The Mathematical Principles Of Scale Relativity Physics
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The Mathematical Principles of Scale Relativity Physics by Nicolae Mazilu,Maricel Agop,Ioan Merches Pdf
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.
The Theory of Scale Relativity by Laurent Nottale Pdf
Provides a comprehensive survey of the state-of-the-art in the development of the relativity theory of scales Transcends and integrates the classical and the quantum regimes Enables quantum mechanics to be based on the principle of relativity provided this principle is extended to scale transformations of the reference system Collects and organizes developments and applications from diverse fields for easy reference
The Mathematical Principles of Scale Relativity Physics by Nicolae Mazilu,Maricel Agop,Ioan Merches Pdf
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.
Scale Relativity and Fractal Space-Time by Laurent Nottale Pdf
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. Contents:General IntroductionTheory:IntroductionStructure of the TheoryNondifferentiable Geometry and Fractal Space-TimeLaws of Scale TransformationsFrom Fractal Space to Non-Relativistic Quantum MechanicsFrom Fractal Space-Time to Relativistic Quantum MechanicsGeometric Theory of Gauge Fields in Scale RelativityQuantum-type Mechanics in Scale SpaceApplications:IntroductionApplications to Laboratory and Earth Scale PhysicsApplications to Elementary Particle and High Energy PhysicsApplications to CosmologyApplications to Gravitational Structuring in AstrophysicsApplications to Life Sciences and Other Sciences Readership: Academics, post-graduates and professionals interested in astrophysics and cosmology. Keywords:Scale Relativity;Fractals;Quantum Mechanics;Space-Time GeometryKey Features:No competing title: it describes the state-of-the art of the theory of scale relativity and of its applications to various sciences by its founderApplications of the theory to various branches of physical science, including elementary particle physics, cosmology, and life sciences, are presented in detail in individual chaptersReviews:“The sweep of this book is enormous. It has implications for every aspect of physics. But it also has important implications for biological science. Systems Biology is multi-scale since integration of function can occur at many different levels from genes to whole organisms and populations in what some of us have called a principle of biological relativity. Could scale relativity provide the framework for systematizing that principle? Models at different levels could be seen to be working with different scale resolutions, or even scale dimensions. The prospect is tantalising and forms a major challenge to mathematical systems biologists. Those who would welcome that challenge will need to read this book.”Denis Noble, FRS Oxford University author of The Music of Life “Scale Relativity seeks to refine our understanding of the nature of space itself. Extended to its natural limits, it has the potential to unify the description of phenomena one associates with Quantum Mechanics, Biology and even Astrophysics and Cosmology.”Jean-Patrick Connerade Emeritus Professor and Distinguished Research Fellow Imperial College London President of the European Academy of Science, Arts and Literature “This is a rich and lovely book. The elegant approach to unifying many concepts in physics provides new ways of seeing things — some things we know in new ways and some very new ideas. It is also exciting to see some conceptual tools for thinking about problems as complex as those we face in understanding biological systems.”David J Galas Professor and Senior Vice President Institute for Systems Biology “Nottale's new book, from the first paragraph to the last section, is a bold, courageous and thoughtful work that addresses this problem directly through the paradigm of scale relativity. The book contains a wealth of insight to accompany an astonishing collection of numerical data from many scales of observation. Nottale has succeeded in going beyond the limitations inherent in conventional differential approaches to produce a convincing picture of scale-dependent physics. The book is a must-read for any scientist contemplating bridging the gap between the large and small-scale approximations of modern physics.”Garnet Ord Ryerson University
Fractal Space-time and Microphysics by Laurent Nottale Pdf
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.
