Quantum Gravity (Cambridge Monographs on Mathematical Physics) 1st Edition by Carlo Rovelli (PDF)

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Quantum gravity is perhaps the most important open problem in fundamental physics. It is 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 2004 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.

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⭐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.

⭐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.

⭐thank yoi

⭐The headline which caps my review, “how to rethink physics from scratch,” originates from the dust-jacket from the hardcover edition. I have followed trends in ‘quantum gravity’ since the 1970s. There were three Oxford conferences devoted to the topic: Quantum Gravity, An Oxford Symposium (1975), Quantum Gravity 2 (1981) and Quantum Concepts in Space and Time (1986). There is much to hold your interest in each of those volumes (the second is my favorite). What surprises me, in regards to my own evolution in thinking, is that as interesting as Carlo Rovelli’s book can be, the textbooks on string theory are at least as interesting (Zweibach, Becker, West are the three books I have studied). Thus, I am neither a proponent of string theory nor loop quantum gravity. But, I do advocate for study of both approaches simultaneously.Progressing through Rovelli’s monograph:(1) “The world is made up of fields. Physically, these do not live on spacetime. They live, so to say, on one another. No more fields on spacetime, just fields on fields.” (page 75).(2) “There is a one to one correspondence between instantaneous states and relativistic states.” (page 116).(3) “In a fully relativistic context, mechanics is the theory of correlations between partial observables.” (page 120).(4) “The time coordinate in Maxwell’s theory is a partial observable. The time-coordinate in general relativity is an unphysical parameter.” (page 127).(5) ” On the other hand, the conventional structure of quantum mechanics is certainly incomplete in the light of general relativity.” (page 179).(6) “In the quantum theory, a complete experiment consists of two events, a preparation and a quantum measurement.” (page 198).(7) “A key result of the theory developed in the second part of this book (LQG) is that the eigenstates of the gravitational field on a 3d surface are not smooth fields.” (page 202).(8) “The notion of vacuum is strictly connected to the notion of energy.” (page 203).The lines above are extracts from part one (pages 1-224). Those pages are preliminary to part two.So, you get loop quantum gravity in the span of 150 pages. There are three appendices: groups, history, reflections of methodology: “the best we can say about the physical world, and about what is physically real out there, is what good physics says about it.” (page 423).Let us learn more:(1) Read: “the most surprising and intriguing aspect of LQG is the fact that it predicts an inflationary phase in the expansion of the early universe.” (page 301).(2) I highlight Black Hole thermodynamics (pages 301-315). Read: “fluctuations of the shape of the horizon” (page 304). Learn of John Wheeler’s “it from bit” (page 310) and Mukhanov’s “discrete emission spectrum” (page 313). Learn more from Wheeler and Mukhanov in the book “Complexity, Entropy and the Physics of Information.”(3) I highlight Tullio Regge: “The surprising discovery of Ponzano and Regge was that the 6j-symbol approximates the action of general relativity.” (page 336).(4) Rovelli updated in 2008 Living Reviews article (available online): “I give here a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.” Turn to the American Physical Society, Carlo Rovelli: “Loop quantum gravity—a theory that extends general relativity by quantizing spacetime—predicts that black holes evolve into white holes.” (December 10, 2018• Physics 11, 127).(5) Ultimately, my review is not much of a book review. Partly, this is due to the issue I have with all of the quantum gravity proposals: no experimental evidence to substantiate anything (yet). Bibliographic notes are useful, a twenty-five page reference list invaluable (also, Mathematical Apparatus of the Theory of Angular Momentum, 1962, by Yutsin is now available online).Back to the beginning of my review. Can we really expect to “rethink physics from scratch” ?The reader will have to decide if this book gets close to accomplishing that aim (I am dubious).Words from Steven Weinberg: ” I still expect there to be a final theory, but I’m less confident that humans will discover it in this century.” (2015, Scientific American interview). I echo his sentiment.

⭐Carlo Rovelli is a world renowned Physicist . This book explaining the possible link between Relativistic theory and quantum theory is well explained. However a knowledge of advanced mathematics cosmology and physics is required. It is not for everyone.

⭐the part 1 (220 pages) is covering the General Relativity and the Quantum mechanics and is by itself worth buying the book.the part 2 is covering the Loop quantum gravity

⭐Il volume è eccellente ed autorevole ma il servizio reso dal fornitore (Amazon Italia vendita e spedizione), ha vanificato il tutto, recapitando un collo devastato da incuria e negligenza del fornitore. Ho rappresentato più volta la scadente qualità dei cartoni utilizzati da Amazon Italia, ma le mie doglianze sono state sistematicamente ignorato. Vergogna …

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⭐Quantum Gravity de Carlo Rovelli est un excellent livre pour aborder la quantification canonique de la gravitation.Le livre est divisé en deux parties. La première, mis à part un court chapitre, n’aborde pas absolument pas la gravitation quantique mais cherche à construire un formalisme quantique covariant. La seconde partie applique ce qui a été ainsi développé dans le cadre de la gravitation quantique.N’ayant pas tout à fait fini le livre, voici ce que j’en ai pensé jusqu’à présent :- Le livre est très clair avec de longues discussions physiques, assez appréciables pour développer une intuition dans le domaine.- On s’approche même parfois de la métaphysique ; j’apprécie ce genre de discussion mais c’est une question de goût. Cela peut en exaspérer certains.- Même si la rigueur mathématique n’est pas parfaite (c’est un livre de physique) l’auteur fait des efforts et donne souvent des références pour approfondir ce côté.- Bien qu’il y ait des rappels de relativité générale et de théorie quantique des champs, autant dire qu’ils sont inutiles si vous n’avez pas étudié ces sujets en détail auparavant. Cela semble une évidence, mais par exemple le formalisme de vierbein (tetrad) n’est pas toujours abordé dans un premier cours de relativité.- Ce livre reste une introduction. De nombreux résultats ne sont pas abordés. Même s’ils sont abordables en tant qu’exercice, je trouve dommage qu’un livre aussi épais ne puisse être utilisé comme livre de référence.Finalement, c’est un excellent livre, très clair, et même pédagogique sans pour autant négliger l’aspect mathématique. Malgré les petits défauts, je donne 5 étoiles. Il les mérite largement.

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⭐Quantum GravityOuvrage de Physique intéressant sur le fond, clair et très pédagogique. Agréable à lire. Nécessite un bon niveau de connaissances Physique Quantique et Relativité.S’adresse principalement aux chercheurs.

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