- #1
JustinLevy
- 895
- 1
Since there are several people here who intently follow the developements of LQG, I was wondering if someone could give some overview to help understand the 'historical path' of research on this topic better. What methods were developed, which died off, what was learned, where they are going now, etc.
To get things started, my (very rough, and possibly incorrect) understanding is the following:
(Due to the roughness/possibly incorrect info, please don't add to this ... this is more to give an example what kind of history I'm interested in.)
It is my understanding that there is a difficulty when setting out to quantize gravity in choosing the dynamical variables due to the large equivalences given by diffeomorphism invariance. So the starting point was the reformulation of Einstein-Cartan theory (GR extended to allow matter with inherent spin) with Ashtekar variables. This reformulation with the Ashtekar variables as the dynamical variables to be quantized was chosen as the starting point of LQG.
The 'loops' of LQG are wilson loops on the continuous spacetime (despite some claims by non LQG people, it is my understanding that LQG does NOT claim spacetime is discrete). Quantizing this describes the geometry of spacetime with a 'weave' of loops, and it was found at some point that this could be described with spin networks.
I don't understand what happened next, but I got the impression that the spin networks and canonical loop methods somehow diverged? I don't really understand how this was possible. It was found that there was some arbitrariness in how the dynamics was described, is this how the two departed from each other?
At one point (I don't know any dates), the Barrett-Crane LQG description of gravity was shown to be inconsistent with reality. When I first heard about this, it was from a string theorist who didn't like LQG for several philosophical reasons, and so used this as the 'last straw' to consider LQG as thrown in the waste basket. Based on impressions from other people, I also got the impression people were considering LQG 'dead' at this point. Is that a fair characterization of the outlook for LQG at the time?
I don't fully understand what was wrong with the Barrett-Crane model, but then some researchers narrowed down what was wrong and learned from it (what?) to create a better model of dynamics? There appears to be a real push now to get GR in the classical limit back out with this new model.
Some things I don't know how to fit in. How many seriously pursued 'versions' of LQG are there (how many died off, how many are still fighting forward)? How did LQC jump in, since it is somehow separate?
And Marcus sometimes refers to a 'mini-revolution' where spin-networks and the canonical loop methods were 'rejoined' or something. What happened? People here also refer to something as 'covariant loops', and sometimes say even the term 'loop' is just a hold-over from the historical birth of LQG. So what is covariant loops? (Didn't LQG already have poincare symmetry?) And are 'loops' not really involved anymore... how does it make contact with the Ashtekar reformulation of Einstein-Cartan without the wilson loops? I thought that was the whole starting point!?
Sorry for the length of this. Hopefully someone can explain what the current status is, and how we got here.
Thanks.
To get things started, my (very rough, and possibly incorrect) understanding is the following:
(Due to the roughness/possibly incorrect info, please don't add to this ... this is more to give an example what kind of history I'm interested in.)
It is my understanding that there is a difficulty when setting out to quantize gravity in choosing the dynamical variables due to the large equivalences given by diffeomorphism invariance. So the starting point was the reformulation of Einstein-Cartan theory (GR extended to allow matter with inherent spin) with Ashtekar variables. This reformulation with the Ashtekar variables as the dynamical variables to be quantized was chosen as the starting point of LQG.
The 'loops' of LQG are wilson loops on the continuous spacetime (despite some claims by non LQG people, it is my understanding that LQG does NOT claim spacetime is discrete). Quantizing this describes the geometry of spacetime with a 'weave' of loops, and it was found at some point that this could be described with spin networks.
I don't understand what happened next, but I got the impression that the spin networks and canonical loop methods somehow diverged? I don't really understand how this was possible. It was found that there was some arbitrariness in how the dynamics was described, is this how the two departed from each other?
At one point (I don't know any dates), the Barrett-Crane LQG description of gravity was shown to be inconsistent with reality. When I first heard about this, it was from a string theorist who didn't like LQG for several philosophical reasons, and so used this as the 'last straw' to consider LQG as thrown in the waste basket. Based on impressions from other people, I also got the impression people were considering LQG 'dead' at this point. Is that a fair characterization of the outlook for LQG at the time?
I don't fully understand what was wrong with the Barrett-Crane model, but then some researchers narrowed down what was wrong and learned from it (what?) to create a better model of dynamics? There appears to be a real push now to get GR in the classical limit back out with this new model.
Some things I don't know how to fit in. How many seriously pursued 'versions' of LQG are there (how many died off, how many are still fighting forward)? How did LQC jump in, since it is somehow separate?
And Marcus sometimes refers to a 'mini-revolution' where spin-networks and the canonical loop methods were 'rejoined' or something. What happened? People here also refer to something as 'covariant loops', and sometimes say even the term 'loop' is just a hold-over from the historical birth of LQG. So what is covariant loops? (Didn't LQG already have poincare symmetry?) And are 'loops' not really involved anymore... how does it make contact with the Ashtekar reformulation of Einstein-Cartan without the wilson loops? I thought that was the whole starting point!?
Sorry for the length of this. Hopefully someone can explain what the current status is, and how we got here.
Thanks.