Download or read book Illustrated Special Relativity through Its Paradoxes A Fusion of Linear Algebra Graphics and Reality written by John dePillis and published by American Mathematical Soc.. This book was released on 2013-12-31 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Assuming a minimum of technical expertise beyond basic matrix theory, the authors introduce inertial frames and Minkowski diagrams to explain the nature of simultaneity, why faster-than-light travel is impossible, and the proper way to add velocities. We resolve the twin paradox, the train-in-tunnel paradox, the pra-shooter paradox along with the lesser-known bug-rivet paradox that shows how rigidity is incompatible with special relativity. Since Einstein in his seminal 1905 paper introducing special relativity, acknowledged his debt to Clerk Maxwell, we fully develop Maxwell's four equations that unify the theories of electricity, optics, and magnetism. These equations also lead to a simple calculation for the frame independent speed of electromagnetic waves in a vacuum."--Cover.

Download or read book Illustrated Special Relativity Through Its Paradoxes written by John de Pillis and published by J Depillis Illustrations. This book was released on 2014-08-21 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. The appendices The self-contained overview of linear algebra, key properties of hyperbolic functions used to add relativistic speeds graphically, 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.

Download or read book Very Special Relativity written by Sander Bais and published by Harvard University Press. This book was released on 2007 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Einstein's Special Theory of Relativity, first published in 1905, radically changed our understanding of the world. Familiar notions of space and time and energy were turned on their head, and our struggle with Einstein's counterintuitive explanation of these concepts was under way. The task is no easier today than it was a hundred years ago, but in this book Sander Bais has found an original and uniquely effective way to convey the fundamental ideas of Einstein's Special Theory. Bais's previous book, The Equations, was widely read and roundly praised for its clear and commonsense explanation of the math in physics. Very Special Relativity brings the same accessible approach to Einstein's theory. Using a series of easy-to-follow diagrams and employing only elementary high school geometry, Bais conducts readers through the quirks and quandaries of such fundamental concepts as simultaneity, causality, and time dilation. The diagrams also illustrate the difference between the Newtonian view, in which time was universal, and the Einsteinian, in which the speed of light is universal. Following Bais's straightforward sequence of simple, commonsense arguments, readers can tinker with the theory and its great paradoxes and, finally, arrive at a truly deep understanding of Einstein's interpretation of space and time. An intellectual journey into the heart of the Special Theory, the book offers an intimate look at the terms and ideas that define our reality.

Download or read book The Geometry of Special Relativity written by Tevian Dray and published by CRC Press. This book was released on 2012-07-02 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Mathematical and Algorithmic Puzzles written by Pramod Ganapathi and published by . This book was released on 2024-05-29 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents serious mathematical and algorithmic puzzles that are mostly counterintuitive. The presented puzzles are simultaneously entertaining, challenging, intriguing, and haunting. This book introduces its readers to counterintuitive mathematical ideas and revolutionary algorithmic insights from a wide variety of topics. The presented solutions that are discovered by many mathematicians and computer scientists are highly counterintuitive and show supreme mathematical beauty. These counterintuitive solutions are intriguing to the degree that they shatter our preconceived notions, shake our long-held belief systems, debunk our fundamental intuitions, and finally rob us of sleep and haunt us for a lifetime. Multiple ways of attacking the same puzzle are presented which teach the application of elegant problem-solving strategies.

Download or read book The G H Hardy Reader written by Donald J. Albers and published by Cambridge University Press. This book was released on 2016-04-11 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: G. H. Hardy ranks among the greatest twentieth-century mathematicians. This book introduces this extraordinary individual and his writing.

Download or read book I Mathematician written by Peter Casazza and published by The Mathematical Association of America. This book was released on 2015-03-10 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematicians have pondered the psychology of the members of our tribe probably since mathematics was invented, but for certain since Hadamard’s The Psychology of Invention in the Mathematical Field. The editors asked two dozen prominent mathematicians (and one spouse thereof) to ruminate on what makes us different. The answers they got are thoughtful, interesting and thought-provoking. Not all respondents addressed the question directly. Michael Atiyah reflects on the tension between truth and beauty in mathematics. T.W. Körner, Alan Schoenfeld and Hyman Bass chose to write, reflectively and thoughtfully, about teaching and learning. Others, including Ian Stewart and Jane Hawkins, write about the sociology of our community. Many of the contributions range into philosophy of mathematics and the nature of our thought processes. Any mathematician will find much of interest here.

Download or read book How Euler Did Even More written by C. Edward Sandifer and published by The Mathematical Association of America. This book was released on 2014-11-19 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sandifer has been studying Euler for decades and is one of the world’s leading experts on his work. This volume is the second collection of Sandifer’s “How Euler Did It” columns. Each is a jewel of historical and mathematical exposition. The sum total of years of work and study of the most prolific mathematician of history, this volume will leave you marveling at Euler’s clever inventiveness and Sandifer’s wonderful ability to explicate and put it all in context.

