Book Description
Spacetime and Geometry: An Introduction to General Relativity provides a lucid and thoroughly modern introduction to general relativity. With an accessible and lively writing style, it introduces modern techniques to what can often be a formal and intimidating subject. Readers are led from the physics of flat spacetime (special relativity), through the intricacies of differential geometry and Einstein's equations, and on to exciting applications such as black holes, gravitational radiation, and cosmology. For advanced undergraduates and graduate students, or anyone interested in astronomy, cosmology, physics, or general relativity.
Customer Reviews:
Wordy and Wonderful.......2006-12-12
This is an advanced text, but all the same it is not particularly rigorous or dense, so it is in principle accessible to the beginner. With an easy authority, Carroll leads us on a wandering journey through the mystical lands of general relativity. This is very different from, and compliments nicely, the clarity and directness of Wald. As a student of GR, I use Wald for the bottom line on any subject, and Carroll for the random physical or computational insights that I invariably find in any section of the book. Carroll's prose is like music to the ear and I always enjoy myself when I decide to open up this book.
Be warned that there are lots of mistakes in this first edition--you might want to wait for the second one.
Also, his chapter on cosmology is better than any I've seen.
BY FAR the best book on GR.......2006-10-21
I am currently on the 4th chapter of Carroll's "Spacetime and Geometry" and thus far I am amazed at how clear it is. Sure there is a lot of math in it however that also is very clearly explained. In fact, I think that Carroll explains the differential geometry material better than any mathematician has in any book on the subject. If you want to learn general relativity, there is no getting around the math; sooner or later you'll have to learn it. I'd suggest, especially if you are self-studying the subject, to rather pick up this book and go through it than pick up a more "elementary" text and a book on Riemannian geometry to look at later.
(Although I do also highly recommend Kay's (Schaum outline) "Tensor Calculus" for self study. The prima donnas don't like Kay's book because it "doesn't have enough theory." I suppose if a freshman calculus book does not have the Lebesgue integral defined in ti they'll complain about that too.)
Because, you can always skip through certain sections if the math is too heavy and go back through it later. And like I wrote earlier, you won't find a better introduction to the mathematical material than here.
Carroll should be given the Nobel prize for this book. If not in Physics, then in literature. I'd give this textbook 10 stars if I could.
A nice blend of the ideas of physics with mathematics.......2006-04-11
Kudos to Carroll.
This book is an excellent INTRODUCTION to SR and GR for the graduate physics student as well as the graduate mathematics students.
Pure mathematics often loses sight of the ideas which motivated it and physics often loses the mathematical foundations from which it is built.
This book offers some level of mathematical formalism to the physics student while exposing the ideas motivating the mathematical concepts.
I particularly like how he builds up the mathematical machinery of GR by introducing sets then topology on this set giving a topological space. Now he adds in the ideas of a manifold which make this topological space look like Rn locally with the patches sewn together smoothly. The manifold comes equipped with tangent space, cotangent spaces and their product spaces giving tensor spaces. These are defined nicely with reference to component formalism as well as the multilinear algebra approach as maps from products spaces to the reals, etc. He delves into forms and tantalized the reader with deRham cohomology although doesnt go into it. He shows how these can be differentiated ( exterior derivative ) and integrated.
Now the metric is introduced giving a geometry. To this is added a connection which is independent of the metric and leads to notions of parallel transport and differentiation of tensors ( covariant derivative ). One sees that in a special case one can derive a unique connection from the metric ( Levi-Cevita ) which is used in GR.
Fibre bundles, Lie derivatives, pullbacks etc are introduced as needed.
He then presents some introductory GR material by applying the mathematics.
Great Book But Won't Get You To The Promised Land.......2005-12-14
My comments come with a few caveats.
1. This is my fourth GR book.
2. I'm not hardcore into physics. I'm not a physic grad and I'm reading GR for fun. I have a decent graduate math background but I've been corrupted with 10+ years in working in various roles software engineering, electronics engineering and marketing.
