The Mathematical Principles of Scale Relativity Physics

The Mathematical Principles of Scale Relativity Physics
Author: Nicolae Mazilu
Publisher: CRC Press
Total Pages: 256
Release: 2019-09-12
Genre: Mathematics
ISBN: 1000751023

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

The Theory of Scale Relativity
Author: Laurent Nottale
Publisher: Birkhäuser
Total Pages:
Release: 2010-11-16
Genre: Mathematics
ISBN: 9780817671921

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

The Mathematical Principles of Scale Relativity Physics
Author: Nicolae Mazilu
Publisher: CRC Press
Total Pages: 182
Release: 2019-09-24
Genre: Science
ISBN: 1000751260

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

Scale Relativity and Fractal Space-time
Author: Laurent Nottale
Publisher: World Scientific
Total Pages: 766
Release: 2011
Genre: Science
ISBN: 1848166508

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.

Fractal Space-time and Microphysics

Fractal Space-time and Microphysics
Author: Laurent Nottale
Publisher: World Scientific
Total Pages: 358
Release: 1993
Genre: Science
ISBN: 9789810208783

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.

The Relativity of All Things

The Relativity of All Things
Author: Laurent Nottale
Publisher:
Total Pages: 372
Release: 2019-03-28
Genre:
ISBN: 9780578456508

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

Introduction to Einstein’s Theory of Relativity

Introduction to Einstein’s Theory of Relativity
Author: Øyvind Grøn
Publisher: Springer Nature
Total Pages: 536
Release: 2020-05-27
Genre: Science
ISBN: 3030438627

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

Relativity
Author: Albert Einstein
Publisher: Createspace Independent Publishing Platform
Total Pages: 172
Release: 2017-08-22
Genre:
ISBN: 9781974692286

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.

Oscillatory Models in General Relativity

Oscillatory Models in General Relativity
Author: Esra Russell
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 154
Release: 2017-11-20
Genre: Science
ISBN: 3110515369

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