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Author: Laurent Nottale
Publisher: World Scientific
ISBN: 1848166508
Category : Science
Languages : en
Pages : 766
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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: Laurent Nottale
Publisher: World Scientific
ISBN: 1848166508
Category : Science
Languages : en
Pages : 766
Get Book Here
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: Nicolae Mazilu
Publisher: CRC Press
ISBN: 1000751260
Category : Science
Languages : en
Pages : 171
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Book Description
The Mathematical Principles of Scale Relativity Physics: The Concept of Interpretation explores and builds upon the principles of Laurent Nottale’s scale relativity. The authors address a variety of problems encountered by researchers studying the dynamics of physical systems. It explores Madelung fluid from a wave mechanics point of view, showing that confinement and asymptotic freedom are the fundamental laws of modern natural philosophy. It then probes Nottale’s scale transition description, offering a sound mathematical principle based on continuous group theory. The book provides a comprehensive overview of the matter to the reader via a generalization of relativity, a theory of colors, and classical electrodynamics. Key Features: Develops the concept of scale relativity interpreted according to its initial definition enticed by the birth of wave and quantum mechanics Provides the fundamental equations necessary for interpretation of matter, describing the ensembles of free particles according to the concepts of confinement and asymptotic freedom Establishes a natural connection between the Newtonian forces and the Planck’s law from the point of view of space and time scale transition: both are expressions of invariance to scale transition The work will be of great interest to graduate students, doctoral candidates, and academic researchers working in mathematics and physics.
Author: Laurent Nottale
Publisher: World Scientific
ISBN: 9789810208783
Category : Science
Languages : en
Pages : 358
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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: S. W. Hawking
Publisher: Cambridge University Press
ISBN: 1139810952
Category : Science
Languages : en
Pages : 406
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Book Description
Einstein's General Theory of Relativity leads to two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational collapse and to disappear from view, leaving behind a 'black hole' in space; and secondly, that there will exist singularities in space-time itself. These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large. Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions. A discussion of the Cauchy problem for General Relativity is also included in this 1973 book.
Author: Moshe Carmeli
Publisher: World Scientific
ISBN: 9810249365
Category : Science
Languages : en
Pages : 225
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Book Description
This book presents Einstein's theory of space and time in detail, and describes the large-scale structure of space, time and velocity as a new cosmological special relativity. A cosmological Lorentz-like transformation, which relates events at different cosmic times, is derived and applied. A new law of addition of cosmic times is obtained, and the inflation of the space at the early universe is derived, both from the cosmological transformation. The relationship between cosmic velocity, acceleration and distances is given. In the appendices gravitation is added in the form of a cosmological general relativity theory and a five-dimensional unified theory of space, time and velocity. This book is of interest to cosmologists, astrophysicists, theoretical physicists, mathematical physicists and mathematicians.
Author: B. Dubrulle
Publisher: Springer Science & Business Media
ISBN: 3662097990
Category : Science
Languages : en
Pages : 291
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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: Susie Vrobel
Publisher: World Scientific
ISBN: 9812792422
Category : Mathematics
Languages : en
Pages : 490
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Book Description
Pt. I. Observer perspectives: epistemological background. 1. Fractal time: extended observer perspectives / S. Vrobel. 2. Mirror neurons: evidence for the great simulator and Vrobelism / O.E. Rössler. 3. The concept of now in Dogen's philosophy / M.E. Luetchford. 4. Systems and observers from a holistic viewpoint / F.-G. Winkler. 5. A systems-theoretical generalization of non-local correlations / N. von Stillfried. 6. Brain time and physical time / U. Fidelman -- pt. II. Identifying temporal observer perspectives. 7. Simultaneity in emotional moments / G.L. Clore. 8. On time experience in depression / H.M. Emrich, C. Bonnemann and D.E. Dietrich. 9. Contextualization: memory formation and retrieval in a nested environment / M. Piefke and H.J. Markowitsch. Complexity and emergent temporal structure / P.M. Allen. 11. Ordinate logics of living systems / J. LR. Chandler. 12. Skill learning, brain engagement, context and the arts / M.F. Gardiner. 13. Utilizing fractal time / T. Marks-Tarlow -- pt. III. Disentangling temporal simultaneous contrasts. 14. Relativity of scales: application to an endo-perspective of temporal structures / L. Nottale and P. Timar. 15. Unpacking simultaneity for differing observer perspectives and qualities of environment / B. Seaman. 16. Circumcising the void: (de)contextualising in complex Lacanian psychoanalysis / D. De Grave. 17. A review of Flicker-Noise spectroscopy: information in chaotic signals / S.F. Timashev and Y.S. Polyakov. 18. Hidden perspectives in emergent structures produced by neural networks / R. Pavloski. 19. Modeling common-sense decisions / M. Zak -- pt. IV. Synchronization. 20. Synchrony in Dyadic psychotherapy sessions / F. Ramseyer and W. Tschacher. 21. Temporal perspective from auditory perception / G. Baier and T. Hermann. 22. Perception of simultaneous auditive contents / C. Tschinkel. 23. Computer simulations as hidden time-ecologies / G. Koehler. 24. Anti-flaring: how to prevent the market from overheating / A.P. Schmidt and O.E. Rössler. 25. Leveraging the future - existence of a new endo-reality in economics / A.P. Schmidt and O.E. Rössler. 26. Endonomics: looking behind the economic curtain / A.P. Schmidt and O.E. Rössler. 27. Possible quantum absorber effects in cortical synchronization / U. Kämpf. 28. Time and timing in our body and life / O. van Nieuwenhuijze
Author: David Bohm
Publisher: Psychology Press
ISBN: 9780415148092
Category : Philosophy
Languages : en
Pages : 260
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Book Description
The book presents the theory of relativity as a unified whole. By showing that the concepts of this theory are interrelated to form a unified totality David Bohm supplements some of the more specialist courses which have tended to give students a fragmentary impression of the logical and conceptual nature of physics as a whole.
Author: Craig Callender
Publisher: Cambridge University Press
ISBN: 9780521664455
Category : Science
Languages : en
Pages : 380
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Book Description
Was the first book to examine the exciting area of overlap between philosophy and quantum mechanics with chapters by leading experts from around the world.
Author: Piotr T. Chrusciel
Publisher: Birkhäuser
ISBN: 3034879539
Category : Science
Languages : en
Pages : 487
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Book Description
The book presents state-of-the-art results on the analysis of the Einstein equations and the large scale structure of their solutions. It combines in a unique way introductory chapters and surveys of various aspects of the analysis of the Einstein equations in the large. It discusses applications of the Einstein equations in geometrical studies and the physical interpretation of their solutions. Open problems concerning analytical and numerical aspects of the Einstein equations are pointed out. Background material on techniques in PDE theory, differential geometry, and causal theory is provided.
