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Covariant Loop Quantum Gravity: An Elementary Introduction to Quantum Gravity and Spinfoam Theory
Quantum gravity is among the most fascinating problems in physics. It modifies our understanding of time, space and matter. The recent development of the loop approach has allowed us to explore domains ranging from black hole thermodynamics to the early Universe. This book provides readers with a simple introduction to loop quantum gravity, centred on its covariant approach. It focuses on the physical and conceptual aspects of the problem and includes the background material needed to enter this lively domain of research, making it ideal for researchers and graduate students. Topics covered include quanta of space; classical and quantum physics without time; tetrad formalism; Holst action; lattice QCD; Regge calculus; ADM and Ashtekar variables; Ponzano-Regge and Turaev-Viro amplitudes; kinematics and dynamics of 4D Lorentzian quantum gravity; spectrum of area and volume; coherent states; classical limit; matter couplings; graviton propagator; spinfoam cosmology and black hole thermodynamics.
Available for free download from http://www.cpt.univ-mrs.fr/~rovelli/I...
Available for free download from http://www.cpt.univ-mrs.fr/~rovelli/I...
277 pages, Hardcover
First published October 23, 2014
19 people are currently reading
677 people want to read
About the author
Carlo Rovelli
50 books3,950 followersCarlo Rovelli is an Italian theoretical physicist and writer who has worked in Italy and the USA, and currently works in France. His work is mainly in the field of quantum gravity, where he is among the founders of the loop quantum gravity theory. He has also worked in the history and philosophy of science. He collaborates regularly with several Italian newspapers, in particular the cultural supplements of Il Sole 24 Ore and La Repubblica.
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Displaying 1 - 9 of 9 reviews
July 2, 2020
[Original review, Aug 17 2017]
Last week, I read Carlo Rovelli's Reality Is Not What It Seems , a book which does a great job of explaining loop quantum gravity to the layperson. According to more and more physicists, LQG is the theory that does what string theory was supposed to do, and provides us with a "theory of everything": a coherent description of the fundamental structure of the universe which combines the two main physical theories of the twentieth century, quantum mechanics and gravity. Reality Is Not What It Seems is strong on philosophical and poetic intuitions, but weak on detail; given that it's a popular account, that's entirely as it should be. All the same, I wanted to know more, and soon found my way to this slightly earlier book, which Rovelli co-authored with Francesca Vidotto. I've now finished it.
I must say that I have rarely found it so difficult to write a review. Unless you are very knowledgeable about quantum mechanics and relativity (I would say, approaching PhD level), I'm warning you at once that you're going to find much of the text difficult or impossible to understand. The greater part of it is complex mathematical formulas. That said, and despite the fact that I had to skip or skim a great deal, I was astonished to find that the book was not merely engaging but, it's not too strong a word, compulsive. I finished it in four days and could hardly put it down; on one occasion, I went to bed at midnight, then got up again at 2 am because I had to read another chapter. I am not sure I have done this for any remotely similar book.
Why? I'm struggling to explain. The overwhelming impression is one of architecture, a precise, meticulously constructed architecture that you feel the authors revealing to you, even though you don't properly understand what it is. Oddly enough, the book it most reminded me of was Jan Kjærstad's "Jonas Wergeland" trilogy, where I had the same sensation: there is a plan that holds all this together, though I can't quite identify it. I am sure it is not a coincidence that both Rovelli and Kjærstad are fervent admirers of Dante. I had this Dantean feeling of architectural revelation throughout "Jonas Wergeland", but I felt it even more strongly here. Everything fits. There is a long and scarily incomprehensible piece of mathematics, but the whole time the authors are accompanying you, Virgil-like*, and telling you where you're going; we got this result from here, we're going to need that notion a bit later on, you see now why we did the third thing the way we did. You don't completely grasp it. All the same, you find you have to continue.
They say at the beginning that they aren't going to give you the history of the subject, but they show you in rough outline the route they and their colleagues had to take: where the basic intuitions came from, what encouraged them to continue, bits of mathematics that magically came out right and pointed the way towards a hidden pass, the very hard work they had to do to get round a steep overhang. I find myself wanting to use metaphors from mountain-climbing. Well, that's thematic: they seem to have spent many years climbing Mount Purgatory. Now they have reached the Earthly Paradise, where they have been given a first consistent form of the theory, and they are heading off into the stars. The last chapters of the book are about astronomy and cosmology, but they are only tentative compared to the early ones. Some promising initial results on black holes, some glimpses of what may have happened very early on in the history of the Big Bang. They haven't yet reached the Empyrean, and they encourage other, younger pilgrims to join them on their quest. They are more humble than triumphant, because they know the job is not finished yet.
Of course, it could all be an illusion; it wouldn't be the first time that had happened. But I'd say there's an appreciable chance that this is the real deal. If you want to watch a scientific revolution happening in front of you in real time, I don't know of any better place to sit.