Introduction to Einstein’s Theory of Relativity by Øyvind Grøn Pdf
The revised and updated 2nd edition of this established textbook provides a self-contained introduction to the general theory of relativity, describing not only the physical principles and applications of the theory, but also the mathematics needed, in particular the calculus of differential forms. Updated throughout, the book contains more detailed explanations and extended discussions of several conceptual points, and strengthened mathematical deductions where required. It includes examples of work conducted in the ten years since the first edition of the book was published, for example the pedagogically helpful concept of a "river of space" and a more detailed discussion of how far the principle of relativity is contained in the general theory of relativity. Also presented is a discussion of the concept of the 'gravitational field' in Einstein's theory, and some new material concerning the 'twin paradox' in the theory of relativity. Finally, the book contains a new section about gravitational waves, exploring the dramatic progress in this field following the LIGO observations. Based on a long-established masters course, the book serves advanced undergraduate and graduate level students, and also provides a useful reference for researchers.
Einstein wrote this book for people who are interested in understanding the Theory of Relativity but aren't experts in scientific and mathematical principles. I'm sure many people have heard about Einstein's Theory of Relativity, but most of them don't really know what it is all about. This book gives them a chance to know more about this very famous theory without the need to take a Physics course first. This book is divided into three parts. The first part explains what special relativity is all about. The second part discusses general relativity thoroughly and the last part deals with the considerations of the universe as a whole. The first part explains the principles of the special theory of relativity. Here the relationship between space and time are thoroughly discussed. The derivation of Einstein's most famous formula which is E = mc2 is also explained in this part in a very simple way. The second part which is about the general theory of relativity is about the generalization of the special theory, Einstein's thoughts about Newton's Universal Law of Gravitation and how they affect the space time continuum. The last part explains how the universe actually works on a cosmic scale. These things may sound too complicated at first glance but Einstein was able to explain them to his readers in the book without sounding too technical. Reading Einstein's "Relativity: The Special and General Theory" may not sound very attractive at first. We've all heard of Einstein's equation but how many people can actually explain what it means. This book will elucidate all the iconic thoughts of Einstein without requiring a physics degree from the reader. Einstein wrote this book for people who are interested in understanding the Theory of Relativity but aren't experts in scientific and mathematical principles. I'm sure many people have heard about Einstein's Theory of Relativity, but most of them don't really know what it is all about. This book gives them a chance to know more about this very famous theory without the need to take a Physics course first. This book is divided into three parts. The first part explains what special relativity is all about. The second part discusses general relativity thoroughly and the last part deals with the considerations of the universe as a whole. The first part explains the principles of the special theory of relativity. Here the relationship between space and time are thoroughly discussed. The derivation of Einstein's most famous formula which is E = mc2 is also explained in this part in a very simple way. The second part which is about the general theory of relativity is about the generalization of the special theory, Einstein's thoughts about Newton's Universal Law of Gravitation and how they affect the space time continuum. The last part explains how the universe actually works on a cosmic scale. These things may sound too complicated at first glance but Einstein was able to explain them to his readers in the book without sounding too technical. Reading Einstein's "Relativity: The Special and General Theory" may not sound very attractive at first. We've all heard of Einstein's equation but how many people can actually explain what it means. This book will elucidate all the iconic thoughts of Einstein without requiring a physics degree from the reader.
Principles of Quantum General Relativity by Eduard Prugove?ki Pdf
This monograph explains and analyzes the principles of a quantum-geometric framework for the unification of general relativity and quantum theory. By taking advantage of recent advances in areas like fibre and superfibre bundle theory, Krein spaces, gauge fields and groups, coherent states, etc., these principles can be consistently incorporated into a framework that can justifiably be said to provide the foundations for a quantum extrapolation of general relativity. This volume aims to present this approach in a way which places as much emphasis on fundamental physical ideas as on their precise mathematical implementation. References are also made to the ideas of Einstein, Bohr, Born, Dirac, Heisenberg and others, in order to set the work presented here in an appropriate historical context.
