The Mathematics Of Minkowski Space Time
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The Mathematics Of Minkowski Space Time
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Author : Francesco Catoni
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-06-29
The Mathematics Of Minkowski Space Time written by Francesco Catoni 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 2008-06-29 with Mathematics categories.
This book arose out of original research on the extension of well-established applications of complex numbers related to Euclidean geometry and to the space-time symmetry of two-dimensional Special Relativity. The system of hyperbolic numbers is extensively studied, and a plain exposition of space-time geometry and trigonometry is given. Commutative hypercomplex systems with four unities are studied and attention is drawn to their interesting properties.
Geometry Of Minkowski Space Time
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Author : Francesco Catoni
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-07
Geometry Of Minkowski Space Time written by Francesco Catoni 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 2011-05-07 with Science categories.
This book provides an original introduction to the geometry of Minkowski space-time. A hundred years after the space-time formulation of special relativity by Hermann Minkowski, it is shown that the kinematical consequences of special relativity are merely a manifestation of space-time geometry. The book is written with the intention of providing students (and teachers) of the first years of University courses with a tool which is easy to be applied and allows the solution of any problem of relativistic kinematics at the same time. The book treats in a rigorous way, but using a non-sophisticated mathematics, the Kinematics of Special Relativity. As an example, the famous "Twin Paradox" is completely solved for all kinds of motions. The novelty of the presentation in this book consists in the extensive use of hyperbolic numbers, the simplest extension of complex numbers, for a complete formalization of the kinematics in the Minkowski space-time. Moreover, from this formalization the understanding of gravity comes as a manifestation of curvature of space-time, suggesting new research fields.
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.
Minkowski Space
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Author : Joachim Schröter
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-06-12
Minkowski Space written by Joachim Schröter 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 2017-06-12 with Science categories.
In Minkowski-Space the space-time of special relativity is discussed on the basis of fundamental results of space-time theory. This idea has the consequence that the Minkowski-space can be characterized by 5 axioms, which determine its geometrical and kinematical structure completely. In this sense Minkowski-Space is a prolegomenon for the formulation of other branches of special relativity, like mechanics, electrodynamics, thermodynamics etc. But these applications are not subjects of this book. Contents Basic properties of special relativity Further properties of Lorentz matrices Further properties of Lorentz transformations Decomposition of Lorentz matrices and Lorentz transformations Further structures on Ms Tangent vectors in Ms Orientation Kinematics on Ms Some basic notions of relativistic theories
Geometrical Physics In Minkowski Spacetime
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Author : E.G.Peter Rowe
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Geometrical Physics In Minkowski Spacetime written by E.G.Peter Rowe 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 2013-04-17 with Science categories.
From the reviews: "This attractive book provides an account of the theory of special relativity from a geometrical viewpoint, explaining the unification and insights that are given by such a treatment. [...] Can be read with profit by all who have taken a first course in relativity physics." ASLIB Book Guide
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 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.
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.
Extensions Of The Stability Theorem Of The Minkowski Space In General Relativity
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Author : Lydia Bieri
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-06-30
Extensions Of The Stability Theorem Of The Minkowski Space In General Relativity written by Lydia Bieri and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-30 with General relativity (Physics) categories.
A famous result of Christodoulou and Klainerman is the global nonlinear stability of Minkowski spacetime. In this book, Bieri and Zipser provide two extensions to this result. In the first part, Bieri solves the Cauchy problem for the Einstein vacuum equations with more general, asymptotically flat initial data, and describes precisely the asymptotic behavior. In particular, she assumes less decay in the power of $r$ and one less derivative than in the Christodoulou-Klainerman result. She proves that in this case, too, the initial data, being globally close to the trivial data, yields a solution which is a complete spacetime, tending to the Minkowski spacetime at infinity along any geodesic. In contrast to the original situation, certain estimates in this proof are borderline in view of decay, indicating that the conditions in the main theorem on the decay at infinity on the initial data are sharp. In the second part, Zipser proves the existence of smooth, global solutions to the Einstein-Maxwell equations. A nontrivial solution of these equations is a curved spacetime with an electromagnetic field. To prove the existence of solutions to the Einstein-Maxwell equations, Zipser follows the argument and methodology introduced by Christodoulou and Klainerman. To generalize the original results, she needs to contend with the additional curvature terms that arise due to the presence of the electromagnetic field $F$; in her case the Ricci curvature of the spacetime is not identically zero but rather represented by a quadratic in the components of $F$. In particular the Ricci curvature is a constant multiple of the stress-energy tensor for $F$. Furthermore, the traceless part of the Riemann curvature tensor no longer satisfies the homogeneous Bianchi equations but rather inhomogeneous equations including components of the spacetime Ricci curvature. Therefore, the second part of this book focuses primarily on the derivation of estimates for the new terms that arise due to the presence of the electromagnetic field.