__________________
* I suppose I should actually say "Virgil- and Beatrice-like", but that sounded too clunky, and also they never guide Dante at the same time. If you want to know what the authors look like:
_____________________________
[Update, Sep 17 2019]
Here's an intriguing passage from Wolfram's Adventures of a Computational Explorer (p. 100 in the paperback edition). He is talking about creating simulated universes with different fundamental laws of physics and examining their properties:
_____________________________
[Update, Sep 29 2019]
After looking around a bit more, I find this 2017 interview, where Wolfram talks briefly about the relationship between his work and LQG. He gives a link to what he calls
_____________________________
[Update, Jul 2 2020]
Wolfram's A Project to Find the Fundamental Theory of Physics, published last week, gives a little more detail on the above claims, but it's still extremely sketchy. Given that the book is 770 pages long, this is disappointing. There is however a link to an arXiv paper by one of Wolfram's students, which presents further information.
Last week, I read Carlo Rovelli's Reality Is Not What It Seems , a book which does a great job of explaining loop quantum gravity to the layperson. According to more and more physicists, LQG is the theory that does what string theory was supposed to do, and provides us with a "theory of everything": a coherent description of the fundamental structure of the universe which combines the two main physical theories of the twentieth century, quantum mechanics and gravity. Reality Is Not What It Seems is strong on philosophical and poetic intuitions, but weak on detail; given that it's a popular account, that's entirely as it should be. All the same, I wanted to know more, and soon found my way to this slightly earlier book, which Rovelli co-authored with Francesca Vidotto. I've now finished it.
I must say that I have rarely found it so difficult to write a review. Unless you are very knowledgeable about quantum mechanics and relativity (I would say, approaching PhD level), I'm warning you at once that you're going to find much of the text difficult or impossible to understand. The greater part of it is complex mathematical formulas. That said, and despite the fact that I had to skip or skim a great deal, I was astonished to find that the book was not merely engaging but, it's not too strong a word, compulsive. I finished it in four days and could hardly put it down; on one occasion, I went to bed at midnight, then got up again at 2 am because I had to read another chapter. I am not sure I have done this for any remotely similar book.
Why? I'm struggling to explain. The overwhelming impression is one of architecture, a precise, meticulously constructed architecture that you feel the authors revealing to you, even though you don't properly understand what it is. Oddly enough, the book it most reminded me of was Jan Kjærstad's "Jonas Wergeland" trilogy, where I had the same sensation: there is a plan that holds all this together, though I can't quite identify it. I am sure it is not a coincidence that both Rovelli and Kjærstad are fervent admirers of Dante. I had this Dantean feeling of architectural revelation throughout "Jonas Wergeland", but I felt it even more strongly here. Everything fits. There is a long and scarily incomprehensible piece of mathematics, but the whole time the authors are accompanying you, Virgil-like*, and telling you where you're going; we got this result from here, we're going to need that notion a bit later on, you see now why we did the third thing the way we did. You don't completely grasp it. All the same, you find you have to continue.
They say at the beginning that they aren't going to give you the history of the subject, but they show you in rough outline the route they and their colleagues had to take: where the basic intuitions came from, what encouraged them to continue, bits of mathematics that magically came out right and pointed the way towards a hidden pass, the very hard work they had to do to get round a steep overhang. I find myself wanting to use metaphors from mountain-climbing. Well, that's thematic: they seem to have spent many years climbing Mount Purgatory. Now they have reached the Earthly Paradise, where they have been given a first consistent form of the theory, and they are heading off into the stars. The last chapters of the book are about astronomy and cosmology, but they are only tentative compared to the early ones. Some promising initial results on black holes, some glimpses of what may have happened very early on in the history of the Big Bang. They haven't yet reached the Empyrean, and they encourage other, younger pilgrims to join them on their quest. They are more humble than triumphant, because they know the job is not finished yet.
Of course, it could all be an illusion; it wouldn't be the first time that had happened. But I'd say there's an appreciable chance that this is the real deal. If you want to watch a scientific revolution happening in front of you in real time, I don't know of any better place to sit.
__________________
* I suppose I should actually say "Virgil- and Beatrice-like", but that sounded too clunky, and also they never guide Dante at the same time. If you want to know what the authors look like:
_____________________________
[Update, Sep 17 2019]
Here's an intriguing passage from Wolfram's Adventures of a Computational Explorer (p. 100 in the paperback edition). He is talking about creating simulated universes with different fundamental laws of physics and examining their properties:
A particular representation that I have studied involves setting up a large number of nodes, connected in a network, and repeatedly updating according to some local rewrite rule. Within this representation, one can in effect just start enumerating possible universes, specifying initial conditions and updating rules. Some candidate universes are very obviously not our physical universe. They have no notion of time, or no communication between different parts, or an infinite number of dimensions of space, or some other obviously fatal pathology.Well... the spin networks that Rovelli and Vidotta focus on in their book are, if I'm understanding Wolfram correctly, an example of the kind of thing he's referring to. And spin networks do indeed imply General Relativity - though the way R&V tell it, that was an extremely nontrivial discovery which took decades to establish. But Wolfram says it's a special case of a much more general result. If so, quite amazing. I just checked, and R&V do not mention Wolfram at all; so far, Wolfram has not mentioned LQG.
