There's a good paper overviewing quantum loop theory. It is Nicolai, Peeters and Zamaklar's "Loop Quantum Gravity: an Outside View" For those not familiar with quantum gravity efforts, loop quantum gravity is basically the main competitor to superstring theory (which is now M-theory). Lee Smolin is its noted proponent. It's not really basic enough for people not already generally familiar with the topic. But since it takes a somewhat critical stance, many might find it interesting. From the conclusions
String theory and LQG pursue the same goal, a consistent theory of quantum gravity, though with very different means. Both approaches address core issues of quantum gravity, but concentrate on complementary aspects of the problem, and have led to valuable insights. For this reason, the opinion has been voiced that string theory and LQG may ultimately merge together in a grand synthesis, or that LQG might become part of string theory. However, on the basis of the available evidence (summarised in this review), this does not appear a likely outcome to us.
We have reported here on the status of loop quantum gravity from a somewhat uncommon perspective. Our general conclusion is that, despite the optimism prevalent in many other reviews, more attention should be paid to basic aspects and unresolved problems of the theory. The large number of ambiguities present in the formalism is, in our opinion, a reason for concern. These ambiguities are most clearly visible in the discussion of the Hamiltonian constraint. As we have stressed, it is this constraint which reflects the main problems of quantum gravity, not only in the loop approach but also in geometrodynamics. However, in the latter approach, it is at least possible to carry out some elementary checks at the dynamical level, and to demonstrate by explicit computation its failure to produce a theory of quantum gravity with all the requisite properties. For the time being, such an examen crucis does not appear possible for LQG due to the mathematical complexity of the Hamiltonian constraint, despite many other proposed tests of its viability in the literature. Another important issue which has not received the attention which it deserves is the ultra-local behaviour of the Hamiltonian constraint in LQG. Without an understanding of this problem, it seems premature to discuss applications of the formalism, which assume that a classical limit exists, or possible experimental signatures.
In summary, we feel that there are still too many problems at a basic level that need to be addressed and resolved before one can tell whether the loop quantum gravity programme will succeed or fail. We hope that the present paper will provide an incentive to re-focus attention to these basic issues.
Clark,
trying to find a thread here where I'm not asking something totally off topic. I bought Penrose's "Guide to Reality" yesterday and wondered what you think of it. I was pretty excited to find it I admit, because it looks like kind of a compromise between newspaper science and the real thing, he's a great expositer and it also has some math. Looking over the information on the official "String Theory" website, they have three levels of math required to get into it, I have (or had!) level one down http://superstringtheory.com/math/index.html
but level 2, ok, not going to happen with the time I have. Anyway, if you've read it or heard anything about it from people "in the know" i'd be curious. It's pretty long and I'm a one-book-a-year kind of guy so I want to make it count.
I've not read it. I tend to find Penrose a genius in terms of physics and kind of naive in terms of philosophy. Although I like him better than Hawkings. (I have a few books of their debates) But I've just not read Penrose. He goes after the spinor-theory route doesn't he? I've really wanted to learn spinor-algebra but just never have had the time.
Apparently yes. Though I don't know what that means. I skipped the first few pages on his interpretation of Plato I don't even have the curiosity. The appeal was getting one-stop treatment of core ideas to theoretical physics. I've read a few reviews now, of course professional researchers who are working on current problems complain its outdated and barely scratches the surface blah blah. But then I was surprised to see a number of reviewers claiming graduate degrees, even phds in theoretical physics no less, complain that the math is too hard. so i'm a little less optimistic that he's dumbed down graduate math than i was yesterday.
so we'll see..
Sorry, that should have said, "but I've just not read this book of Penrose's." But I assume you got the general gist. I've thought about picking it up. But I have a backlog of books right now and I'm more interested in cognitive science until I can dedicate the time to do the math. If it has a lot of math I'm probably more apt to pick up one of the textbooks on string theory or loop quantum gravity.
BTW - if you are interested Dissoi Blogoi did a writeup on Penrose's treatment of Plato. I've also read that he get Pythagoras wrong and a few other ancient philosophers. But since you skipped his musings on Plato that's probably not of interest to you.
I got that part, my response was actually to your question about going the "spinor-theory" route. Since I don't have any idea what that is.
Oh. Clifford algebra and spinors are pretty cool. I had a friend who studied them in the context of QM fairly heavily. I really want to but as I've said haven't (yet) had the time. As I've often said it's my dream to have enough time so as to do less philosophy and far more theoretical physics. The wiki for the algebra of physical space is pretty good on it. While wikipedia for various reasons is often dangerous relative to philosophy it typically is pretty good for the hard sciences.
I've closed comments in order to avoid spam since I don't check this older blog as much anymore.
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