Illustrated Special Relativity Through Its Paradoxes: Standard Edition: A Fusion of Linear Algebra, Graphics, and Reality (Spectrum) by John de Pillis (PDF)

Description

This accessible work, with its plethora of full-color illustrations by the author, shows that linear algebra — actually, 2×2 matrices — provide a natural language for special relativity. The book includes an overview of linear algebra with all basic definitions and necessary theorems. There are exercises with hints for each chapter along with supplemental animations at special-relativity-illustrated.com. Since Einstein acknowledged his debt to Clerk Maxwell in his seminal 1905 paper introducing the theory of special relativity, we fully develop Maxwell’s four equations that unify the theories of electricity, optics, and magnetism. Using just two laboratory measurements, these equations lead to a simple calculation for the frame-independent speed of electromagnetic waves in a vacuum. (Maxwell himself was unaware that light was a special electromagnetic wave.) Before analyzing the paradoxes, we establish their linear algebraic context. Inertial frames become ( 2-dimensional vector spaces ) whose ordered spacetime pairs ( x , t ) are linked by “line-of-sight” linear transformations. These are the Galilean transformations in classical physics, and the Lorentz transformations in the more general relativistic physics. The Lorentz transformation is easily derived once we show how a novel swiveled line theorem, ( a geometric concept ) is equivalent to the speed of light being invariant for all observers a ( a physical concept ). Six paradoxes are all analyzed using Minkowski spacetime diagrams. These are (1) The Accommodating Universe paradox, (2) Time and distance asymmetry between frames, (3) The Twin paradox, (4) The Train-Tunnel paradox, (5) The Pea-Shooter paradox, and the lesser known (6) Bug-Rivet paradox. The Bug-Rivet paradox, animated by the author at Special-Relativity-Illustrated.com, presents another proof that rigidity is incompatible with special relativity. E = mc2 finds a simple derivation using only the relativistic addition of speeds ( the Pea-Shooter paradox ), conservation of momentum, and a power series. Finally, three appendices contain the self-contained overview of linear algebra, key properties of hyperbolic functions used to add relativistic speeds graphically, and a deconstruction of a moving train that proves the non-intuitive fact that when a moving train pulls into a station, its front car is always younger than its rear car, even though the front car has been in the station for a longer time. Both this standard edition (red cover) and the Deluxe edition (blue cover) contain all the previous topics. The Deluxe edition (blue cover) will add 74 pages containing chapters on Dimensional Analysis. Mathematical Rings, which also shows why a minus x minus is positive. The Scientific Method, a self-correcting intellectual invention. Mathematical Logic outlines the “algebraic” structure of thought. From this we learn that Sherlock Holmes almost never deduced anything! Early Attempts to Measure the Speed of Light, and how these primitive efforts were uncannily accurate. A bonus in this chapter is a 20-second experiment that allows the reader to measure the speed of light using any kitchen microwave.

User’s Reviews

Editorial Reviews: About the Author After training as a commercial artist, John de Pillis earned a Mechanical Engineering degree from Stevens Institute of Technology. His interests in engineering led him to obtain his Ph.D. in mathematics from the University of California at Berkeley. As Professor of Mathematics at the University of California, Riverside (UCR), he taught numerical analysis, computer science, and CGI. His research took him to Europe where he worked extensively in England, Norway, Germany and Italy in which he became Director of the student exchange program of the University of California. He is also a private pilot and illustrator.

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

⭐This book is really on three separate topics: elementary mathematics (matrices), special relativity, and Maxwell’s equations for electromagnetism. The material on special relativity is fairly standard, but the cute drawings are helpful in visualizing the effects. The treatment of Maxwell’s equations is at a level comparable with that in many introductory college physics textbooks, and is all for a single frame of reference; that is, there is no discussion of the transformation of field quantities between inertial frames (relativity).If you are looking for an introductory book that is just on special relativity there are better alternatives, particularly some of the older texts such as R. Resnick, Introduction to Special Relativity, which is generally available in used condition for a lower price than the book under review.

⭐Clear explanation of special relativity using unique graphical approach.

