheslav Mukhanov
Author: Patrice Abry
Author: M.M. Novak