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|A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity
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Author: Peter Collier
(1) "Fantastic book ... very easy to follow and leads you gradually and gently to the full mathematical detail of general relativity." (2) "Highly recommended for anyone willing to invest some time and effort." - Amazon.com
(1) " ... do not be put off by the title! This is a great book on relativity which nicely bridges the gap between those books catering for readers who know little or nothing about relativity and those texts intended for physics mathematical specialists." (2) "A new gold standard for physics books." (3) "A unique book. Well done the author." - Amazon.co.uk
Based on the concept of four-dimensional spacetime - curved in the vicinity of mass-energy, flat in its absence - Einstein's theories of special and general relativity together form a cornerstone of modern physics. Special relativity has some strangely counter-intuitive consequences, including time dilation, length contraction, the relativity of simultaneity and mass-energy equivalence, whilst general relativity is at the heart of our understanding of black holes and the evolution of the universe.
Using straightforward, accessible language, with numerous fully solved problems and clear derivations and explanations, this book is aimed at the enthusiastic general reader who wants to move beyond maths-lite popularisations and tackle the essential mathematics of this fascinating theory. (To paraphrase Euclid, there is no royal road to relativity - you have to do the mathematics.) For those with minimal mathematical background, the first chapter provides a crash course in foundation mathematics. The reader is then taken gently by the hand and guided through a wide range of fundamental topics, including Newtonian mechanics; the Lorentz transformations; tensor calculus; the Einstein field equations; the Schwarzschild solution; the four classical tests of general relativity; simple black holes; the mysteries of dark energy and the cosmological constant; and the Friedmann equations and Friedmann-Robertson-Walker cosmological models.
Understand even the basics of Einstein's amazing theory and the world will never seem the same again.
1 Foundation mathematics
2 Newtonian mechanics
3 Special relativity
4 Introducing the manifold
5 Scalars, vectors, one-forms and tensors
6 More on curvature
7 General relativity
8 The Newtonian limit
9 The Schwarzschild metric
10 Schwarzschild black holes
Appendix - Planetary motion data
|Einstein: His Life and Universe
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Author: Walter Isaacson
Brand: Baker and Taylor
By the author of the acclaimed bestsellers Benjamin Franklin and Steve Jobs, this is the definitive biography of Albert Einstein.
How did his mind work? What made him a genius? Isaacson’s biography shows how his scientific imagination sprang from the rebellious nature of his personality. His fascinating story is a testament to the connection between creativity and freedom.
Based on newly released personal letters of Einstein, this book explores how an imaginative, impertinent patent clerk—a struggling father in a difficult marriage who couldn’t get a teaching job or a doctorate—became the mind reader of the creator of the cosmos, the locksmith of the mysteries of the atom, and the universe. His success came from questioning conventional wisdom and marveling at mysteries that struck others as mundane. This led him to embrace a morality and politics based on respect for free minds, free spirits, and free individuals.
These traits are just as vital for this new century of globalization, in which our success will depend on our creativity, as they were for the beginning of the last century, when Einstein helped usher in the modern age.
As a scientist, Albert Einstein is undoubtedly the most epic among 20th-century thinkers. Albert Einstein as a man, however, has been a much harder portrait to paint, and what we know of him as a husband, father, and friend is fragmentary at best. With Einstein: His Life and Universe, Walter Isaacson (author of the bestselling biographies Benjamin Franklin and Kissinger) brings Einstein's experience of life, love, and intellectual discovery into brilliant focus. The book is the first biography to tackle Einstein's enormous volume of personal correspondence that heretofore had been sealed from the public, and it's hard to imagine another book that could do such a richly textured and complicated life as Einstein's the same thoughtful justice. Isaacson is a master of the form and this latest opus is at once arresting and wonderfully revelatory. --Anne Bartholomew
Read "The Light-Beam Rider," the first chapter of Walter Isaacson's Einstein: His Life and Universe.
Five Questions for Walter Isaacson
Amazon.com: What kind of scientific education did you have to give yourself to be able to understand and explain Einstein's ideas?
