The Mathematics Of Minkowski Space Time
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The Geometry Of Minkowski Spacetime
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Author : Gregory L. Naber
language : en
Publisher: Courier Corporation
Release Date : 2003-01-01
The Geometry Of Minkowski Spacetime written by Gregory L. Naber and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.
This mathematically rigorous treatment examines Zeeman's characterization of the causal automorphisms of Minkowski spacetime and the Penrose theorem concerning the apparent shape of a relativistically moving sphere. Other topics include the construction of a geometric theory of the electromagnetic field; an in-depth introduction to the theory of spinors; and a classification of electromagnetic fields in both tensor and spinor form. Appendixes introduce a topology for Minkowski spacetime and discuss Dirac's famous "Scissors Problem." Appropriate for graduate-level courses, this text presumes only a knowledge of linear algebra and elementary point-set topology. 1992 edition. 43 figures.
The Global Nonlinear Stability Of The Minkowski Space
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Author : Demetrios Christodoulou
language : en
Publisher: Princeton University Press
Release Date : 2014-07-14
The Global Nonlinear Stability Of The Minkowski Space written by Demetrios Christodoulou and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Mathematics categories.
The aim of this work is to provide a proof of the nonlinear gravitational stability of the Minkowski space-time. More precisely, the book offers a constructive proof of global, smooth solutions to the Einstein Vacuum Equations, which look, in the large, like the Minkowski space-time. In particular, these solutions are free of black holes and singularities. The work contains a detailed description of the sense in which these solutions are close to the Minkowski space-time, in all directions. It thus provides the mathematical framework in which we can give a rigorous derivation of the laws of gravitation proposed by Bondi. Moreover, it establishes other important conclusions concerning the nonlinear character of gravitational radiation. The authors obtain their solutions as dynamic developments of all initial data sets, which are close, in a precise manner, to the flat initial data set corresponding to the Minkowski space-time. They thus establish the global dynamic stability of the latter. Originally published in 1994. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Independent Axioms For Minkowski Space Time
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Author : John W Schutz
language : en
Publisher: CRC Press
Release Date : 1997-10-08
Independent Axioms For Minkowski Space Time written by John W Schutz and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-10-08 with Science categories.
The primary aim of this monograph is to clarify the undefined primitive concepts and the axioms which form the basis of Einstein's theory of special relativity. Minkowski space-time is developed from a set of independent axioms, stated in terms of a single relation of betweenness. It is shown that all models are isomorphic to the usual coordinate model, and the axioms are consistent relative to the reals.
The Geometry Of Spacetime
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Author : James J. Callahan
language : en
Publisher: Springer Science & Business Media
Release Date : 2000
The Geometry Of Spacetime written by James J. Callahan 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 2000 with Computers categories.
Hermann Minkowski recast special relativity as essentially a new geometric structure for spacetime. This book looks at the ideas of both Einstein and Minkowski, and then introduces the theory of frames, surfaces and intrinsic geometry, developing the main implications of Einstein's general relativity theory.
Space Time Algebra
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Author : David Hestenes
language : en
Publisher: Birkhäuser
Release Date : 2015-04-25
Space Time Algebra written by David Hestenes and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-25 with Mathematics categories.
This small book started a profound revolution in the development of mathematical physics, one which has reached many working physicists already, and which stands poised to bring about far-reaching change in the future. At its heart is the use of Clifford algebra to unify otherwise disparate mathematical languages, particularly those of spinors, quaternions, tensors and differential forms. It provides a unified approach covering all these areas and thus leads to a very efficient ‘toolkit’ for use in physical problems including quantum mechanics, classical mechanics, electromagnetism and relativity (both special and general) – only one mathematical system needs to be learned and understood, and one can use it at levels which extend right through to current research topics in each of these areas. These same techniques, in the form of the ‘Geometric Algebra’, can be applied in many areas of engineering, robotics and computer science, with no changes necessary – it is the same underlying mathematics, and enables physicists to understand topics in engineering, and engineers to understand topics in physics (including aspects in frontier areas), in a way which no other single mathematical system could hope to make possible. There is another aspect to Geometric Algebra, which is less tangible, and goes beyond questions of mathematical power and range. This is the remarkable insight it gives to physical problems, and the way it constantly suggests new features of the physics itself, not just the mathematics. Examples of this are peppered throughout ‘Space-Time Algebra’, despite its short length, and some of them are effectively still research topics for the future. From the Foreward by Anthony Lasenby
Space And Time
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Author : Hermann Minkowski
language : en
Publisher: Minkowski Institute Press
Release Date : 2013-08-27
Space And Time written by Hermann Minkowski and has been published by Minkowski Institute Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-27 with Young Adult Nonfiction categories.
This is the first publication (in German or English) of Hermann Minkowski's three papers on relativity together: The Relativity Principle - lecture given at the meeting of the Göttingen Mathematical Society on November 5, 1907. This is the first English translation. The Fundamental Equations for Electromagnetic Processes in Moving Bodies - lecture given at the meeting of the Göttingen Scientific Society on December 21, 1907. New translation. Space and Time - lecture given at the 80th Meeting of Natural Scientists in Cologne on September 21, 1908. New translation.
Exact Space Times In Einstein S General Relativity
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Author : Jerry B. Griffiths
language : en
Publisher: Cambridge University Press
Release Date : 2009-10-15
Exact Space Times In Einstein S General Relativity written by Jerry B. Griffiths and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-15 with Science categories.
Einstein's theory of general relativity is a theory of gravity and, as in the earlier Newtonian theory, much can be learnt about the character of gravitation and its effects by investigating particular idealised examples. This book describes the basic solutions of Einstein's equations with a particular emphasis on what they mean, both geometrically and physically. Concepts such as big bang and big crunch-types of singularities, different kinds of horizons and gravitational waves, are described in the context of the particular space-times in which they naturally arise. These notions are initially introduced using the most simple and symmetric cases. Various important coordinate forms of each solution are presented, thus enabling the global structure of the corresponding space-time and its other properties to be analysed. The book is an invaluable resource both for graduate students and academic researchers working in gravitational physics.
Springer Handbook Of Spacetime
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Author : Abhay Ashtekar
language : en
Publisher: Springer
Release Date : 2014-09-01
Springer Handbook Of Spacetime written by Abhay Ashtekar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with Science categories.
The Springer Handbook of Spacetime is dedicated to the ground-breaking paradigm shifts embodied in the two relativity theories, and describes in detail the profound reshaping of physical sciences they ushered in. It includes in a single volume chapters on foundations, on the underlying mathematics, on physical and astrophysical implications, experimental evidence and cosmological predictions, as well as chapters on efforts to unify general relativity and quantum physics. The Handbook can be used as a desk reference by researchers in a wide variety of fields, not only by specialists in relativity but also by researchers in related areas that either grew out of, or are deeply influenced by, the two relativity theories: cosmology, astronomy and astrophysics, high energy physics, quantum field theory, mathematics, and philosophy of science. It should also serve as a valuable resource for graduate students and young researchers entering these areas, and for instructors who teach courseson these subjects. The Handbook is divided into six parts. Part A: Introduction to Spacetime Structure. Part B: Foundational Issues. Part C: Spacetime Structure and Mathematics. Part D: Confronting Relativity theories with observations. Part E: General relativity and the universe. Part F: Spacetime beyond Einstein.
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.