3. I assume that since you're considering buying this book, you're goal is to get at the "real" GR, not the watered down discover channel version.
With these caveats in mind, here are my comments.
First, on a scale of 1-5, I rank Carroll at level 3 in terms of math/physics maturity and thoroughness. Here is my full ranking of authors from my limited reading: 1. schutz 2. hartle 3. penrose 3. carroll 4. wald 5. physics journal articles
Second, using the rankings above, I recommend Carroll as the second port of entry. If you're comfortable with multivariable calculus, start with schutz (#1). You'll get warm fuzzies doing the toy exercises. But Schutz is tensor/math-lite. If you've had advanced calculus and geometry already, jump in with carroll (#3). But you'll be hard-pressed to find anyone else as polite to the reader. He won't prepare you for 80 percent of what's published. If you're ready to throw off the training wheels and jump dive into mainstream GR go with Wald (#4).
Note that Hartle (#2) is a good "tweener" book with feel-good exercises and some of the full-on GR equations at the end. I bet most instructors teaching a first year grad course would go with Hartle along with a dose of supplementary material.
Third, don't expect Carroll to be your last GR book purchase if you want to reach the promised land (see caveat #4). Living and breathing GR is found in physics journals and for that you'll need Wald or another advanced GR book.
good math chapters, not at beginner's level after that.......2005-03-07
I had a course based on that book and I've read chapters 1-6 (out of 9 chapters total) plus all the appendices. Also, I've solved some of the problems.
Please keep in mind my review is from a beginner point of veiw. Readers more experienced in GR may feel different but that book is supposedly written for beginners right?
The math chapters 2 and 3 are worth reading because they will teach you tensor analysis on manifolds in much clearer way than other books. The book makes a clear distinction between assumptions, choices (like working with a metric compatible connection), or derived facts. It is nice that the book makes a difference between a Christoffel connection and a generic connection. The appendices are worth reading too cause they will give you a feeling for some new to you math necessary for GR like pullbacks, Lie Derivatives, hypersurfaces etc.
Chapter 4 is worth reading too cause it makes clear that Einstein's equations are just the simplest guess out of many other possibilities. Also it shows how we generalize physical laws from special relativity to GR making it clear our choices are the simplest ones but not the only ones possible.
The chapters after that discuss applications of GR like black holes, gravitational radiation, cosmology etc. Of these, I've read only the black holes chapters 5 and 6 and I wasn't able to understand 100% what was goin on. The problem was that the book uses concepts that you still don't quite understand if you are a beginner like 'spacelike singularity' or 'conformal diagrams'. That is informative but the book doesn't provide the necessary level of detail and examples for beginners so you could really master such concepts and use them in your practise.
There are problems after each chapter but not the necessary beginners problems that increase your conceptual understanding of the theory. Instead, some of the problems are just tedious algebra of type 'find the curvature for some general form of the metric' for which specialists in the field use symbolic programs like Mathematica. Solving these by hand proves that you can take derivatives and you are a mazochist but not that you understand GR. Other problems are really relevant to your education but are not dirrectly connected to the discussion in the text. Because of that you have to solve them from scratch and it will take you ages ...
If you are a beginner like me, you should read the math chapters and all appendices of Carroll's book plus chapter 4. Then you should read a real book for beginners with a lot of examples how to apply GR in real calculations and how to understand it. For that I recommend James Hartle's "Gravity: An Introduction to Einstein's General Relativity" and Bernard Schutz's "A first course in General Relativity". After that hopefully you will understand the rest of Carroll's book better. My experience was that often I had to read Hartle's book in order to understand and solve a problem in Carroll's book.
Book Description
In this book, Robert Wald provides a coherent, pedagogical introduction to the formulation of quantum field theory in curved spacetime. He begins with a treatment of the ordinary one-dimensional quantum harmonic oscillator, progresses through the construction of quantum field theory in flat spacetime to possible constructions of quantum field theory in curved spacetime, and, ultimately, to an algebraic formulation of the theory. In his presentation, Wald disentangles essential features of the theory from inessential ones (such as a particle interpretation) and clarifies relationships between various approaches to the formulation of the theory. He also provides a comprehensive, up-to-date account of the Unruh effect, the Hawking effect, and some of its ramifications. In particular, the subject of black hole thermodynamics, which remains an active area of research, is treated in depth.
