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Unfortunately when a key subject left me rather clueless, (Boundary of a Boundary) I spent quite a few frustrated hours being uncertain on whether or not to continue reading without the support of the material on those pages. As it turned out, the subject became clearer once I read on and returned again. I never did grasp it as completely as the rest of the book.
The book contains the most enlightening description of transverse wave propagation I've ever seen. It also helps solidify one's understanding of interval and relativity.
Not a book to be read overnight.
The first chapter is an overview of the history behind the subject, via the work of people who contributed to our current understanding of gravity. And then, with a masterfull use of diagrams he gives the reader a taste of the simplicity of the equivalence principle and the need to tack on an additional dimension (time) to the 3-dimensional space of everyday experience. The Pound-Rebka experiment is discussed as one that illustrates the idea of the spacetime interval, and the role of time dilation is discussed via the possibility of practical space travel. And such enthusiasm in his dialog: "the universe will grow ever more exciting", he says, and looking at the developments now taking place in today's science, he is indeed correct.
Chapter 4 gives a fascinating overview of what the author calls the boomerang, which illustrates the action of curvature on nearby test masses. This thought experiment involves the motion of a spacecraft through an imaginary tunnel through the Earth. The author analyzes the motion from the standpoint of Newtonian physics and general relativity. Curvature as the "grammar of gravity" is the topic of the next chapter, with illustrations of the paths of ants on spaces of zero, positive, and negative curvature. A very intuitive treatment of parallel transport around a closed path on a curved surface is given. The tides are discussed as a natural manifestation of the gravitational influence of the Moon on Earth.
Must difficult for a layman to understand is how spacetime acts on masive objects, but the author explains it brilliantly in the next chapter, taught via the concept of "momenergy". This entity is a 4-vector, and the author uses it to show how its creation in a spacetime region can be written as the sum of 8 terms, reflecting the fact that the "boundary" of a four-dimensional block in spacetime consists of eight three-dimensional cubes. That the contents of these cubes sum to zero is the famous "boundary of a boundary is zero", which is discussed in the next chapter. This chapter is one of the best explanations ever given (at this level) of the physics behind spacetime curvature and massive objects. The actual mathematical quantification of curvature is detailed in chapters 8 and 9, using elementary mathematics. The author discusses nicely the famous Scharwzschild geometry.
Concepts of a more concrete nature are discussed in chapter 10, wherein the author discusses the famous Pound-Rebka experiment and planetary motion. This is followed by a discussion of the elusive gravitational waves in chapter 11. Again with a clever use of illustrations, the author explains the transverse property of gravitational waves, and compares gravitational waves with electromagnetic waves. The role of the quadrupole moment in the creation of gravitational waves is brought out briliantly by the author. He discusses briefly various attempts to detect gravitational waves.
Black holes are the topic of chapter 12, wherein the famous Penrose process for extracting energy from a black hole is discussed, and the "no-hair" theorem for black holes. A neat symbolic representation of the Bekenstein number of a black hole is given. The role of the Hawking process, connection quantum processes with the physics of black holes is briefly discussed. The author ends the book with a look at the expansion of the universe, the missing mass problem, and another very interesting topic that has gained much attention recently: the concept of gravitomagnetism. This is a "weak-field" prediction of general relativity, and predicts that the rotation of the Earth should influence the motion of orbiting satellites. This topic is currently bringing together ideas such as the quantum Zeno effect, Mach's principle, and the notorious "frame dragging" effect in general relativity. Experiments do measure it are currently in play and in the proposal stage, namely the LAGEOS and LAGEOS II experiments, which measure the gravitomagnetic orbital perturbation, which is known as the Lense-Thirring effect.
Wheeler is able to pull off a major accomplishment: He explains Einstein's General Relativity in a clear, straightforward manner, with a minimum of math. It's "conventional wisdom" that General Relativity is seriously serious stuff, the domain of hardcore Physics geeks. That doesn't faze Wheeler. He leads the reader along, gleefully pointing out the scenery, making it all look quite simple and understandable. And then all of a sudden, when you least expect it, you find he's derived and presented Einstein's field equations with only a teensy-tiny bit of algebra! Even if you know this stuff already, his presentation makes you think about it with a new perspective.
And did I mention the illustrations? They are really exceptional.
If you have any interest or dealings with GR, ya gotta have this book!