Isaacson: I've always loved science, and I had a group of great physicists--such as Brian Greene, Lawrence Krauss, and Murray Gell-Mann--who tutored me, helped me learn the physics, and checked various versions of my book. I also learned the tensor calculus underlying general relativity, but tried to avoid spending too much time on it in the book. I wanted to capture the imaginative beauty of Einstein's scientific leaps, but I hope folks who want to delve more deeply into the science will read Einstein books by such scientists as Abraham Pais, Jeremy Bernstein, Brian Greene, and others.
Amazon.com: That Einstein was a clerk in the Swiss Patent Office when he revolutionized our understanding of the physical world has often been treated as ironic or even absurd. But you argue that in many ways his time there fostered his discoveries. Could you explain?
Isaacson: I think he was lucky to be at the patent office rather than serving as an acolyte in the academy trying to please senior professors and teach the conventional wisdom. As a patent examiner, he got to visualize the physical realities underlying scientific concepts. He had a boss who told him to question every premise and assumption. And as Peter Galison shows in Einstein's Clocks, Poincare's Maps, many of the patent applications involved synchronizing clocks using signals that traveled at the speed of light. So with his office-mate Michele Besso as a sounding board, he was primed to make the leap to special relativity.
Amazon.com: That time in the patent office makes him sound far more like a practical scientist and tinkerer than the usual image of the wild-haired professor, and more like your previous biographical subject, the multitalented but eminently earthly Benjamin Franklin. Did you see connections between them?
Isaacson: I like writing about creativity, and that's what Franklin and Einstein shared. They also had great curiosity and imagination. But Franklin was a more practical man who was not very theoretical, and Einstein was the opposite in that regard.
Amazon.com: Of the many legends that have accumulated around Einstein, what did you find to be least true? Most true?
Isaacson: The least true legend is that he failed math as a schoolboy. He was actually great in math, because he could visualize equations. He knew they were nature's brushstrokes for painting her wonders. For example, he could look at Maxwell's equations and marvel at what it would be like to ride alongside a light wave, and he could look at Max Planck's equations about radiation and realize that Planck's constant meant that light was a particle as well as a wave. The most true legend is how rebellious and defiant of authority he was. You see it in his politics, his personal life, and his science.
Amazon.com: At Time and CNN and the Aspen Institute, you've worked with many of the leading thinkers and leaders of the day. Now that you've had the chance to get to know Einstein so well, did he remind you of anyone from our day who shares at least some of his remarkable qualities?
Isaacson: There are many creative scientists, most notably Stephen Hawking, who wrote the essay on Einstein as "Person of the Century" when I was editor of Time. In the world of technology, Steve Jobs has the same creative imagination and ability to think differently that distinguished Einstein, and Bill Gates has the same intellectual intensity. I wish I knew politicians who had the creativity and human instincts of Einstein, or for that matter the wise feel for our common values of Benjamin Franklin.
More to Explore
|The Perfect Theory: A Century of Geniuses and the Battle over General Relativity
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Author: Prof. Pedro G. Ferreira
How did one elegant theory incite a scientific revolution? Physicists have been exploring, debating, and questioning the general theory of relativity ever since Albert Einstein first presented it in 1915. Their work has uncovered a number of the universe’s more surprising secrets, and many believe further wonders remain hidden within the theory’s tangle of equations, waiting to be exposed. In this sweeping narrative of science and culture, astrophysicist Pedro Ferreira brings general relativity to life through the story of the brilliant physicists, mathematicians, and astronomers who have taken up its challenge. For these scientists, the theory has been both a treasure trove and an enigma, fueling a century of intellectual struggle and triumph.. Einstein’s theory, which explains the relationships among gravity, space, and time, is possibly the most perfect intellectual achievement of modern physics, yet studying it has always been a controversial endeavor. Relativists were the target of persecution in Hitler’s Germany, hounded in Stalin’s Russia, and disdained in 1950s America. Even today, PhD students are warned that specializing in general relativity will make them unemployable. Despite these pitfalls, general relativity has flourished, delivering key insights into our understanding of the origin of time and the evolution of all the stars and galaxies in the cosmos. Its adherents have revealed what lies at the farthest reaches of the universe, shed light on the smallest scales of existence, and explained how the fabric of reality emerges. Dark matter, dark energy, black holes, and string theory are all progeny of Einstein’s theory. We are in the midst of a momentous transformation in modern physics. As scientists look farther and more clearly into space than ever before, The Perfect Theory reveals the greater relevance of general relativity, showing us where it started, where it has led, and where it can still take us.