⭐When I saw the positive reviews of this book, I felt highly concerned since this book is not good and, in fact, can introduce many subtle misconceptions and provide wrong information to its reader. Hence, my review that I hope potential future buyers take it seriously into account.As I wrote in the title, the Mathematical Association of America (MAA) should not be publishing books with physics content! MAA does a great job with its math publications, both journals and books. However, when it attempts to publish a book with a physics content assumes a great risk which can prove quite dangerous for the reputation of the association. The risk assumed with the publication of this book, according to my opinion, has delivered a blow to the reputation of MAA. There was no serious review of the manuscript or, if a review did happen, it was done by people who did not know the subject (Relativity).There are many problems with the book and it would take a very long review to enumerate everything. Hence, I will try to state a bunch and provide a few examples.Let me start with the least serious problems. (a) This is a very pricey book for its kind. One would expect half the price or less. It is true that color has been used in the printing but, unfortunately, it serves absolutely no purposed. Therefore, a B&W version would be equally fine for the communication of the ideas. (b) The quality of the cartoons is really low. (c) The typesetting is terrible. The author thought that the more features he uses from those available to him, the greater the visual appeal. Unfortunately, this is not the case. One of the first rules of typography is to be modest with the number of features used. Any potential buyer only needs to open the sample file offered by Amazon to see the displeasing visual effect: The text is written in enumerated sections and bulleted paragraphs (similar to a shopping list) which mixes all kinds of fonts (bolded and unbolded, italics and normal, underlined and not underlined). Blue, red, and yellow colors are used, often in a very displeasing combination (such as the `line’ which separates sections). Incidentally, if you want to read an excellent book which suffers none of these problems (and those mentioned below), read Martin Gardner’s classic Relativity Simply Explained. It has beautiful illustrations in black and blue, black text in normal fonts and an amazing content. All this for $14 (Amazon price at the time of this writing.) As bonus minor problems I will mention the following: (a) If you use a pdf viewer other from Acrobat, then you may not be able to see some of the illustrations. (b) The cover of the book lists two authors. However, the dedication on page xvi of the front matter clearly identifies only de Pillis as the author of the book. So what did Jose Wudka do? I cannot be 100% sure but here is my assumption: When the book first came out, I had looked at it and the typesetting (as far as I remember) was even worse. It is possible that the second author did such improvements and, maybe, some other corrections in the text which are much harder to detect. In any case, the sloppiness with which the authorship of the book is handled is indicative of the overall book quality.Now let me move to the more serious problems. Strangely enough there is no a real preface in the book. There is a Chapter 0 entitled Preface but it is written as another chapter and calling it Introduction to Paradoxes and Our Topics would be a better title. Hence, there is no preface to explain to the reader what the goals of the book are, why it is written in such an awkward way, etc. Absolutely no information is provided for any of the idiosyncrasies. (Therefore, the author should not complain if I only guess and I rate his abilities low.)From the Amazon webpage, we learn that “This accessible work, with its plethora of full-color illustrations by the author, shows that linear algebra — actually, 2×2 matrices — provide a natural language for special relativity.” If the goal is to show the use of matrices in Relativity, then this can be done in a much more concise way. I could rewrite his material (in the same style) in 33% of the pages he used, perhaps even less. And again: The color illustrations are not necessary although it is always good to have visual diagrams. Perhaps, this book should be marketed as an exposition of Relativity. This is after all what the book title suggests. As a Relativity text, the `shopping list’ presentation style mentioned previously creates a fragmented delivery of information that I find highly misleading and impossible to present the full essence and value of any topic.Unfortunately the author is not familiar with physics. As a result, the book is plagues with lots of mistakes and misconceptions despite the fact that author thinks that he has mastered the discussed topics. Let me provide some examples: 1. The postulates of Relativity (1.52) are stated incorrectly. In the first postulate, Quantum Mechanics is not included since there was no such theory at the time Relativity was born. However, if one wants to include it, it is already present since Quantum Mechanics is really Mechanics combined with Electromagnetism wherever needed. The second postulate talks only about the source and states that “light is emitted in vacuum with speed c irrespective of the motion of the source” . As a result of the two postulates, it can be proved that the speed of light is the same in all frames — i.e. this statement is a theorem. A mathematician must be more careful with axioms and theorems.2. The author does not use the accepted terminology (sometimes intentionally, sometimes unaware of such issue). For the example, to create an effect, he calls the Lorentz factor the shrinking factor. However, this shrinking factor gives also expansion, not only shrinking! Using this terminology introduces a mental biases in the minds of young readers that may be hard to undo later.3. In Section (11.4.3b) the author claims that the twin paradox is a result of acceleration. However this is not true! The twin paradox exists without acceleration. The initial name of the paradox was `Clock Paradox’. The readings of the clocks of the moving frames are compared as the frames are passing from the same points. No person has to jump from frame to frame. In Section (11.5) he uses General Relativity to persuade us that the Twin Paradox is real! He converts acceleration to gravity and from this he tells us about the discrepancy. Unfortunately for the author, he has not understood that the acceleration is not the key player in the resolution; the key player is the underlying asymmetry.4. The author talks about rest mass. It has been known for long time that there is no rest mass, only mass of a particle. The moving and rest mass were introduced early in Relativity when physicists were still trying to understand the theory better. Once, the concepts were understood, the separation to rest and moving was dropped since it creates inconsitencies and only people who do not understand Relativity make this mistake.5. In principle, equation (15.2.3a) is incorrect since the author does not explain anything about the interaction of particles. This equation needs considerable discussion.The above list can be continued on and on. However, I have no time and no energy to write such a precise and long list. However, as a result of my evaluation, I want to let readers know that many mistakes exist throughout this book and it would be a mistake to use it as a source of learning anything in Relativity.