Oscillatory Models in General Relativity by Esra Russell,Oktay K. Pashaev Pdf
The book employs oscillatory dynamical systems to represent the Universe mathematically via constructing classical and quantum theory of damped oscillators. It further discusses isotropic and homogeneous metrics in the Friedman-Robertson-Walker Universe and shows their equivalence to non-stationary oscillators. The wide class of exactly solvable damped oscillator models with variable parameters is associated with classical special functions of mathematical physics. Combining principles with observations in an easy to follow way, it inspires further thinking for mathematicians and physicists. Contents Part I: Dissipative geometry and general relativity theory Pseudo-Riemannian geometry and general relativity Dynamics of universe models Anisotropic and homogeneous universe models Metric waves in a nonstationary universe and dissipative oscillator Bosonic and fermionic models of a Friedman–Robertson–Walker universe Time dependent constants in an oscillatory universe Part II: Variational principle for time dependent oscillations and dissipations Lagrangian and Hamilton descriptions Damped oscillator: classical and quantum theory Sturm–Liouville problem as a damped oscillator with time dependent damping and frequency Riccati representation of time dependent damped oscillators Quantization of the harmonic oscillator with time dependent parameters
Scale Transitions As Foundations Of Physics by Ioan Merches,Maricel Agop,Nicolae Mazilu Pdf
The scale transitions are essential to physical knowledge. The book describes the history of essential moments of physics, viewed as necessary consequences of the unavoidable process of scale transition, and provides the mathematical techniques for the construction of a theoretical physics founded on scale transition. The indispensable mathematical technique is analyticity, helping in the construction of space coordinate systems. The indispensable theoretical technique from physical point of view is the affine theory of surfaces. The connection between the two techniques is provided by a duality in defining the physical properties.
A First Course on Symmetry, Special Relativity and Quantum Mechanics by Gabor Kunstatter,Saurya Das Pdf
This book provides an in-depth and accessible description of special relativity and quantum mechanics which together form the foundation of 21st century physics. A novel aspect is that symmetry is given its rightful prominence as an integral part of this foundation. The book offers not only a conceptual understanding of symmetry, but also the mathematical tools necessary for quantitative analysis. As such, it provides a valuable precursor to more focused, advanced books on special relativity or quantum mechanics. Students are introduced to several topics not typically covered until much later in their education.These include space-time diagrams, the action principle, a proof of Noether's theorem, Lorentz vectors and tensors, symmetry breaking and general relativity. The book also provides extensive descriptions on topics of current general interest such as gravitational waves, cosmology, Bell's theorem, entanglement and quantum computing. Throughout the text, every opportunity is taken to emphasize the intimate connection between physics, symmetry and mathematics.The style remains light despite the rigorous and intensive content. The book is intended as a stand-alone or supplementary physics text for a one or two semester course for students who have completed an introductory calculus course and a first-year physics course that includes Newtonian mechanics and some electrostatics. Basic knowledge of linear algebra is useful but not essential, as all requisite mathematical background is provided either in the body of the text or in the Appendices. Interspersed through the text are well over a hundred worked examples and unsolved exercises for the student.
The Relativity of All Things by Laurent Nottale Pdf
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
The Principle of the Fermionic Projector by Felix Finster Pdf
The "principle of the fermionic projector" provides a new mathematical framework for the formulation of physical theories and is a promising approach for physics beyond the standard model. This book begins with a brief review of relativity, relativistic quantum mechanics, and classical gauge theories, emphasizing the basic physical concepts and mathematical foundations. The external field problem and Klein's paradox are discussed and then resolved by introducing the fermionicprojector, a global object in space-time that generalizes the notion of the Dirac sea. At the mathematical core of the book is a precise definition of the fermionic projector and the use of methods of hyperbolic differential equations for detailed analysis. The fermionic projector makes it possible toformulate a new type of variational principle in space-time. The mathematical tools are developed for the analysis of the corresponding Euler-Lagrange equations. A particular variational principle is proposed that gives rise to an effective interaction which shows many similarities to the interactions of the standard model. The main chapters of the book are easily accessible for beginning graduate students in mathematics or physics. Several appendices provide supplementary material, which willbe useful to the experienced researcher.
Fractal Space-time And Microphysics: Towards A Theory Of Scale Relativity by Laurent Nottale Pdf
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.
