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This accessible work, with its plethora of full-color illustrations by the author, shows that linear algebra --- actually, 2x2 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.
- Sales Rank: #2815531 in Books
- Published on: 2014-01-16
- Original language: English
- Number of items: 1
- Dimensions: 10.00" h x .91" w x 7.00" l, 2.05 pounds
- Binding: Paperback
- 384 pages
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.
Most helpful customer reviews
4 of 4 people found the following review helpful.
A most excellent book about Einstein's theory of special relativity
By Al Kelley
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 2x2 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 link
to 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 777 Mathematical Conversation Starters (Spectrum), 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.
2 of 2 people found the following review helpful.
Learn Special Relativity with rigor and fun
By David Ellerman
This book presents a new approach to explaining SR using basic linear algebra which is important and illuminating in itself, but it is all illustrated with attractive and humorous diagrams. Einstein was actually motivated, not by the Michelson-Morley Experiment, by certain apparent asymmetries in the Maxwell's equations so the book explores that approach in a welcome contrast to just giving instrumental definitions of simultaneity and distance in the usual textbook treatments.
The understanding and enjoyment is deepened by using the approach to explain some "paradoxes" such as the well-known twins paradox and the less well-known bug-rivet paradox (with a simple slinky illustration). Once you have worked through the bug-rivet paradox, you (and your students) will not forget the lessons!
2 of 3 people found the following review helpful.
Adding some fun, and lots of insight, to Special Relativity!
By Amazon Customer
Decades after studying Special Relativity, it was a treat to encounter this approach to the subject - bringing full-color illustrations together with many of the paradoxes of the subject. While the illustrations provide an informal touch to understanding the subject, this book is also a serious contribution. The role of linear algebra is emphasized, vector fields make a strong appearance in the development of Maxwell's equations, and rigor is used to firmly establish many relationships.
While some of the paradoxes used to develop the subject are classic, others were new to me. As noted by another reviewer, the rivet-bug paradox was especially interesting. The action of instantly stopping the motion of the rivet has to result in a stretching of the rivet as the signal to stop propagates down the length, otherwise causality would be violated. (The similarity of this with the question of what happens when a suspended "slinky" is released is developed following the rivet-bug analysis.)
Another development which was new to me concerned using Maxwell's equations to demonstrate the invariance of the speed of light (or any electro-magnetic wave) relative to a moving observer. Bits of history make brief appearances throughout the book, with descriptions of classic experiments relating the theory to the lab.
I would strongly recommend this book to anyone with some background in university-level mathematics and physics. Even with less of a background, the illustrations may be sufficient to provide some basic ideas behind Special Relativity. There are links provided to online animations which provide a further easing into the subject.
This is a very complete book, and the illustrations are a wonderful complement to the theory.
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