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Space prohibits a thorough review, so I will instead highlight the parts of the book that I found particularly exceptional: 1. The example of how coordinate singularities arise: the "cells of the egg crate" squashed to zero volume. 2. The beautiful illustration of the Roll-Krotkov-Dicke experiment. 3. The "physics demo" of a local inertial frame of reference (it is not very difficult to construct this demonstration for actual use in a classroom). 4. The presentation of a 2-form as a honeycomb of tubes with a sense of circulation. Such an explanation is lacking in the general mathematical literature. 5. The flying ring demonstration illustrating Faraday stresses. This demonstration is done very often in physics classes, and is simple to set up. 6. The excellent discussion (with illustrations) of the covariant derivative and the Schild ladder construction. 7. The presentation of parallel transport around a closed curve. 8. The treatment of Riemann normal coordinates. These are typically presented in a purely formal way in most texts on general relativity, ignoring their status as providing a local inertial frame in curved spacetime. 9. The (philosophical) discussion on the principal of general covariance in the context of Newtonian gravity in tensorial form. 10. The illustration, with accompanying discussion, on a situation where two events can be connected by more than one geodesic. The authors mention the relation of this example to the Morse theory of critical points. 11. The discussion of the Bianchi identities and the topological result on the boundary of a boundary being empty. 12. The discussion on the gravity gradiometer. 13. The exceptional discussion on six routes to the Einstein field equation. 14. The variational principle and the initial value problem in the Einstein equation. 15. The connection between the Gauss-Weingarten equations and extrinsic curvature. 16. The ADm formulation of the dynamics of geometry. 17. The discussion on Mach's principle. 18. The radial oscillations of a Newtonian star. 19. The Hamilton-Jacobi description of motion and its employment in analyzing the central force problem. 20. The effect of the value of the cosmological constant on cosmological models and evolution of the universe. 21. The cosmological redshift and its explanation via the expansion of the universe. 22. The mathematics of the Mixmaster cosmology. 23. The dynamics of the Schwarzschild geometry. 24. The discussion on the global properties of spacetime and singularity theorems. 25. The short biographies of Hawking and Penrose. 26. The quadrupole nature of gravitational radiation. 27. The experimental justification of general relativity, particularly the description of Pound-Rebka experiment on the gravitational redshift.
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This collection of texts taken from writings by Plato, Copernicus, Galilei, Ptolomy, Einstein, Hubble and other theorists discus what the universe is made of, how it works and (ultimately) what our place is in the Grand Scheme of Things, offering good insight into how our knowledge of the universe has developed over the last 40 centuries from Babylonian times to the 20th Century.
As this book was originally published in 1957 and reprinted in 1965, the latest theories are not included. It is therefore not a book for mathematicians or physicists interested in learning the latest theories, but rather a book for those interested in a well-written, general introduction to the field of cosmology.
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Wheeler's remarkable character pervades the book and helps make it unique and interesting. In a profession legendary for strong intellects and egos, he has achieved and maintained a pomposity coefficient of zero. His judgments of other people are unfailingly generous, but also astute enough to be interesting and revealing. He provides candid firsthand impressions of legendary figures such as Bohr, Einstein, Oppenheimer, Teller, Ulam, Heisenberg, Fermi, Szilard and Feynman . We also learn about many less well-known colleagues, friends and students whom he finds memorable for various reasons. In contrast to the eminent-scientist stereotype, Wheeler has always enjoyed teaching undergraduates and is genuinely interested in the problems and aspirations of the young people entrusted to his care.
Like the brilliant George Gamow, Wheeler has a talent for explaining difficult concepts and illustrating them with whimsically inventive diagrams. The book's autobiographical threads are interwoven with a rich tapestry of subtle but plainly-spoken physical insights on dozens of topics, some arcane enough to leave even the author slightly bemused. I believe anyone interested in physics will find a personal revelation or two among Wheeler's lucid, informal scientific explanations. There are touches of Gamowesque humor too, such as his theory that the fates somehow conspired to entangle him with a string of Hungarian emigres.
The title concepts of the book -- Geons, Black Holes and Quantum Foam -- were all named by Wheeler himself. He began his career at the minute scale of particle physics, moved on to the grand sweep of relativistic cosmology, and finally circled back to the hyperminuteness of quantum foam. Of course there is nothing really disjointed about such a journey, since connections among the nested scales of nature constitute one of the grand unifying themes of physics.
This present work of his traces his life, a life that is (as the cover says) one of science. However, one of the nice facets of this book is that it goes beyond just the laboratory & reveals the personal life of this great man. We learn of the moving death of his brother in WWII, his worries and concerns over nuclear war (as well as the grapples with his conscience that he endured over the invention of the hydrogen bomb) and many other aspects of his life. He also tells stories of some of his most memorable students; not all of these were necessarily his most gifted pupils. Above all, Wheeler reveals a genuine human passion that has characterized his approach to science over the greater part of this century. One of the best biographies of a scientist I have ever read.
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Another thing I like about this book is that it projects an enthusiasm for the subject that few textbooks do. The authors of this book are not afraid to have a little fun with physics while also learning, something lesser authors are afraid to do. They also portray the beauty in Relativity--especially the beauty of the unity of space and time and the unity of matter and energy.
