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Author: Paul F. Kisak Publisher: Createspace Independent Publishing Platform ISBN: 9781533561688 Category : Languages : en Pages : 252
Book Description
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."
Author: Paul F. Kisak Publisher: Createspace Independent Publishing Platform ISBN: 9781533561688 Category : Languages : en Pages : 252
Book Description
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."
Author: Hermann Minkowski Publisher: Minkowski Institute Press ISBN: 0987987119 Category : Languages : en Pages : 134
Book Description
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.
Author: Gregory L. Naber Publisher: Courier Corporation ISBN: 9780486432359 Category : Mathematics Languages : en Pages : 276
Book Description
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.
Author: E.G.Peter Rowe Publisher: Springer Science & Business Media ISBN: 1447138937 Category : Science Languages : en Pages : 263
Book Description
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
Author: Demetrios Christodoulou Publisher: Princeton University Press ISBN: 1400863171 Category : Mathematics Languages : en Pages : 525
Book Description
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.
Author: John W Schutz Publisher: CRC Press ISBN: 9780582317604 Category : Science Languages : en Pages : 260
Book Description
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.
Author: Vesselin Petkov Publisher: Springer Science & Business Media ISBN: 9048134757 Category : Science Languages : en Pages : 326
Book Description
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.
Author: A.K. Dewdney Publisher: Springer Science & Business Media ISBN: 1461301998 Category : Science Languages : en Pages : 247
Book Description
A classic book about life in a two-dimensional universe, written by a well-known author. Now brought back into print in this revised and updated edition, the book is written within the great tradition of Abbott's Flatland, and Hinton's famous Sphereland. Accessible, imaginative, and clever, it will appeal to a wide array of readers, from serious mathematicians and computer scientists, to science fiction fans.
Author: Vesselin Petkov Publisher: Springer Science & Business Media ISBN: 3642135382 Category : Science Languages : en Pages : 316
Book Description
Dedicated to the centennial anniversary of Minkowski's discovery of spacetime, this volume contains papers, most presented at the Third International Conference on the Nature and Ontology of Spacetime, that address some of the deepest questions in physics.
Author: Joachim Schröter Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110485737 Category : Science Languages : en Pages : 129
Book Description
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
Author: Paul F. Kisak
Author: Paul F. Kisak
Author: Hermann Minkowski
Author: Gregory L. Naber
Author: E.G.Peter Rowe
Author: Demetrios Christodoulou
Author: John W Schutz
Author: Vesselin Petkov
Author: A.K. Dewdney
Author: Vesselin Petkov
Author: Joachim Schröter