Spacetime Minkowski S Papers On Spacetime Physics
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Author : Hermann Minkowski
language : en
Publisher:
Release Date : 2020-03-20
Spacetime Minkowski S Papers On Spacetime Physics written by Hermann Minkowski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-20 with Science categories.
Not only the general public, but even students of physics appear to believe that the physics concept of spacetime was introduced by Einstein. This is both unfortunate and unfair. It was Hermann Minkowski (Einstein's mathematics professor) who announced the new four-dimensional (spacetime) view of the world in 1908, which he deduced from experimental physics by decoding the profound message hidden in the failed experiments designed to discover absolute motion. Minkowski realized that the images coming from our senses, which seem to represent an evolving three-dimensional world, are only glimpses of a higher four-dimensional reality that is not divided into past, present, and future since space and all moments of time form an inseparable entity (spacetime). Einstein's initial reaction to Minkowski's view of spacetime and the associated with it four-dimensional physics (also introduced by Minkowski) was not quite favorable: "Since the mathematicians have invaded the relativity theory, I do not understand it myself any more." However, later Einstein adopted not only Minkowski's spacetime physics (which was crucial for Einstein's revolutionary theory of gravity as curvature of spacetime), but also Minkowski's world view as evident from Einstein's letter of condolences to the widow of his longtime friend Besso: "Now Besso has departed from this strange world a little ahead of me. That means nothing. People like us, who believe in physics, know that the distinction between past, present and future is only a stubbornly persistent illusion." Besso left this world on 15 March 1955; Einstein followed him on 18 April 1955. This volume contains Hermann Minkowski's four works, which laid the foundations of spacetime physics: Space and Time, The Relativity Principle, The Fundamental Equations for Electromagnetic Processes in Moving Bodies and A Derivation of the Fundamental Equations for the Electromagnetic Processes in Moving Bodies from the Standpoint of the Theory of Electrons. These papers have never been published together either in German or English and the second and the last paper have not been translated into English so far.
Spacetime
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Author : Marcus Kriele
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-07-01
Spacetime written by Marcus Kriele 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 2003-07-01 with Science categories.
One of the most of exciting aspects is the general relativity pred- tion of black holes and the Such Big Bang. predictions gained weight the theorems through Penrose. singularity pioneered In various by te- books on theorems general relativity singularity are and then presented used to that black holes exist and that the argue universe started with a To date what has big been is bang. a critical of what lacking analysis these theorems predict-’ We of really give a proof a typical singul- theorem and this ity use theorem to illustrate problems arising through the of possibilities violations" and "causality weak "shell very crossing These singularities". add to the problems weight of view that the point theorems alone singularity are not sufficient to the existence of predict physical singularities. The mathematical theme of the book In order to both solid gain a of and intuition understanding good for any mathematical theory, one,should to realise it as model of try a a fam- iar non-mathematical theories have had concept. Physical an especially the important on of and impact development mathematics, conversely various modern theories physical rather require sophisticated mathem- ics for their formulation. both and mathematics Today, physics are so that it is often difficult complex to master the theories in both very s- in the of jects. However, case differential pseudo-Riemannian geometry or the general relativity between and mathematics relationship physics is and it is therefore especially close, to from interd- possible profit an ciplinary approach.