|Six Easy Pieces: Essentials of Physics Explained by Its Most Brilliant Teacher
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Author: Richard P. Feynman
Brand: Basic Books
The six easiest chapters from Feynman's landmark work, Lectures on Physics-specifically designed for the general, non-scientist reader.
|Flatland: A Romance of Many Dimensions (Dover Thrift Editions)
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Author: Edwin A. Abbott
This masterpiece of science (and mathematical) fiction is a delightfully unique and highly entertaining satire that has charmed readers for more than 100 years. The work of English clergyman, educator and Shakespearean scholar Edwin A. Abbott (1838-1926), it describes the journeys of A. Square, a mathematician and resident of the two-dimensional Flatland, where women-thin, straight lines-are the lowliest of shapes, and where men may have any number of sides, depending on their social status.
Through strange occurrences that bring him into contact with a host of geometric forms, Square has adventures in Spaceland (three dimensions), Lineland (one dimension) and Pointland (no dimensions) and ultimately entertains thoughts of visiting a land of four dimensions—a revolutionary idea for which he is returned to his two-dimensional world. Charmingly illustrated by the author, Flatland is not only fascinating reading, it is still a first-rate fictional introduction to the concept of the multiple dimensions of space. "Instructive, entertaining, and stimulating to the imagination." — Mathematics Teacher.
Flatland is one of the very few novels about math and philosophy that can appeal to almost any layperson. Published in 1880, this short fantasy takes us to a completely flat world of two physical dimensions where all the inhabitants are geometric shapes, and who think the planar world of length and width that they know is all there is. But one inhabitant discovers the existence of a third physical dimension, enabling him to finally grasp the concept of a fourth dimension. Watching our Flatland narrator, we begin to get an idea of the limitations of our own assumptions about reality, and we start to learn how to think about the confusing problem of higher dimensions. The book is also quite a funny satire on society and class distinctions of Victorian England.
|Einstein Gravity in a Nutshell
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Author: A. Zee
This unique textbook provides an accessible introduction to Einstein's general theory of relativity, a subject of breathtaking beauty and supreme importance in physics. With his trademark blend of wit and incisiveness, A. Zee guides readers from the fundamentals of Newtonian mechanics to the most exciting frontiers of research today, including de Sitter and anti-de Sitter spacetimes, Kaluza-Klein theory, and brane worlds. Unlike other books on Einstein gravity, this book emphasizes the action principle and group theory as guides in constructing physical theories. Zee treats various topics in a spiral style that is easy on beginners, and includes anecdotes from the history of physics that will appeal to students and experts alike. He takes a friendly approach to the required mathematics, yet does not shy away from more advanced mathematical topics such as differential forms. The extensive discussion of black holes includes rotating and extremal black holes and Hawking radiation. The ideal textbook for undergraduate and graduate students, Einstein Gravity in a Nutshell also provides an essential resource for professional physicists and is accessible to anyone familiar with classical mechanics and electromagnetism. It features numerous exercises as well as detailed appendices covering a multitude of topics not readily found elsewhere.
- Provides an accessible introduction to Einstein's general theory of relativity
- Guides readers from Newtonian mechanics to the frontiers of modern research
- Emphasizes symmetry and the Einstein-Hilbert action
- Covers topics not found in standard textbooks on Einstein gravity
- Includes interesting historical asides
- Features numerous exercises and detailed appendices
- Ideal for students, physicists, and scientifically minded lay readers
- Solutions manual (available only to teachers)
|Dancing Wu Li Masters: An Overview of the New Physics
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Author: Gary Zukav
“The most exciting intellectual adventure I've been on since reading Robert Pirsig’s Zen and the Art of Motorcycle Maintenance.”
