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by Tevian Dray

  • ISBN: 1466510471
  • Author: Tevian Dray
  • ePub ver: 1884 kb
  • Fb2 ver: 1884 kb
  • Rating: 4.2 of 5
  • Language: English
  • Pages: 150
  • Publisher: A K Peters/CRC Press; 1 edition (July 2, 2012)
  • Formats: lrf doc docx txt
  • Category: Other
  • Subcategory: Science & Mathematics
epub The Geometry of Special Relativity download

Tevian Dray (born March 17, 1956) is an American mathematician who has worked in general relativity, mathematical physics, geometry, and both science and mathematics education.

Tevian Dray (born March 17, 1956) is an American mathematician who has worked in general relativity, mathematical physics, geometry, and both science and mathematics education. He was elected a Fellow of the American Physical Society in 2010. He has primarily worked in the area of classical general relativity

He clearly explains the interesting ways in which the geometry of space must be adapted to include time and develops the ideas of relativity in a purely geometrical form. The value of this geometrical approach is shown in a number of carefully worked examples, in which the reader is left to do some of the work and thereby acquire an intuitive understanding of the theory. Dr. Dray's book presents special relativity the way Wheeler thought about it. There was very little, if anything in this book that I hadn't previously encountered. Nonetheless, I learned a lot by reading it.

After covering special relativity again from the geometric point of view, the text discusses standard paradoxes, applications to relativistic mechanics, the relativistic unification of electricity and magnetism, and further steps leading to Einstein’s general theory of relativity. The book also briefly describes the further steps leading to Einstein’s general theory of relativity and then explores applications of hyperbola geometry to non-Euclidean geometry and calculus, including a geometric construction of the derivatives of trigonometric functions and the exponential function.

The book first describes the basic physics of special relativity to set the stage for the geometric treatment that follows.

This manuscript expands on class notes developed as part of the NSF-funded Paradigms in Physics Project

This manuscript expands on class notes developed as part of the NSF-funded Paradigms in Physics Project. It is intended either as a supplement to a traditional physics course which includes special relativity, or as a textbook for a mathematics topics course in geometry or relativity.

But special relativity has a geometry of its own: the Minkowskian geometry of spacetime, as opposed to the usual Euclidean geometry of space. Now The Geometry of Special Relativity by Tevian Dray comes along with a beautiful treatment of this much neglected approach

But special relativity has a geometry of its own: the Minkowskian geometry of spacetime, as opposed to the usual Euclidean geometry of space. Now The Geometry of Special Relativity by Tevian Dray comes along with a beautiful treatment of this much neglected approach. The book is written in an extremely clear and engaging style. There are many examples as well as exercises for the reader. Anyone who wants to have a deep understanding of special relativity should read this book. David Garfinkle, Oakland University.

Geometry of Special Relativity Dray Tevian Taylor&Francis 9781466510470 : The Geometry of Special . The book first describes the basic physics of special relativity to set the stage for the geometric treatment that follows.

Geometry of Special Relativity Dray Tevian Taylor&Francis 9781466510470 : The Geometry of Special Relativity provides an introduction to special relativity that encourages readers to see beyon.

SPECIAL RELATIVITY Tevian Dray Department of Mathematics, Oregon State University tevian. This short book treats the geometry of hyperbolas as the key to understanding special relativity

SPECIAL RELATIVITY Tevian Dray Department of Mathematics, Oregon State University tevian. Lorentz transformations are just hyperbolic rotations. c 20002003 by Tevian Dray. This short book treats the geometry of hyperbolas as the key to understanding special relativity. This approach can be summarized succinctly as the replacement of the ubiquitous symbol of most standard treatments with the appropriate hyperbolic trigonometric functions.

Tevian Dray20 octobre 2014. Requiring little more than calculus and some linear algebra, it helps readers learn just enough differential geometry to grasp the basics of general relativity. Ajouter à la liste de souhaits. The book contains two intertwined but distinct halves. Designed f. Lire la suite. Règles relatives aux avis.

Place of Publication. Introduction Newton's Relativity Einstein's RelativityThe Physics of Special Relativity Observers and Measurement The Postulates of Special Relativity Time Dilation and Length Contraction Lorentz Transformations Addition of Velocities The IntervalCircle Geometry Distance Trigonometry Triangle Trig Rotations Projections Addition FormulasHyperbola Geometry Trigonometry Distance Triangle Trig Rotations Projections Addition Formulas The Geometry of Special Relativity The Surveyors Spacetime Diagrams Lorentz Transformations Space and Time.

The Geometry of Special Relativity provides an introduction to special relativity that encourages readers to see beyond the formulas to the deeper geometric structure. The text treats the geometry of hyperbolas as the key to understanding special relativity. This approach replaces the ubiquitous γ symbol of most standard treatments with the appropriate hyperbolic trigonometric functions. In most cases, this not only simplifies the appearance of the formulas, but also emphasizes their geometric content in such a way as to make them almost obvious. Furthermore, many important relations, including the famous relativistic addition formula for velocities, follow directly from the appropriate trigonometric addition formulas.