Yes, at points the book is unconventional, some might even say silly. But when was it decreed that physicists cannot have fun? The unconventional parts enhance, rather than detract from, clarity. Apparent paradoxes become clear, common pitfalls are pointed out nicely--it's a great book for anyone curious about what it means to say that space and time are unified, two aspects of a single entity we call Spacetime.
In its course, Taylor and Wheeler present over a dozen "paradoxes" relating to Special Relativity. Several of these appear in the main text, while the remainder appear as problems. I believe my intuition is lacking because I was unable to get the right answer for the paradox problems without working through the math first - although this intuition may come only with further experience. I would have been happy if the authors had included a few more paradox problems with solutions from an "intuition" perspective (as well as a mathematical solutions) to help gain this intuition.
The mathematics throughout the book is nothing harder than algebra and the occasional trigonometry, so it should well be accessible to anyone with a high-school calculus understanding of math. One mathematical trick the authors introduce in their next book would be helpful for this one as well: when solving for a number which is only slightly less than one, (as in several of the problems with particles moving near light speed) instead of trying to solve for .9999999999992343, which would be rounded to 1 by most calculators, solve for "1 - X" instead.
Scattered copiously throughout the book are solved sample problems which guide the reader through the easier problems, as well as "boxes" which discuss interesting ramifications and related material. The more involved problems often include step by step instructions on how to reach a solution which would otherwise be by no means obvious at first glance (at least, not to me). Many problems deal with actual experiments performed to test and validate relativity.
In sum, I cannot find any substantial problems with this book. It is clear, concise, battle-tested (having been originally published over thirty years ago), and an excellent formal introduction into the pardoxical world of Special Relativity. One author maintains a web site at http://www.eftaylor.com/ with, among other material, an interesting article on the writing of this book and his collaboration with John Wheeler.
The interested reader can find a history of the development of Special and General Relativity in Kip Thorne's Black Holes and Time Warps.
PS: Professor Taylor confirms that the answer to sample problem 8-17b in the seventh printing (which I have) is off by a factor of 1000.
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Unfortunately many of the essays are directed at the professional scientist and are beyond the level of even the well read amateur. Reading some of Professor Wheeler's discussions of the philosophy of science is like being thrown into a discussion being conducted by people who have known each other for a very long time and have developed a special language. For instance, "With a slight rewording of Bohr's formulation, we say, 'The use of certain concepts in the description of nature automatically excludes the use of other concepts, which however, in another connection are equally necessary for the description of the phenomenon.'"
There are some gems in this book, though. John A. Wheeler seems to have personally known every great scientist of the Twentieth Century: Albert Einstein, Niels Bohr, Richard Feynman, Andrei Sakharov, Kurt Godel, John von Neumann, Steven Weinberg. His comments on them and their work are invaluable.
Wheeler also has some interesting comments on the risks of a nuclear energy. One does not need to accept his optimistic viewpoint in order to appreciate his insight.
"At Home In The Universe" is really two books: one for the professional scientist and another for the general public. If the volume was separated, we would have two excellent books instead of a single disappointing one.
In the present book, he spends most of his pages paying homage to people who dedicated their lives to science over the centuries. Such venerable names as Nicolaus Copernicus, Benjamin Franklin, Albert Einstein, Niels Bohr, Hideki Yukawa, Maria Sklodowska Curie, Hermann Weyl and others form the objects of Wheeler's praise. Much of the book is made up of snippets of terse speeches which Wheeler has made at various symposiums and celebrations during his lengthy sojourn at Princeton. For example, there is a brief poem which he wrote for Joseph Henry which is included, as well as an oration on the "colleagueship at Princeton" which he delivered in 1966.
Interspersed throughout the book are essays which Wheeler has written on quantum mechanics, black holes, cosmology & the like. These are not the easiest pieces to read; I would suggest that readers browse through some preliminary books on QM before attempting to read Wheeler ("Taking The Quantum Leap" by Fred Alan Wolf might be a good place to start). The essays are well written & Wheeler uses some helpful analogies, but the going is still pretty rough. One of Wheeler's quotes which I really like (not from this book, though) is "If you haven't found something strange during the day, it hasn't been much of a day." One is sure to find many-a-strange scientific phenomenom in this book.
This book lacks a central, cohesive theme & the order in which it was put together does not follow any specific chronology or format. However, I don't think this takes away from the book's superb picture of what one of the premiere scientists of the 20th century spends his days thinking about. There are several passages in which he compares and contrasts science with philosophy as well as with the pragmatism of everyday existence. I would recommend this book to anyone who has an interest in John Archibald Wheeler, physics, or the scientific community of Princeton university. Make yourself at home....
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