Quantum Gravity 2: A Second Oxford Symposium [Hardcover]

C.J. Isham (Editor), etc. (Editor)

Book Description

Publication Date: February 4, 1982

Quantum gravity poses the problem of merging quantum mechanics and general relativity, the two great conceptual revolutions in the physics of the twentieth century. The loop and spinfoam approach, presented in this book, is one of the leading research programs in the field. The first part of the book discusses the reformulation of the basis of classical and quantum Hamiltonian physics required by general relativity. The second part covers the basic technical research directions. Appendices include a detailed history of the subject of quantum gravity, hard-to-find mathematical material, and a discussion of some philosophical issues raised by the subject. This fascinating text is ideal for graduate students entering the field, as well as researchers already working in quantum gravity. It will also appeal to philosophers and other scholars interested in the nature of space and time.

--This text refers to the Paperback edition.

Editorial Reviews

Review

"This is a truly great book!...a must for someone interested in quantum gravity." -
Mathematical Reviews, Jose A. Zapata

"... an excellent text for graduate courses."
SciTech Book News --This text refers to the Paperback edition.

Book Description

Quantum gravity is one of the major open problems in theoretical physics. The loop and spinfoam approach, presented in this book, is a leading research program in the field. Emphasis is given to conceptual and foundational issues raised by quantum gravity, especially on the nature of space and time. This text is intended for researchers working in quantum gravity and, in particular, graduate students entering the field. It will also appeal to philosophers and scientists interested in the general issue of the nature of space and time. --This text refers to the Paperback edition.

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Product Details

• Hardcover: 684 pages
• Publisher: Oxford University Press, USA (February 4, 1982)
• Language: English
• ISBN-10: 0198519524
• ISBN-13: 978-0198519522
• Product Dimensions: 9.1 x 6.5 x 1.7 inches
• Shipping Weight: 2.5 pounds
• Average Customer Review: 4.4 out of 5 stars  See all reviews (10 customer reviews)
• Amazon Best Sellers Rank: #8,500,489 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

28 of 32 people found the following review helpful:

5.0 out of 5 stars A useful overview of an alternative theory, April 24, 2005

By 

Dr. Lee D. Carlson (Baltimore, Maryland USA) - See all my reviews
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This review is from: Quantum Gravity (Cambridge Monographs on Mathematical Physics) (Hardcover)

This book gives a detailed overview of that "other theory" of quantum gravity called `loop quantum gravity'. String theory has been viewed by many as a promising theory of quantum gravity and there are many reasons to believe this is the case. String theory though requires a formidable amount of mathematics for its construction, and has yet to have any experimental verification. Therefore, it is not surprising that other alternative theories of quantum gravity would be constructed, these needing a minimal amount of formalism and staying as close as possible to what can be observed. Loop quantum gravity is one of these, and is the most popular alternative to string theory as a theory of quantum gravity.

The initial five chapters of the book motivate the need for quantum gravity and also phrase the theories of general relativity and relativistic quantum physics in a language that will be used to formulate the theory of loop quantum gravity. General relativity (GR) is formulated as a dynamical system defined by the Hamilton-Jacobi equation for a functional defined on the space G of three-dimensional SU(2) connections. The equation is invariant under internal gauge transformations and 3D diffeomorphisms.

The quantization of GR is obtained in terms of complex-valued Schrodinger wave functionals on G. The derivatives of the Hamilton-Jacobi functional are replaced by derivative operators in order to obtain the quantum dynamics. The Hamilton-Jacobi equation then becomes the Wheeler-DeWitt equation governing the quantum dynamics of spacetime. The quantum (kinematical) state space is defined letting G be the space of smooth 3D real connections defined everywhere on a 3D surface S. The functionals are defined in terms of an ordered collection of smooth oriented paths L (essentially a lattice) on S, and are called "cylindrical functions" by the author. Scalar products are defined, which when completed gives the (kinematical) Hilbert space K. Lest the reader believe that this is nothing more than a quantum Yang-Mills theory on a lattice, the author is careful to note that a continuous theory over all possible lattices in S is being considered. The space K is nonseparable, but factoring out the diffeomorphisms gives a separable one. It has an orthonormal basis, and contains a subspace K0 of states invariant under local SU(2) gauge transformations. The ubiquitous spin network states form a orthonormal basis for K0. Again the author cautions against viewing this as ordinary lattice gauge theory, since diffeomorphism invariance makes it different from the latter. The spin networks are graphs L with links and nodes. The nodes are joined by links and the curves in L overlap only at the nodes. Each node has a multiplicity that measures the number of links going in and out of it. The author shows explicitly how to construct the spin network states, which are an orthornormal basis for K0.