But it turns out that there are large classes of candidate universes that already show remarkably suggestive features. For example, any universe that has a notion of time with certain robustness properties turns out in an appropriate limit to exhibit Special Relativity. And even more significantly, any universe that exhibits a certain conservation of finite dimensionality - as well as generating a certain level of microscopic randomness - will lead on a large scale to spacetime that follows Einstein's equations for General Relativity.
_____________________________
[Update, Sep 29 2019]
After looking around a bit more, I find this 2017 interview, where Wolfram talks briefly about the relationship between his work and LQG. He gives a link to what he calls
A big result I found nearly 20 years ago (that still hasn’t been widely understood) is that when you look at a large enough network of the kind I studied you can show that its averaged behavior follows Einstein’s equations for gravity. In other words, without putting any fancy physics into the underlying model, it ends up automatically emerging. I think it’s pretty exciting.The link doesn't work properly any more, but it certainly looks like it's meant to go to section 15 of chapter 9 of his 2002 book A New Kind of Science. This, however, only gives further vague hints.
_____________________________
[Update, Jul 2 2020]
Wolfram's A Project to Find the Fundamental Theory of Physics, published last week, gives a little more detail on the above claims, but it's still extremely sketchy. Given that the book is 770 pages long, this is disappointing. There is however a link to an arXiv paper by one of Wolfram's students, which presents further information.
November 23, 2016
Only managed to cover up to chapter 5. This book has skipped a lot of details and thus while the writing is made such that it sounds light for newcomers in loop quantum gravity, there are actually quite a lot of heavy-lifting to be done while reading. For one, one cannot read this book without some basic understanding of Lie groups and Lie algebras, on top of sufficient understanding of classical mechanics and Hamiltonian formalism of GR.
But definitely it conveys the flavour of what LQG tries to achieve and schematics of how it tries to do things.
Will read this again once I am at higher level. My current undergraduate knowledge is not enough --- even with the help of PhD students around me.
But definitely it conveys the flavour of what LQG tries to achieve and schematics of how it tries to do things.
Will read this again once I am at higher level. My current undergraduate knowledge is not enough --- even with the help of PhD students around me.
October 10, 2019
An absolutely excellent introduction, however the claim that only basic QFT knowledge is required is a bit of a stretch.
You’ll need a comfortable working relationship with LIE algebra, as well as differential forms and alternative formulations of the Einstein-Hilbert action.
Other than overselling the “basic” knowledge required, this book is incredibly well put together and easy to follow for serious enthusiasts.
You’ll need a comfortable working relationship with LIE algebra, as well as differential forms and alternative formulations of the Einstein-Hilbert action.
Other than overselling the “basic” knowledge required, this book is incredibly well put together and easy to follow for serious enthusiasts.
December 13, 2018
free download pdf here:
www.cpt.univ-mrs.fr/~rovelli/Introduc...
Starts well, by telling us that to integrate two seemingly incompatible branches of physics, the aim is to look for something that reduces to each, at ordinary scales. Schrödinger did this, to find his wave equation. (p. 50 of 277 in the pdf) And that it’s good that theorists are constrained by having to explain the real world. (p. 14 of 277)
You'd need all but dissertation in field theory to even understand his notation. He almost never says what his symbols mean. The equations are almost all not actual equations, but meta-equations, and in shorthand. Integrals without a dsomething; a letter meant to stand in for a group of coordinates, vectors, operators. You’d have to read all the books and papers he cites to find out what, if anything, he’s talking about. (And if you did read them all, would this book add anything? No way to know until you do.) Sloppiness and facetiousness don’t make the book an introduction. If you can’t be understood, maybe you don’t understand the subject as well as you thought.
A few easy bits of trivia from early on:
goodreads.com/trivia/work/42044329-co...
Some brilliant scientists who write brilliantly for the general reader:
Richard Feynman. For example, QED: The Strange Theory of Light and Matter and The Feynman Lectures on Physics
Edwin F. Taylor: Spacetime Physics
Isaac Asimov: any and all of his nonfiction
Erwin Schrödinger. For example, What Is Life? with Mind and Matter and Autobiographical Sketches
www.cpt.univ-mrs.fr/~rovelli/Introduc...
