The Geometry of Special Relativity 1st Edition by Tevian Dray (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

⭐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.

⭐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.

⭐This thoughtful and straight-to-the-point book will give you insight and understanding that is hard to come by. A true gem.

⭐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”.

⭐The opening chapters were very sparse. More detailed explanations would have been more helpful.

⭐Very well one

⭐This is a book which promises much but fails to deliver. After a good summary of the basic results of the special theory it can not then decide if it’s an elementary book offering a useful alternative interpretation of the basic results or not. For example it describes the dot product as to a beginner and then presents some no intuitive results in a foot note with a partial derivation of them and declaring that the bit left out involves some difficult integration but doesn’t show it. Hopeless.

⭐Special relativity is an option for those doing I.B. Diploma physics. Unfortunately the presentation of this topic in what is meant to be one of the better texts for this syllabus is pathetic. So, I decided to get this book and would certainly recommend it. Its approach may be a bit different, but that’s part of the appeal.Unlike the writer of the high school text, Dray knows what he is writing about.

⭐I took this book into hospital with me as something to read and study and it was a joy to read and work through the approach. It is clear and basic but it introduces you to Minkowskian space and using it to calculate problems with.Straight forward for me to understand with my background as a mathematics teacher and an elegant way of introducing Special Relativity.A damn good read.

⭐Avevo bisogno di farmi un’idea della Geometria di Lorentz e di capire un po’ come usarla, e questo libretto è stato veramente utile. Avrei solo preferito che fosse un po’ più particolareggiato nella trattazione.

⭐

⭐This books sets a period after all the quarrels about misunderstanding and false explanations.Time dilatation and length contraction are explained in a correct way, leaving no room for misinterpretations.

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