This book will be accessible to students and researchers who have had introductory courses in general relativity and quantum field theory, and will be of interest to scientists in general relativity and related fields.
Book Description
For more than a century, quantum mechanics has served as a very powerful theory that has expanded physics and technology far beyond their classical limits, yet it has also produced some of the most difficult paradoxes known to the human mind. This book represents the combined efforts of sixteen of today's most eminent theoretical physicists to lay out future directions for quantum physics. The authors include Yakir Aharonov, Anton Zeilinger; the Nobel laureates Anthony Leggett and Geradus 't Hooft; Basil Hiley, Lee Smolin and Henry Stapp. Following a foreword by Roger Penrose, the individual chapters address questions such as quantum non-locality, the measurement problem, quantum insights into relativity, cosmology and thermodynamics, and the possible bearing of quantum phenomena on biology and consciousness.
Book Description
Naber provides an elementary introduction to the geometrical methods and notions used in special and general relativity. Particular emphasis is placed on the ideas concerned with the structure of space-time and that play a role in the Penrose-Hawking singularity theorems. The author's primary purpose is to give a rigorous proof of the simplest of these theorems, by the one that is representative of the whole. He provides exercises and examples at the end of each chapter. No previous exposure either to relativity theory of differential geometry is required of the reader, as necessary concepts are developed when needed, though some restrictions ae imposed on the types of space considered.
Customer Reviews:
A Stimulating and Interesting Book.......2000-11-01
This book is concerned primarily with a geometrical and in places, a topological approach to spacetime, leading to a full proof of one of Hawking's singularity theorems.The first part introduces the geometry of Minkowski Spacetime as.. 'a 4-dimensional ral vector space on which is defined a nondegenerate symmetric bilinear form of index one'.Some mathematical maturity is required to attempt this book on one's own.Chapter two develops relativistic mechanics in quite an abstract way (certainly for a first encounter) and chapter three develops spacetimes from the point of view of maps between manifolds.This chapter ends with a statement of one of Hawking's theorems. Chapter four sets out a full rigorous proof. There are no hints/partial solutions for the exercises although there are some 'examples'. The first three chapters were enjoyable and I managed to do quite a lot of the exercises and problems.As someone who works entirely independently at this kind of thing for 'fun',I found chapter four very hard going.Having no-one to ask when stuck made it a bit frustrating.The book was very stimulating though and encouraged me to research other sources for similar material to fill in gaps in my mathematical knowledge.
Customer Reviews:
Spacetime physics.......2007-06-27
A must for everyone who really wants to penetrate the mysteries of Einstein's special relativity. In my opinion the principal merit of the book is an special emphasis on the intuitive space-time concept with a very simplified mathematical presentation, all without lessening the subject. Few maths needed. Generously illustrated ! Many conceptual questions make one think hard. Also many problems with solutions( Odd numbers only ). One ends with a firm grasp on special relativity. A very amazing book !!
Geometry of spacetime!.......2006-06-17
The aim of this book is to explain to one the essential of the theory of special relativity: The GEOMETRY of spacetime! Keyword: GEOMETRY. Those who give this book one or two stars because they think this book is too wordy or does not retain enough rigor simply do not see the simplicity and elegance in the authors' presentation.
Yes. You don't see complicated equations in this book because the ideas are, as I said, geometric. The authors even tell the reader not to pay too much attention to things like the Lorentz transformation because it conceals the intuitive geometric ideas. Everything in speical relativity can be done without appealing to any local coordinate frames because spacetime IS geometry, the quantities we are interested in are inheritedly covariant. This is all built into the theory of relavity.
And the paradoxes that arise when one first studies the subject can all be expalined by the relativity of simultaneity, which is again because space or time alone is not covariant but spacetime as a whole.
