i have already read carlo rovelli's 'reality is not what it seems' and lee smolin's three roads to quantum gravity, how should i proceed from here and what books do i read that balance theoretical approach with the mathematical approach, i was looking forward to a first course LQG and string theory should i go ahead with them?
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4$\begingroup$ What's the difference between a theoretical approach and a mathematical one? Quantum gravity is really only speculative in its various approaches, so you can pick whatever approach you think fulfills your goals. $\endgroup$– AvantgardeCommented Jul 22, 2023 at 14:56
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$\begingroup$ i think its not right to call it only speculative although still not completely developed, it has potential and is going in the right direction $\endgroup$– Bhavya SinghCommented Jul 22, 2023 at 15:26
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1$\begingroup$ Do you know any quantum field theory or general relativity? $\endgroup$– Mitchell PorterCommented Jul 23, 2023 at 5:23
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$\begingroup$ As far as we know, it is completely speculative since there is no experimental evidence of any quantum gravity phenomenon, up to now. $\endgroup$– Valter MorettiCommented Jul 23, 2023 at 9:28
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3 Answers
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Based on your previous reading, it seems as though your background is based on popular science. As such, a traditional course on the subject is of course not possible. As such, to bridge the gap, I would recommend,
- The Road to Reality by Sir Roger Penrose.
PROS -
The book covers most of the grander concepts and problems in theoretical physics in spectacular fashion for a popular science text considering that it is not shy of the math.
It is the ideal place to start for the balance you are looking for. I assume you mean conceptual when you say theoretical considering you are making a distinction between that and a mathematical approach, which is typically attributed to rigor and is not considered separate but rather complementary.
You also get exposure to and access to a wealth of information with regards to other literature and also learn about lesser-known ideas in quantum gravity like the author's own twistor theory.
Regardless of your physical or mathematical background, this book will be able to put you in a better position to understand these areas of physics in depth while tackling papers and monographs.
CONS -
The quantum gravity and theory of everything side of things is a bit biased (leading into twistor theory) in the book, albeit very clearly mentioned.
This is a big jump from your run-of-the-mill popular science books. A decent understanding of it can only be achieved by having productive conversations about your reading.
There is a tendency to avoid math in popular science texts. This one doesn't do that via a work-around in teaching the math visually. This is a big hurdle one needs to clear before getting into the physics.
While a great exposition, it is definitely not a substitute for formal texts, papers and monographs.
That being siad, if you do in fact have some mathematical background and a decent knowledge of general relativity and quantum field theory, you ought to try,
- Quantum Gravity by Prof. Dr. Claus Kiefer.
This is a far better place to start for someone with the background than any typical loopy or stringy text because it gives you an overview of all three major approaches (including quantum geometrodynamics) and also relatively modern ideas such as AdS/CFT aka Holography. One can make a decision to take up loops or strings in more detail after having an overview on the bigger picture.
Hope you find this answer useful :)
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2$\begingroup$ Have you actually used The Road to Reality? It goes from $1+1=2$ to calculus in 100 pages, and then to fiber bundles in another 100 pages. Nobody can actually learn math at that pace. The book is good for people who already know the material, or as casual reading for people who aren’t actually trying to understand it. $\endgroup$– knzhouCommented Jul 25, 2023 at 16:11
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1$\begingroup$ @knzhou I have indeed read the book. Took me a few years to finish it so I'm aware of how dense some of the content is. However, having gone through it I also realised that it does a pretty solid job in conveying the conceptual ideas that are either oversimplified in typical popular books and articles or hidden far beneath layers of complicated mathematics. $\endgroup$ Commented Jul 25, 2023 at 22:58
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$\begingroup$ The bottomline is that while the content can be very confusing at times, it helps to have conversations with people who know their stuff in the field as you read it. The book combined with some of my professors, peers and quite a few folks online helped me learn a lot. I'm sure it can be the same for the intended audience if they use the book cleverly. That could be true of any book of course, but with this one you tend to have more questions than most regular pop science ones which tend to give you a false sense of understanding. $\endgroup$ Commented Jul 25, 2023 at 23:02
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$\begingroup$ @knzhou keep in mind that I've not recommended the book as a text or a coursework reference. It's a good place to start for someone who has made a journey mostly via popular science to get a taste for what it really is like to think about the things us physicists think about. I believe my answer was pretty clear on that matter anyways. $\endgroup$ Commented Jul 25, 2023 at 23:08
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A First Course in Loop Quantum Gravity by Gambini and Pullin is a textbook aimed at advanced undergraduates. While it claims in the preface that the reader only needs minimal familiarity with quantum mechanics and hamiltonian mechanics, I would not advise anyone to attempt to work through it unless they have the equivalent of three years of undergraduate physics behind them. In the USA this would include a full year of introductory physics, "modern physics" (including special relativity and basic quantum), a dedicated quantum mechanics class, and a dedicated analytical classical mechanics class. This would give you the mathematical and problem solving experience to tackle such a book.
If you are trying to learn the LQG, you want that to be the bulk of the new material. You won't get as much LQG out of it if you are teaching yourself differential equations and Hamiltonian dynamics at the same time.
Covariant Loop Quantum Gravity by Rovelli and Vidotto is a introductory graduate text on LQG. This expects you to know some general relativity and quantum field theory in addition to the basic undergraduate material. The preface to this text points to the Gambini and Pullin book as providing useful background.
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Covariant LQG are separated into 2 networks. 1: spin network, 2: Foam like structure network. These networks are the gravitational fields, these fields are the GRAVITONS, but they are not because, they are loops. The foam network and spin network work function accurately according to the newton’s gravitational constant G. When mass or energy is entered into the field, depending on the wide spread of the energy, the loops start to move or jiggle in a chaotic order. They move and jiggle every PLANCK SECOND. The loops also contain all the fundamental Planck scales. While the loops are jiggling, the spin network spins the entire loops which are attracted to that gravitational field, they create the curvature of SPACE-TIME!!!! That’s it, this covariant LQG. LQG also predicts some amazing features of the standard model particle and relativity such as the behavior light, it predicts that light slows down when they have high energy. But, this had not been proven since we cannot measure the speed of the light accurately.