Book Description:
This accessible work, with its plethora of fullcolor 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
 specialrelativityillustrated.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 frameindependent 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 ( 2dimensional vector spaces ) whose ordered spacetime pairs ( x , t ) are linked by “lineofsight” 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 TrainTunnel paradox, (5) The PeaShooter paradox, and the lesser known (6) BugRivet paradox. The BugRivet paradox, animated by the author at SpecialRelativityIllustrated.com, presents another proof that rigidity is incompatible with special relativity.
E = mc^{2} finds a simple derivation using only the relativistic addition of speeds ( the PeaShooter paradox ), conservation of momentum, and a power series.
Finally, three appendices contain the selfcontained 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 nonintuitive 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 selfcorrecting 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 20second experiment that allows the reader to measure the speed of light using any kitchen microwave.
Book Details:
Illustrated Special Relativity Through Its Paradoxes PDF: A Fusion Of Linear Algebra Graphics And Reality 

Author  John de Pillis 
Isbn  0615947654 
File size  6 Mb 
Year  2014 
Pages  384 
Language  English 
File format  
Category  Mathematics 
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