—Christopher Lehmann-Haupt, New York Times
Gary Zukav’s timeless, humorous, New York Times bestselling masterpiece, The Dancing Wu Li Masters, is arguably the most widely acclaimed introduction to quantum physics ever written. Scientific American raves: “Zukav is such a skilled expositor, with such an amiable style, that it is hard to imagine a layman who would not find his book enjoyable and informative.” Accessible, edifying, and endlessly entertaining, The Dancing Wu Li Masters is back in a beautiful new edition—and the doors to the fascinating, dazzling, remarkable world of quantum physics are opened to all once again, no previous mathematical or technical expertise required.
At an Esalen Institute meeting in 1976, tai chi master Al Huang said that the Chinese word for physics is Wu Li, "patterns of organic energy." Journalist Gary Zukav and the others present developed the idea of physics as the dance of the Wu Li Masters--the teachers of physical essence. Zukav explains the concept further:
The Wu Li Master dances with his student. The Wu Li Master does not teach, but the student learns. The Wu Li Master always begins at the center, the heart of the matter.... This book deals not with knowledge, which is always past tense anyway, but with imagination, which is physics come alive, which is Wu Li.... Most people believe that physicists are explaining the world. Some physicists even believe that, but the Wu Li Masters know that they are only dancing with it.
The "new physics" of Zukav's 1979 book comprises quantum theory, particle physics, and relativity. Even as these theories age they haven't percolated all that far into the collective consciousness; they're too far removed from mundane human experience not to need introduction. The Dancing Wu Li Masters remains an engaging, accessible way to meet the most profound and mind-altering insights of 20th-century science. --Mary Ellen Curtin
|What Is Relativity?: An Intuitive Introduction to Einstein's Ideas, and Why They Matter
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Author: Jeffrey Bennett
It is commonly assumed that if the Sun suddenly turned into a black hole, it would suck Earth and the rest of the planets into oblivion. Yet, as prominent author and astrophysicist Jeffrey Bennett points out, black holes don't suck. With that simple idea in mind, Bennett begins an entertaining introduction to Einstein's theories of relativity, describing the amazing phenomena readers would actually experience if they took a trip to a black hole.
The theory of relativity also reveals the speed of light as the cosmic speed limit, the mind-bending ideas of time dilation and curvature of spacetime, and what may be the most famous equation in history: E = mc2. Indeed, the theory of relativity shapes much of our modern understanding of the universe. It is not "just a theory" -- every major prediction of relativity has been tested to exquisite precision, and its practical applications include the Global Positioning System (GPS). Amply illustrated and written in clear, accessible prose, Bennett's book proves anyone can grasp the basics of Einstein's ideas. His intuitive, nonmathematical approach gives a wide audience its first real taste of how relativity works and why it is so important to science and the way we view ourselves as human beings.
|Relativity: The Special and General Theory
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Author: Albert Einstein
Brand: Empire Books
The Newtonian model of Physics posits absolute time, and relies upon the classical mechanics of Euclidean Geometry. In the early 20th century, scientists began to interrogate this model, intrigued by the possibility of a dimension in which space and time overlap. Intended for readers curious about Relativity but not trained to understand the mathematics behind it, this text is Einstein’s philosophical explanation of the idea that changed the way we understand the physics of space and time.
How better to learn the Special Theory of Relativity and the General Theory of Relativity than directly from their creator, Albert Einstein himself? In Relativity: The Special and the General Theory, Einstein describes the theories that made him famous, illuminating his case with numerous examples and a smattering of math (nothing more complex than high-school algebra). Einstein's book is not casual reading, but for those who appreciate his work without diving into the arcana of theoretical physics, Relativity will prove a stimulating read.
|Einstein's Cosmos: How Albert Einstein's Vision Transformed Our Understanding of Space and Time (Great Discoveries)
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Author: Michio Kaku
In paperback for the centenary of the discovery of relativity, "a fresh and highly visual tour through Einstein's astonishing legacy" (Brian Greene). The year 2005 marks the 100th anniversary of the publication of the paper that launched Einstein's career, made E=mc2 famous, and ushered in a revolution in science—the paper that announced the theory of special relativity. And there's no better short book that explains just what Einstein did than Einstein's Cosmos. Keying Einstein's crucial discoveries to the simple mental images that inspired them, Michio Kaku finds a revealing new way to discuss these ideas, and delivers an appealing and always accessible introduction to Einstein's work.
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