{"product_id":"9780615947655","title":"Illustrated Special Relativity Through Its Paradoxes: Standard Edition: A Fusion of Linear Algebra, Graphics, and Reality","description":"\u003cp\u003e\u003cb\u003eThis accessible work,\u003c\/b\u003e \u003cbr\u003ewith its plethora of \u003cbr\u003e\u003cu\u003efull-color\u003c\/u\u003e\u003cbr\u003e 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 \u003cbr\u003e\u003c\/p\u003e\u003cul\u003especial-relativity-illustrated.com.\u003c\/ul\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003e\u003cbr\u003eSince Einstein acknowledged \u003cbr\u003e\u003c\/b\u003e\u003cbr\u003ehis 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. \u003cbr\u003e(\u003ci\u003eMaxwell himself was unaware that light was a special electromagnetic wave.\u003c\/i\u003e) \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eBefore analyzing the paradoxes,\u003c\/b\u003e\u003cbr\u003e we establish their linear algebraic context. Inertial frames become\u003cbr\u003e( 2-\u003ci\u003edimensional vector spaces\u003c\/i\u003e ) \u003cbr\u003ewhose ordered spacetime pairs ( \u003ci\u003ex , t\u003c\/i\u003e ) are linked by \"line-of-sight\" linear transformations. \u003cbr\u003eThese 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, \u003cbr\u003e( \u003ci\u003ea geometric concept\u003c\/i\u003e )\u003cbr\u003eis equivalent to the speed of light being invariant for all observers a \u003cbr\u003e( \u003ci\u003ea physical concept\u003c\/i\u003e ).\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eSix paradoxes are all analyzed\u003c\/b\u003e\u003cbr\u003e 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 \u003cbr\u003e\u003cu\u003erigidity\u003c\/u\u003e \u003cbr\u003eis incompatible with \u003cbr\u003e\u003cu\u003especial relativity\u003c\/u\u003e.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eE = mc\u003csup\u003e2\u003c\/sup\u003e\u003c\/b\u003e \u003cbr\u003efinds a simple derivation using only the relativistic addition of speeds ( \u003ci\u003ethe Pea-Shooter paradox \u003c\/i\u003e ), conservation of momentum, and a power series.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eFinally, three appendices\u003c\/b\u003e contain the self-contained overview of linear algebra, \u003cbr\u003ekey 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.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003chr\u003e\u003cp\u003eBoth \u003cbr\u003e\u003cu\u003ethis standard edition (red cover)\u003c\/u\u003e \u003cbr\u003eand the Deluxe edition (blue cover) contain all the previous topics. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eThe Deluxe edition\u003c\/b\u003e (blue cover)\u003cbr\u003ewill add 74 pages containing chapters on\u003cbr\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003e Dimensional Analysis.\u003c\/li\u003e\n\u003cli\u003e Mathematical Rings, which also shows why a minus x minus is positive.\u003c\/li\u003e\n\u003cli\u003e The Scientific Method, a self-correcting intellectual invention.\u003c\/li\u003e\n\u003cli\u003e Mathematical Logic outlines the \"algebraic\" structure of thought. From this we learn that Sherlock Holmes almost never deduced anything!\u003c\/li\u003e\n\u003cli\u003e 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.\u003cbr\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003e\u003c\/p\u003e","brand":"J dePillis Illustrations","offers":[{"title":"Default Title","offer_id":50032144023792,"sku":"9780615947655","price":74.99,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9780615947655_p0.jpg?v=1784234972","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9780615947655","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}