The book first describes the basic physics of special relativity to set the stage for the geometric treatment that follows. It then reviews properties of ordinary two-dimensional Euclidean space, expressed in terms of the usual circular trigonometric functions, before presenting a similar treatment of two-dimensional Minkowski space, expressed in terms of hyperbolic trigonometric functions. After covering special relativity again from the geometric point of view, the text discusses standard paradoxes, applications to relativistic mechanics, the relativistic unification of electricity and magnetism, and further steps leading to Einstein’s general theory of relativity. The book also briefly describes the further steps leading to Einstein’s general theory of relativity and then explores applications of hyperbola geometry to non-Euclidean geometry and calculus, including a geometric construction of the derivatives of trigonometric functions and the exponential function.

Comments (6)

Andronrad
This is a great book. I suppose the first chapters of Landau and Lifschitz' book on Electrodynamics are really the best single introduction to special relativity. They're terse and physically insightful in the extreme, but this book is very special. It shows everything in the very simplest correct way, and it shows clearly and with great emphasis the geometry that can convert special relativity from strange and unintuitive to something natural. It makes everything as simple as possible, but not simpler. It's great. Rindler's book is encyclopedic, and there is no replacement for it. Woodhouse has a great point of view and is absolutely worth reading, but I think every student of special relativity will want to work through this text in all detail to obtain much greater real understanding and valid intuition. It could have been expanded, but it doesn't need expansion. Every serious student will want this book.
Kardana
The Geometry of Special Relativity introduces the reader to the hyperbolic geometric nature of special relativity. It is intuitive, easy to follow and illuminates the spacetime diagram particularly well. Prerequisites are almost none, though familiarity with special relativity helps. With a quick over view of results from special relativity, the author introduces Euclidian circle geometry, then hyperbolic geometry and from there discusses all things special relativity based.

The book starts out with using constancy of the speed of light to calculate length contraction and time dilation; the first chapter being largely an overview of what the reader is supposed to know it gives the quick calculations and diagrams associated with the Lorentz transformation. Even for the unfamiliar reader the material is approachable. The author then discusses how trigonometry is about projection of component values and then uses the idea in hyperbolic geometry to familiarize the reader with non-Euclidean projections. The author then discusses how special relativity can be viewed through the lens of hyperbolic geometry and boosts can be considered rotations. The ideas are communicated effectively through space time diagrams which is a big focus for the author to familiarize the student with. The author gives some problems to work on and discusses common paradoxes in relativity and how to resolve them using space time diagrams as well as Lorenz calculations/ The author then gets into relativistic dynamics and momentum and four-velocity. The author also goes through how to make Maxwell's equations covariant. The author also gives a flavor of what one needs to start thinking about gravity, ie differential geometry, but the discussion is just to give a flavor.

The Geometry of Special Relativity builds a lot of intuition for changing coordinates in flat spacetime and how to think about ideas in spacetime diagrams. In particular, length contractions, time dilation are all made to be understood visually through projections in hyperbolic space. Its a great book that focuses on hyperbolic geometry rather than algebra. It is not a good book to solve problems with as there are few and they are relatively straight forward. But as a supplementary text this is really good.
Runeshaper
This book really brings out the geometry/trigonometry of SR, more so than almost all other books on the subject. Most science students spend a significant amount of time using and studying trigonometry, and at least a little time using and studying hyperbolic functions (cosh x, sinh x, etc.) in calculus, an Dray takes advantage of that to make special relativity very understandable - particularly the paradoxes that give students armed with only Lorentz transformations so much trouble. This is a book that fills an important gap in the literature, and fortunately, was written by an expert that has a genuine sensitivity to the needs of his reader's/student's comprehension needs. Dray sincerely wants every reader to "get it".
Akinonris
This is a wonderful little book presenting Minkowski's 4-dimensional reformulation of special relativity, in an intuitively satisfying and accessible form without the use of imaginary coefficients.

Many physicist are unaware of the significance of Hermann Minkowski's contribution to special relativity. If there is one shortcoming in The Geometry of Special Relativity, it is an insufficient recognition of Minkowski. The approach presented is almost completely due to Minkowski's September 21, 1908 presentation. (Minkowski died suddenly January 12, 1909.) The primary difference is that Minkowski used an imaginary coefficient with Euclidean trigonometric operators, where as Dray's presentation uses the mathematically equivalent, but less confusing hyperbolic trigonometric operators.

I have read many treatments of special relativity, and have never seen it presented quite like this. The book is terse and to the point. The closest treatment (other than Minkowski's) to the one presented in The Geometry of Special Relativity that I have seen is the one that Tevian Dray acknowledges. That is the first edition of Taylor and Wheeler's Spacetime Physics.

I had the honor and privilege interacting with Dr. Wheeler. Dr. Dray's book presents special relativity the way Wheeler thought about it.

There was very little, if anything in this book that I hadn't previously encountered. Nonetheless, I learned a lot by reading it. This is the kind of book that is accessible enough for a person with little exposure to special relativity, and substantive enough to be of value to an expert in the field.

There are a few typos in the printing that I have. They have been reported, and I strongly suggest visiting the website for the errata.

Now that I have finished reading the book, the first thing I intend to do is read it again.
Nuadazius
Very well one
Gralsa
The opening chapters were very sparse. More detailed explanations would have been more helpful.

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