Minkowski Space
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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.
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
Minkowski Space
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Author : Paul F. Kisak
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2016-05-25
Minkowski Space written by Paul F. Kisak 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 2016-05-25 with categories.
In mathematical physics, Minkowski space or Minkowski spacetime is a combination of Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded. Although initially developed by mathematician Hermann Minkowski for Maxwell's equations of electromagnetism, the mathematical structure of Minkowski spacetime was shown to be an immediate consequence of the postulates of special relativity. Minkowski space is closely associated with Einstein's theory of special relativity, and is the most common mathematical structure on which special relativity is formulated. While the individual components in Euclidean space and time will often differ due to length contraction and time dilation, in Minkowski spacetime, all frames of reference will agree on the total distance in spacetime between events. Because it treats time differently than the three spatial dimensions, Minkowski space differs from four-dimensional Euclidean space. In Euclidean space, the isometry group (the maps preserving the regular inner product) is the Euclidean group. The analogous isometry group for Minkowski space, preserving intervals of spacetime equipped with the associated non-positive definite bilinear form (here called the Minkowski inner product, ) is the Poincare group. The Minkowski inner product is defined as to yield the spacetime interval between two events when given their coordinate difference vector as argument."
The Geometry Of Minkowski Spacetime
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Author : Gregory L. Naber
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-02-02
The Geometry Of Minkowski Spacetime written by Gregory L. Naber 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 2012-02-02 with Mathematics categories.
This book offers a presentation of the special theory of relativity that is mathematically rigorous and yet spells out in considerable detail the physical significance of the mathematics. It treats, in addition to the usual menu of topics one is accustomed to finding in introductions to special relativity, a wide variety of results of more contemporary origin. These include Zeeman’s characterization of the causal automorphisms of Minkowski spacetime, the Penrose theorem on the apparent shape of a relativistically moving sphere, a detailed introduction to the theory of spinors, a Petrov-type classification of electromagnetic fields in both tensor and spinor form, a topology for Minkowski spacetime whose homeomorphism group is essentially the Lorentz group, and a careful discussion of Dirac’s famous Scissors Problem and its relation to the notion of a two-valued representation of the Lorentz group. This second edition includes a new chapter on the de Sitter universe which is intended to serve two purposes. The first is to provide a gentle prologue to the steps one must take to move beyond special relativity and adapt to the presence of gravitational fields that cannot be considered negligible. The second is to understand some of the basic features of a model of the empty universe that differs markedly from Minkowski spacetime, but may be recommended by recent astronomical observations suggesting that the expansion of our own universe is accelerating rather than slowing down. The treatment presumes only a knowledge of linear algebra in the first three chapters, a bit of real analysis in the fourth and, in two appendices, some elementary point-set topology. The first edition of the book received the 1993 CHOICE award for Outstanding Academic Title. Reviews of first edition: “... a valuable contribution to the pedagogical literature which will be enjoyed by all who delight in precise mathematics and physics.” (American Mathematical Society, 1993) “Where many physics texts explain physical phenomena by means of mathematical models, here a rigorous and detailed mathematical development is accompanied by precise physical interpretations.” (CHOICE, 1993) “... his talent in choosing the most significant results and ordering them within the book can’t be denied. The reading of the book is, really, a pleasure.” (Dutch Mathematical Society, 1993)
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.
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.
Minkowski Spacetime A Hundred Years Later
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Author : Vesselin Petkov
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-03-11
Minkowski Spacetime A Hundred Years Later written by Vesselin Petkov 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 2010-03-11 with Science categories.
Celebrating the one hundredth anniversary of the 1909 publication of Minkowski’s seminal paper "Space and Time", this volume includes a fresh translation as well as the original in German, and a number of contributed papers on the still-controversial subject.
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.
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.