This book gives a concrete meaning to spacetime. Things like 4-vectors are not just something the physicists cook up to make their equations look better on paper; They have their very own existence.
As for the nontechnical language used in the book, I would have to say that any bright high school students can learn from this book.
The strongest point of Spacetime Physics..........2006-05-29
is the exercises.
If you work through all (or nearly all) the exercises, you will have confronted most of the conceptual paradoxes that have come up in the discussion on Special Relativity since 1905. You will not only have mathematical explanations for them, but will be able to explain them in an intuitive way.
(By "intuitive" I do not mean that they explanation will accord with Newtonian physics -- it can't, as they often give different results. What I mean is that you will be able to reason out the way things will turn out without always having to do the algebra.)
On the other hand, if you just read through the text, the coverage might seem unnecessarily wordy and long. One will only find this discussion useful if you are really wrestling with the material, and trying to understand the apparent paradoxes.
Perhaps this explains why there seems to be a "hate it"/"love it" dichotomy among the reviewers of this book. However, those who are tempted to dismiss it as merely wordy should keep in mind that the principal author is John Wheeler, whom Richard Feynman regarded as having incredible physical insight. (Wheeler was Feynman's thesis adviser.)
Profound and interesting.......2006-03-03
Special Relativity (SR) is one of those subjects that require much thinking for maturating of ideas. I doubt even if many physicists really understand it. Of the many books written on this subject, Taylor and Wheeler's blink as a jewel. I believe it has many advantages over most of other books. It is extremely slow paced, but not to the point of being tiresome (the reason for this will be explained below). Most texts of SR start with a lenghty "philosophical" or historical discussion, then get to the maths of it, but in such a way that one has the impression that something is not fitting into the whole structure. The reason for this is, I believe, that SR is much needed in modern theoretical and experimental physics, but most of its intricate details can be left over. In other words, physicists need SR as a tool, but do not, as a general rule, need to think over it. Taylor and Wheeler's book is different. They know what is important, get directly to it (and this explains why, although being slow paced, is not tiresome), and fight the nuts and bolts of explaining in the most clear way up to date. You finish with the impression that you understood it. Good pedagogic machinery include questions and answers all over the book (some questions even somewhat silly, but who never thought about any of them before?), so you really feel that the writers are helping you and, most important, that they cared to write an understandable text. The book itself is appealing, appealing as most physics books are not, with a lot of pictures, boxes and quotes interspeded along the text. It is very pleasant reading, has every important information you need for SR as a working physicist (except the covariant formulation of electrodynamics, but this is not important as most of electrodynamical books treat this topic with all needed details, and the presentation of such a topic would find terrible difficulties for the organization of the text) and, most important, you will enjoy it and be able to read every page. One last note on the exercises. I thing nothing can be more educative for understanding SR than exercises like the ones you find there. They are not mathematically difficult, but as a general rule oblige you to think "four-dimensionally". They are the greatest fun of the book, and will make you really understand the meaning of SR. At this point, I must quote "Wheeler's first moral principle": "Do not make a calculation until you know the answer". This is the theme for all those exercises and, indeed, a moral principle that most physicists should follow - think about Feynman!
If I could give 6 stars..........2005-11-19
If I could give 6 stars I certainly would did that!
This book is a superb in explaining why the special relativity is so true that we think... "Why didn't I found it by myself...". At the beggining the ilustrations seemed kid's playing for me, but they're really important. This book is so good that after reading it I tried by myself to develop a ten parameter group to enclose the Lorentz transformations. (A rotation in 4D space has six parameters... plus four displacements we have ten). And independently found what a friend of mine shown me to be the Poicaré group!!!
Relativity is not aboout what is relative... is just what is invariant with the fundamental playing transferred to the interactions...
