The Mathematical Principles Of Scale Relativity Physics
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The Mathematical Principles Of Scale Relativity Physics
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Author : Nicolae Mazilu
language : en
Publisher: CRC Press
Release Date : 2019-09-24
The Mathematical Principles Of Scale Relativity Physics written by Nicolae Mazilu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-24 with Science categories.
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
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Author : Laurent Nottale
language : en
Publisher: Birkhäuser
Release Date : 2010-11-16
The Theory Of Scale Relativity written by Laurent Nottale and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-16 with Mathematics categories.
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
Introduction To Einstein S Theory Of Relativity
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Author : Øyvind Grøn
language : en
Publisher: Springer Nature
Release Date : 2020-05-27
Introduction To Einstein S Theory Of Relativity written by Øyvind Grøn and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-27 with Science categories.
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.
Relativity
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Author : Albert Einstein
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2017-08-22
Relativity written by Albert Einstein and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-22 with categories.
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.
The General Theory Of Relativity
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Author : Anadijiban Das
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-26
The General Theory Of Relativity written by Anadijiban Das and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-26 with Science categories.
The General Theory of Relativity: A Mathematical Exposition will serve readers as a modern mathematical introduction to the general theory of relativity. Throughout the book, examples, worked-out problems, and exercises (with hints and solutions) are furnished. Topics in this book include, but are not limited to: tensor analysis the special theory of relativity the general theory of relativity and Einstein’s field equations spherically symmetric solutions and experimental confirmations static and stationary space-time domains black holes cosmological models algebraic classifications and the Newman-Penrose equations the coupled Einstein-Maxwell-Klein-Gordon equations appendices covering mathematical supplements and special topics Mathematical rigor, yet very clear presentation of the topics make this book a unique text for both university students and research scholars. Anadijiban Das has taught courses on Relativity Theory at The University College of Dublin, Ireland, Jadavpur University, India, Carnegie-Mellon University, USA, and Simon Fraser University, Canada. His major areas of research include, among diverse topics, the mathematical aspects of general relativity theory. Andrew DeBenedictis has taught courses in Theoretical Physics at Simon Fraser University, Canada, and is also a member of The Pacific Institute for the Mathematical Sciences. His research interests include quantum gravity, classical gravity, and semi-classical gravity.
Oscillatory Models In General Relativity
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Author : Esra Russell
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-11-20
Oscillatory Models In General Relativity written by Esra Russell and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-20 with Science categories.
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
The Physical And Mathematical Foundations Of The Theory Of Relativity
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Author : Antonio Romano
language : en
Publisher: Springer Nature
Release Date : 2019-09-25
The Physical And Mathematical Foundations Of The Theory Of Relativity written by Antonio Romano and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-25 with Science categories.
This unique textbook offers a mathematically rigorous presentation of the theory of relativity, emphasizing the need for a critical analysis of the foundations of general relativity in order to best study the theory and its implications. The transitions from classical mechanics to special relativity and then to general relativity are explored in detail as well, helping readers to gain a more profound and nuanced understanding of the theory as a whole. After reviewing the fundamentals of differential geometry and classical mechanics, the text introduces special relativity, first using the physical approach proposed by Einstein and then via Minkowski’s mathematical model. The authors then address the relativistic thermodynamics of continua and electromagnetic fields in matter – topics which are normally covered only very briefly in other treatments – in the next two chapters. The text then turns to a discussion of general relativity by means of the authors’ unique critical approach, underlining the difficulty of recognizing the physical meaning of some statements, such as the physical meaning of coordinates and the derivation of physical quantities from those of space-time. Chapters in this section cover the model of space-time proposed by Schwarzschild; black holes; the Friedman equations and the different cosmological models they describe; and the Fermi-Walker derivative. Well-suited for graduate students in physics and mathematics who have a strong foundation in real analysis, classical mechanics, and general physics, this textbook is appropriate for a variety of graduate-level courses that cover topics in relativity. Additionally, it will interest physicists and other researchers who wish to further study the subtleties of these theories and understand the contemporary scholarly discussions surrounding them.
A Mathematical Journey To Relativity
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Author : Wladimir-Georges Boskoff
language : en
Publisher: Springer Nature
Release Date :
A Mathematical Journey To Relativity written by Wladimir-Georges Boskoff and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Mathematical Problems Of General Relativity I
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Author : Demetrios Christodoulou
language : en
Publisher: European Mathematical Society
Release Date : 2008
Mathematical Problems Of General Relativity I written by Demetrios Christodoulou and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.
General relativity is a theory proposed by Einstein in 1915 as a unified theory of space, time and gravitation. It is based on and extends Newton's theory of gravitation as well as Newton's equations of motion. It is thus fundamentally rooted in classical mechanics. The theory can be seen as a development of Riemannian geometry, itself an extension of Gauss' intrinsic theory of curved surfaces in Euclidean space. The domain of application of the theory is astronomical systems. One of the mathematical methods analyzed and exploited in the present volume is an extension of Noether's fundamental principle connecting symmetries to conserved quantities. This is involved at a most elementary level in the very definition of the notion of hyperbolicity for an Euler-Lagrange system of partial differential equations. Another method, the study and systematic use of foliations by characteristic (null) hypersurfaces, is in the spirit of Roger Penrose's approach in his incompleteness theorem. The methods have applications beyond general relativity to problems in fluid mechanics and, more generally, to the mechanics and electrodynamics of continuous media. The book is intended for advanced students and researchers seeking an introduction to the methods and applications of general relativity.
Space Time And Gravitation
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Author : Arthur Stanley Eddington
language : en
Publisher: Read Books Ltd
Release Date : 2013-05-31
Space Time And Gravitation written by Arthur Stanley Eddington and has been published by Read Books Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-31 with Science categories.
This text provides an account of various experiments, that demonstrate a simplified reality where space and time are relegated to their proper source – the observer. The principles of these experiments and theories originate from the ideas of Einstein, and this text aims to present this 'new' outlook without the need for extensive knowledge of mathematics, physics, or philosophy. This text will be of considerable use to those with a keen interest in physics, and would make for a great addition to any bookshelf. The chapters of this book include: 'The Fitzgerald Contraction', 'Relativity', 'The World of Four Dimensions', 'Fields of Force', 'Kinds of Space', 'The New Law of Gravitation and the Old Law', 'Weighing Light', 'Other Tests of The Theory', 'Momentum and Energy', etcetera. We are publishing this antiquarian book now in an affordable, modern edition - complete with a new biography of the author.