⭐This book, which is most excellent, contains many new features:1. Full-color animations and illustrations that give genuine insight to the topics.2. A self-contained development of Maxwell’s equations with which the reader can calculate (as did Maxwell himself) the speed of light using only two laboratory measurements.3. A mini-course on the theory of matrices (linear algebra) that includes the matrix decomposition theorem used for a novel linear algebraic approach to the Lorentz transformation.4. A simple proof of E = mc^2 using relativistic addition of speeds and a power series.5. Six paradoxes of special relativity that are all analyzed within the single, unifying intellectual framework of Minkowski diagrams. One notable example is the Bug-Rivet Paradox that also provides another way to see that special relativity is incompatible with rigidity of bodies.Before reading this book, I did not realize that the frame-dependent Maxwell’s equations lead to a frame-independent calculation of the speed c of electromagnetic (EM) waves in a vacuum. (We read that Maxwell did not know that light was a special case of EM waves, but he suspected a connection since the speeds were the same.) That is to say, Maxwell showed that the speed c is independent of the speed of both observer and of source, which is a key assumption in Einstein’s 1905 paper which introduced the theory of special relativity. As this book notes, in the very opening paragraph of his 1905 paper, Einstein acknowledges his debt to Maxwell. This acknowledgment minimizes the importance of whether Einstein knew, or did not know, of the 1887 Michelson-Morley experiment that showed no aether existed that would necessarily cause c to depend on the speed of an observer.I especially liked the linking of graphical concepts with physics. For example, an intuitive “swiveled line theorem” (a geometric phenomenon) is shown to correspond exactly to the speed of light being constant for all observers (a physical property).It is essential to note that this book, for the first time, applies 2×2 matrices to inertial frames moving at constant relative speeds, to give an easy derivation of the Lorentz transformation. This derivation becomes a matter of bookkeeping once the linkto the swiveled line theorem is established.Anyone with an interest in special relativity and its paradoxes will find this book, with its full-color illustrations and self-contained sections on Maxwell’s equations and linear algebra, along with its clear derivation of E=mc^2, to be an excellent single resource.We want to note that the author, John de Pillis, in another book

⭐, beginning on page 248, develops a very nice connection between the Pythagorean theorem [a triangle with sides a, b, and c is a right triangle if and only if a^2 + b^2 = c^2] and special relativity. Along the way you get rewarded with the very nice Tom Lehrer / Bob Osserman pizza connection.

⭐This book was just at the level I was hoping for; after having read one or two ‘popular science’ books on relativity which in the main aimed to keep the use of mathematics to a minimum, I felt i was ready for something a little more in-depth and that used more mathematics for its exposition. I found this in this book. I also liked the approach whereby the ‘paradoxes’ of relativity were described and then resolved. A great book that is not stuffy and yet informative, though clearly I would not recommend it for someone who wants the mathematics kept to a minimum (for that I might recommend Hawking and Mlodinow’s book The Grand Design, or the Manga Guide to Relativity perhaps).

⭐El libro es fantástico, las ilustraciones están llenas de color y son geniales, las explicaciones son realmente claras e ilustrativas, tengo 50 años y para mi la letra es pequeña pero esta bien.

⭐

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