Download or read book Phi Pi e and i written by David Perkins and published by American Mathematical Soc.. This book was released on 2018-10-10 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Certain constants occupy precise balancing points in the cosmos of number, like habitable planets sprinkled throughout our galaxy at just the right distances from their suns. This book introduces and connects four of these constants (φ,Π,e, and i), each of which has recently been the individual subject of historical and mathematical expositions. But here we discuss their properties, as a group, at a level appropriate for an audience armed only with the tools of elementary calculus. This material offers an excellent excuse to display the power of calculus to reveal elegant truths that are not often seen in college classes. These truths are described here via the work of such luminaries as Nilakantha, Liu Hui, Hemachandra, Khayyam, Newton, Wallis, and Euler.

Download or read book American Mathematics 1890 1913 written by Steve Batterson and published by The Mathematical Association of America. This book was released on 2017-06-29 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the turn of the twentieth century, mathematical scholarship in the United States underwent a stunning transformation. In 1890 no American professor was producing mathematical research worthy of international attention. Graduate students were then advised to pursue their studies abroad. By the start of World War I the standing of American mathematics had radically changed. George David Birkhoff, Leonard Dickson, and others were turning out cutting edge investigations that attracted notice in the intellectual centers of Europe. Harvard, Chicago, and Princeton maintained graduate programs comparable to those overseas. This book explores the people, timing, and factors behind this rapid advance. Through the mid-nineteenth century most American colleges followed a classical curriculum that, in mathematics, rarely reached beyond calculus. With no doctoral programs of any sort in the United States until 1860, mathematical scholarship lagged far behind that in Europe. After the Civil War, visionary presidents at Harvard and Johns Hopkins broadened and deepened the opportunities for study. The breakthrough for mathematics began in 1890 with the hiring, in consecutive years, of William F. Osgood and Maxime Bôcher at Harvard and E. H. Moore at Chicago. Each of these young men had studied in Germany where they acquired vital mathematical knowledge and taste. Over the next few years Osgood, Bôcher, and Moore established their own research programs and introduced new graduate courses. Working with other like-minded individuals through the nascent American Mathematical Society, the infrastructure of meetings and journals were created. In the early twentieth century Princeton dramatically upgraded its faculty to give the United States the stability of a third mathematics center. The publication by Birkhoff, in 1913, of the solution to a famous conjecture served notice that American mathematics had earned consideration with the European powers of Germany, France, Italy, England, and Russia.

Download or read book Half a Century of Pythagoras Magazine written by Alex Van Den Brandhof and published by The Mathematical Association of America. This book was released on 2015-09-29 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Half a Century of Pythagoras Magazine is a selection of the best and most inspiring articles from this Dutch magazine for recreational mathematics. Founded in 1961 and still thriving today, Pythagoras has given generations of high school students in the Netherlands a perspective on the many branches of mathematics that are not taught in schools. The book contains a mix of easy, yet original puzzles, more challenging - and at least as original – problems, as well as playful introductions to a plethora of subjects in algebra, geometry, topology, number theory and more. Concepts like the sudoku and the magic square are given a whole new dimension. One of the first editors was a personal friend of world famous Dutch graphic artist Maurits Escher, whose 'impossible objects' have been a recurring subject over the years. Articles about his work are part of a special section on 'Mathematics and Art'. While many books on recreational mathematics rely heavily on 'folklore', a reservoir of ancient riddles and games that are being recycled over and over again, most of the puzzles and problems in Half a Century of Pythagoras Magazine are original, invented for this magazine by Pythagoras' many editors and authors over the years. Some are no more than cute little brainteasers which can be solved in a minute, others touch on profound mathematics and can keep the reader entranced indefinitely. Smart high school students and anyone else with a sharp and inquisitive mind will find in this book a treasure trove which is rich enough to keep his or her mind engaged for many weeks and months.

Download or read book Special Relativity written by Michael Tsamparlis and published by Springer Science & Business Media. This book was released on 2010-05-17 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: Writing a new book on the classic subject of Special Relativity, on which numerous important physicists have contributed and many books have already been written, can be like adding another epicycle to the Ptolemaic cosmology. Furthermore, it is our belief that if a book has no new elements, but simply repeats what is written in the existing literature, perhaps with a different style, then this is not enough to justify its publication. However, after having spent a number of years, both in class and research with relativity, I have come to the conclusion that there exists a place for a new book. Since it appears that somewhere along the way, mathem- ics may have obscured and prevailed to the degree that we tend to teach relativity (and I believe, theoretical physics) simply using “heavier” mathematics without the inspiration and the mastery of the classic physicists of the last century. Moreover current trends encourage the application of techniques in producing quick results and not tedious conceptual approaches resulting in long-lasting reasoning. On the other hand, physics cannot be done a ́ la carte stripped from philosophy, or, to put it in a simple but dramatic context A building is not an accumulation of stones! As a result of the above, a major aim in the writing of this book has been the distinction between the mathematics of Minkowski space and the physics of r- ativity.