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Physics of the Solar System: Dynamics and Evolution, Space Physics, and Spacetime Structure (Astrophysics and Space Science Library)
B. Bertotti ,
P. Farinella , and
D. Vokrouhlicky
Manufacturer: Springer
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The Future of the Universe (Astronomers' Universe)
ASIN: 1402015097 |
Book Description
This volume covers most areas in the physics of the solar system, with special emphasis on gravitational dynamics; its gist is the rational, in particular mathematical, understanding of the main processes at work. Special stress is given to the variety of objects in the planetary system and their long-term evolution. The unique character of this book is its breadth and depth, which aims at bringing the reader to the threshold of original research; however, special chapters and introductory sections are included for the benefit of the beginner.
Physics of the Solar System is based on the earlier work by B. Bertotti and P. Farinella:
Physics of the Earth and the Solar System (Kluwer, 1990), which has been completely revised and updated, and more focused on the solar system. It generally attains a higher level than the previous version. This volume is generally suitable for post-graduate students and researchers in physics, especially in the field related to the solar system. A large amount of figures and diagrams is included, often compiled with real data.
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The Ontology of Spacetime, Volume 1 (Philosophy and Foundations of Physics)
Manufacturer: Elsevier Science
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ASIN: 0444527680 |
Book Description
This book contains selected papers from the First International Conference on the Ontology of Spacetime. Its fourteen chapters address two main questions: first, what is the current status of the substantivalism/relationalism debate, and second, what about the prospects of presentism and becoming within present-day physics and its philosophy? The overall tenor of the four chapters of the books first part is that the prospects of spacetime substantivalism are bleak, although different possible positions remain with respect to the ontological status of spacetime. Part II and Part III of the book are devoted to presentism, eternalism, and becoming, from two different perspectives. In the six chapters of Part II it is argued, in different ways, that relativity theory does not have essential consequences for these issues. It certainly is true that the structure of time is different, according to relativity theory, from the one in classical theory. But that does not mean that a decision is forced between presentism and eternalism, or that becoming has proved to be an impossible concept. It may even be asked whether presentism and eternalism really offer different ontological perspectives at all. The writers of the last four chapters, in Part III, disagree. They argue that relativity theory is incompatible with becoming and presentism. Several of them come up with proposals to go beyond relativity, in order to restore the prospects of presentism.
· Space and time in present-day physics and philosophy
· Introduction from scratch of the debates surrounding time
· Broad spectrum of approaches, coherently represented
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Quantum Fluctuations of Spacetime (World Scientific Series in Contemporary Chemical Physics) (World Scientific Series in Contemporary Chemical Physics) Vol.25
Lawrence B. Crowell
Manufacturer: World Scientific Publishing Company
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ASIN: 9812565159 |
Book Description
Three key aspects of quantum gravity are considered in this book: phenomenology, potential experimental aspects and foundational theory. The phenomenology is the treatment of metric quantum fluctuations as torsional curves that deviate from classical expectations. This leads to possible experimental configurations that may detect such fluctuations. Most of these proposed experiments are quantum optical measurements of subtle quantum gravity effects in the interaction of photons and atoms. The foundational discussions attempt to find an substratum to string theories, which are motivated by the phenomenological treatment. Quantum gravity is not the quantization of general relativity, but is instead the embedding of quantum theory and gravitation into a more fundamental field theoretic framework.
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Special Relativity: Will it Survive the Next 101 Years? (Lecture Notes in Physics)
Manufacturer: Springer
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Relativity and the Nature of Spacetime (The Frontiers Collection)
Vesselin Petkov
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The Geometry of Spacetime
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A First Course in General Relativity
ASIN: 3540238891 |
Book Description
The most important question addressed in this book is "what is the nature (the ontological status) of spacetime?" or, equivalently, "what is the dimensionality of the world at the macroscopic level?" The answer to this question is developed via a thorough analysis of relativistic effects and explicitly asking whether the objects involved in those effects are three-dimensional or four-dimensional. This analysis clearly shows that if the world and the physical objects were three-dimensional, none of the kinematic relativistic effects and the experimental evidence supporting them would be possible. The implications of this result for physics, philosophy, and our entire world view are discussed.
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