So what about the observables of loop quantum gravity? The connection and its momentum are the field variables in the canonical theory, and are replaced by field operators. The momentum operator has a curious operation in this theory: the author describes it as "grasping" a path. The momentum operator though is not gauge invariant on K0, and so the author defines a new gauge-invariant (and self-adjoint) operator associated to S and has a straightforward operation on spin network states. This operator represents the physical area of S, and its spectrum, interestingly, can be interpreted as a quantized area. This result is related to the derivation of the entropy of black holes in the book, and is considered to be one of the significant results given by loop quantum gravity. A similar construction is done with the volume, giving a volume operator, which also has a discrete spectrum, but only has contributions from the nodes of a spin network state. Loop quantum gravity therefore truly gives a "quantized geometry." Each node of a spin network represents a quantum of volume, giving a collection of "chunks" separated from each other by surfaces, the areas of which are governed by the area operator. The graph L of the spin network determines the adjacency relation between these chunks, and is interpreted as the graph dual to a cellular decomposition of physical space. Spin network states therefore determine a discrete quantized three-dimensional metric.

The dynamics of loop quantum gravity requires the construction of the Hamiltonian operator. As in quantum field theories, this involves regularization, and the author shows how the Hamiltonian operator acts only on the nodes of the spin network, and gives a detailed discussion of the background independence of the theory. The latter is one of the most important features of loop quantum gravity, and is frequently advertised as one of its virtues. The author also discusses the extent to which the Hamiltonian operator is unique, outlining in the process several alternatives. When matter fields are considered, the author shows that the total Hamiltonian is finite, again pointing to the background-independence of loop quantum gravity. Loop quantum gravity reduces to classical general relativity as Planck's constant goes to zero, but the author lists many issues that have not been settled by this theory. One of these of course concerns the observable consequences, the lack of which it shares with string theory. Loop quantum gravity also does not attempt to unify the different interactions in nature in a single theory, as does string theory. But loop quantum gravity does give some interesting predictions, one of these being that the size of the universe is quantized. It also predicts an inflationary phase in the expansion of the early universe, as numerical solutions of the Wheeler-DeWitt equation indicate. By far the most interesting consequence of loop quantum gravity, is that it makes more reasonable the Bekenstein-Hawking interpretation of the entropy of a black hole. In fact the Bekenstein-Hawking entropy can be derived in loop quantum gravity, up to a factor called the Immirzi parameter. These are all impressive achievements, considering the status of quantum gravity now as compared to three decades ago.

13 of 15 people found the following review helpful:

5.0 out of 5 stars Clarity and Precision Prevail, December 8, 2005

By 

Douglas Mckenzie (Denville, NJ USA) - See all my reviews
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This review is from: Quantum Gravity (Cambridge Monographs on Mathematical Physics) (Hardcover)

I'm experiencing some hesitation as this is hands down the most advanced book that I have ever 'reviewed' and, in fact, ever read. I have only completed Part 1 -"Relativistic Foundations" as I have to go deeper into Differential Geometry before proceeding into Part II - "Loop Quantum Gravity." Part 1 is a pretty amazing, often philosophical introduction both describing the problem that QG is trying to approach (the contradictions between QFT and GR)and laying the foundation for LQG. It becomes clear (slowly) that our notions of space and time need serious overhauling before we can understand what LQG is all about. String theory doesn't have this problem as it more or less uses our 20th century notions of space and time as its framework. Sure, it adds a few dimensions and curls some up but it's pretty much still the same old space and time. LQG does not use this framework and rather seems to work towards a physics without time. Rovelli does a masterful job in Part 1 of slowly, clearly and precisely helping the reader to make this transition. Most memorable to me is his discusson of the ten meanings of time where he demonstrates that we have already stripped time of many of its seemingly inherent properties ('flowing', 'measured' to name 2). He just proposes stripping off a few others! I'm looking forward to Part II.

41 of 54 people found the following review helpful:

5.0 out of 5 stars excellent ! a milestone of contemporary physics ...., November 23, 2004

By 

Peter Freimann "linux evangelist" (Czech republic) - See all my reviews
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This review is from: Quantum Gravity (Cambridge Monographs on Mathematical Physics) (Hardcover)

These days, a fierce battle is raging between two camps of physicists - strings theory developers and proponents of loop quantum gravity (seems like Amazon is going to be another battlefield :-)) . So far there are no experiments to confirm or reject any of these two theories and it is therefore inevitable to conduct the research in both directions. Rovelli's book seen from this perspective is a major attempt to present a consistent picture of how the LQG fits into the framework of our present knowledge about the world around us. This thoughts provoking book explains the path to the present state of LQG, its current problems and is a great reading not only for active developers but for anyone eager to understand the broader impact of these new physical ideas.

Be warned ! This is not an usual textbook ... You should have a fairly deep understanding of QM, QFT and GR - only then will Rovelli show you how to re-think these ideas from a new point of view.

Still, the rest of us (:-)) can benefit greatly from the crystal clear reasoning and philosofical implications he presents throughout the book.

Note: If you like John Baez books and style - you are going to love this one too ...