Starts well, by telling us that to integrate two seemingly incompatible branches of physics, the aim is to look for something that reduces to each, at ordinary scales. Schrödinger did this, to find his wave equation. (p. 50 of 277 in the pdf) And that it’s good that theorists are constrained by having to explain the real world. (p. 14 of 277)
You'd need all but dissertation in field theory to even understand his notation. He almost never says what his symbols mean. The equations are almost all not actual equations, but meta-equations, and in shorthand. Integrals without a dsomething; a letter meant to stand in for a group of coordinates, vectors, operators. You’d have to read all the books and papers he cites to find out what, if anything, he’s talking about. (And if you did read them all, would this book add anything? No way to know until you do.) Sloppiness and facetiousness don’t make the book an introduction. If you can’t be understood, maybe you don’t understand the subject as well as you thought.
A few easy bits of trivia from early on:
goodreads.com/trivia/work/42044329-co...
Some brilliant scientists who write brilliantly for the general reader:
Richard Feynman. For example, QED: The Strange Theory of Light and Matter and The Feynman Lectures on Physics
Edwin F. Taylor: Spacetime Physics
Isaac Asimov: any and all of his nonfiction
Erwin Schrödinger. For example, What Is Life? with Mind and Matter and Autobiographical Sketches
December 6, 2017
I can't claim to have understood 10% of this but my lay-person take away is that gravity comes about from a property of the fields that make up physical particle instead of being an external field that interacts with it. I'll have to consult a particle physicist to see if I was anywhere close.
February 22, 2020
I went through the book already twice, and I have to say it's quite well-versed and easy to read, even for a bachelor student, I'd say. The basics to know are differential geometry, and visualise things in 4D :) The first chapters are a very gentle introduction, while things speed up at the introduction of the full 4D theory. The last chapters are just touching on Cosmology and scattering, so don't expect anything from them, in concrete terms. After reading this you'll be able to comfortably read the papers now published about it. Also, there are some points in which the authors stress some commonly misunderstood concepts, like the often mentioned breaking Lorentz invariance, which is something the detractors always talk about.
My opinion on the quantum gravity diatribe: After having had string theory in my master course (of physics), corresponding to the first Polchinski volume, and reading this book, I'm quite convinced I'd go more for LQG, being a less-marketed theory but more consistent with reality, and well-anchored with math too.
My opinion on the quantum gravity diatribe: After having had string theory in my master course (of physics), corresponding to the first Polchinski volume, and reading this book, I'm quite convinced I'd go more for LQG, being a less-marketed theory but more consistent with reality, and well-anchored with math too.
Currently reading
February 15, 2023.
-
It's 2023 February 13 and I start a try with this book.
Time and space don't exist, only gravity (my understanding at the moment).
Yes, this author is a challence and not only in this book.
There is a scan on loan of a copy from the fourth printing of 2018.
The paperback edition is the fifth printing in 2020 (May) of this work first published in 2014(5).
doi
lccn 2014028593
CUP hardcover
https://cambridge.org/9781108810258 paperback
https://cambridge.org/9781316147290 ebook
CUP paperback
CUP ebook (publication 2015 february)
preview, content
2018 hardcover 4th printing
2020 May paperback 5th printing
website author
cern on 2008-08-21T17:35:00 44 min
url
-
.
-
It's 2023 February 13 and I start a try with this book.
Time and space don't exist, only gravity (my understanding at the moment).
Yes, this author is a challence and not only in this book.
There is a scan on loan of a copy from the fourth printing of 2018.
The paperback edition is the fifth printing in 2020 (May) of this work first published in 2014(5).
doi
lccn 2014028593
CUP hardcover
https://cambridge.org/9781108810258 paperback
https://cambridge.org/9781316147290 ebook
CUP paperback
CUP ebook (publication 2015 february)
preview, content
2018 hardcover 4th printing
2020 May paperback 5th printing
website author
cern on 2008-08-21T17:35:00 44 min
url
-
.
reference
January 25, 2023❝The astute reader may wonder whether the fact that we have started with a fixed chunk of space plays a role in the argument. Had we chosen a smaller tetrahedron to start with, would we have obtained smaller geometric quanta? The answer is no, and the reason is at the core of the physics of general relativity: there is no notion of size (length, area, volume) independent from the one provided by the gravitational field itself. The coordinates used in general relativity carry no metrical meaning. In fact, they carry no physical meaning at all. If we repeat the above calculation starting from a “smaller” tetrahedron in coordinate space, we are not dealing with a physically smaller tetrahedron, only with a different choice of coordinates. This is apparent in the fact that the coordinates play no role in the derivation. Whatever coordinate tetrahedron we may wish to draw, however small, its physical size will be determined by the gravitational field on it, and this is quantized❞
Want to read
September 24, 2018Will pick up after a course in Relativity and QM
Displaying 1 - 9 of 9 reviews