Download or read book Relativity the Special and General Theory written by Albert Albert Einstein and published by . This book was released on 2017-12-17 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why buy our paperbacks? Expedited shipping High Quality Paper Made in USA Standard Font size of 10 for all books 30 Days Money Back Guarantee BEWARE of Low-quality sellers Don't buy cheap paperbacks just to save a few dollars. Most of them use low-quality papers & binding. Their pages fall off easily. Some of them even use very small font size of 6 or less to increase their profit margin. It makes their books completely unreadable. How is this book unique? Unabridged (100% Original content) Font adjustments & biography included Illustrated Relativity: the Special and General Theory by Albert Einstein According to Einstein himself, this book is intended "to give an exact insight into the theory of Relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus of theoretical physics." When he wrote the book in 1916, Einstein's name was scarcely known outside the physics institutes. Having just completed his masterpiece, The General Theory of Relativity-which provided a brand-new theory of gravity and promised a new perspective on the cosmos as a whole-he set out at once to share his excitement with as wide a public as possible in this popular and accessible book.

Download or read book Special Relativity written by Thomas M. Helliwell and published by . This book was released on 2010 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written in an clear and informal style, this text explores the most accessible of the 20th century revolutions in physics. It allows readers to build up physical intuition for what is going on, before presenting concise mathematical descriptions. It contains many applications, ten appendices, and numerous illustrations, examples and problems.

Download or read book Paradoxes in the Theory of Relativity written by Yakov Terletskii and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: That Einstein's insight was profound goes without saying. A strildng indication of its depth is the abundance of unexpected riches that others have found in his work - riches reserved for those daring to give serious attention to implications that at first sight seem unphysical. A famous instance is that of the de Broglie waves. If, in ac cordance with Fermat's principle, a photon followed the path of least time, de Broglie felt that the photon should have some phys ical means of exploring alternative paths to determine which of them would in fact require the least time. For this and other rea sons, he assumed that the photon had a nonvanishing rest mass, and, in accordance with Einstein's E = h v, he endowed the photon with a spread-out pulsation of the form A Sin(27TEt/h) in the photon's rest frame. According to the theory of relativity such a pulsation, every where simultaneous in a given frame, seemed absurd as a physical entity. Nevertheless de Broglie took it seriously, applied a Lorentz transformation in the orthodox relativistic tradition, and found that the simultaneous pulsation was transformed into a wave whose phase velocity was finite but greater than c while its group velocity was that of the particle. By thus pursuing Einsteinian concepts into thickets that others had not dared to penetrate, de Broglie laid the brilliant foundations of wave mechanics.

Download or read book Paradoxes of Time Travel written by Ryan Wasserman and published by Oxford University Press. This book was released on 2018 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ryan Wasserman explores a range of fascinating puzzles raised by the possibility of time travel, with entertaining examples from physics, science fiction, and popular culture, and he draws out their implications for our understanding of time, tense, freedom, fatalism, causation, counterfactuals, laws of nature, persistence, change, and mereology.

Download or read book Relativity for the Questioning Mind written by Daniel F. Styer and published by JHU Press. This book was released on 2011-03 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: To those of us who are not mathematicians or physicists, Einstein’s theory of relativity often seems incomprehensible, exotic, and of little real-world use. None of this is true. Daniel F. Styer’s introduction to the topic not only shows us why these beliefs are mistaken but also shines a bright light on the subject so that any curious-minded person with an understanding of algebra and geometry can both grasp and apply the theory. Styer starts off slowly and proceeds carefully, explaining the concepts undergirding relativity in language comprehensible to nonscientists yet precise and accurate enough to satisfy the most demanding professional. He demonstrates how the theory applies to various real-life situations with easy equations and simple, clear diagrams. Styer's classroom-tested method of conveying the core ideas of relativity—the relationship among and between time, space, and motion and the behavior of light—encourages questions and shows the way to finding the answers. Each of the book’s four parts builds on the sections that come before, leading the reader by turn through an overview of foundational ideas such as frames of reference, revelatory examples of time dilation and its attendant principles, an example-based exploration of relativity, and explanations of how and why gravity and spacetime are linked. By demonstrating relativity with practical applications, Styer teaches us to truly understand and appreciate its importance, beauty, and usefulness. Featuring worked and end-of-chapter problems and illustrated, nontechnical explanations of core concepts, while dotted throughout with questions and answers, puzzles, and paradoxes, Relativity for the Questioning Mind is an enjoyable-to-read, complete, concise introduction to one of the most important scientific theories yet discovered. The appendixes provide helpful hints, basic answers to the sample problems, and materials to stimulate further exploration.