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Something Abhay Ashtekar said is beginning to sink in.
It is from page 29 of his recent review paper Gravity and the Quantum
http://arxiv.org/gr-qc/0410054
and I quoted it at length here
https://www.physicsforums.com/showthread.php?p=359374#post359374
What I want to focus on is where he is talking about the 4 main ways being explored to include dynamics in the theory. In fact what he says is somewhat more general, he poses two main issues for the future of LQG----(1)quantum geometry and (2)quantum einstein equation----and he says at bottom of page 28 "To address these core issues, at least four different avenues are being pursued..." The four he lists are:
1. Thiemann master constraint
2. Gambini et al knot invariants
3. spinfoam---various people
4. Gambini et al. CD
first note that in Ashtekar perspective, two of the four important avenues to explore are ones opened by Gambini et al. this gives Gambini et al good marks for having creative, possibly fertile, ideas----as I believe Ashtekar would see it.
Now here is the relevant Ashtekar quote
---quote---
In the fourth approach, also due to Gambini and Pullin, one first constructs consistent discrete theories at the classical level and then quantizes them [42]. In this program, there are no constraints; they are solved classically to find lapse and shift fields. This strategy has already been applied successfully to gauge theories and certain cosmological models. An added bonus here is that one can revive a certain proposal made by Page and Wootters to address the difficult issues of interpretation of quantum mechanics which become especially acute in quantum cosmology, and more generally in the absence of a background physical geometry...
---end quote---
the reference [42] which he cites is to
Gambini/Pullin
Consistent Discretizations and Quantum Gravity
http://arxiv.org/gr-qc/0408025
So this CD approach is quite new (first proposed by Gambini and Pullin in 2002) and looks promising---is appealing because obviates the constraint business---and it has a kind of "official Abhay stamp of approval" as being a good direction to look in. Also it puts the wind back into Page Wootter sails, puts new life into an old (1983) idea.
this thread started with a paper of Bojowald.
I said:
and then edgar1813 came in and showed that, as far as being relevant to the topic of Time in Quantum Gravity, this work of Gambini Pullin and others is highly on-target. It looks well worth keeping an eye on and gradually understanding more about it.
In Rovelli's book, chapter on Mechanics, he says that
(1) Nonrelativistic mechanics is about evolution in time.
(2) Relativistic mechanics is about correlation between partial observables.
In the preface he warns that when he says "relativity" he means GENERAL relativity----he says that if you always have to say general it can begin to sound like a Frenchman discussing Charles de Gaulle. So the thing is to mean gen rel when you say rel, so for Rovelli "nonrelativistic" includes 1905 special rel.
What Rovelli says about Mechanics goes back to the 1983 idea of Page Wootters, and what makes Gambini-team's CD approach especially interesting to me is that it implements Page Wootters idea for the first time.
(when they proposed it in 1983, Kuchar blocked it by pointing to the 'miltonian constraint, which now CD bypasses)
I guess this means we have to look at Kuchar which is online, just to better understand the context.
http://www.phys.lsu.edu/faculty/pullin/kvk.pdf
BTW this looks like a scan of a xerox, you have to allow some time for it to download, like over half an hour, as if it were a hundred low-resolution black and white photographs
Pullin gave the first talk Saturday morning 30 October at Perimeter
Americas LQG conference:
Jorge Pullin: Semi-discrete solution to the dynamics of loop quantum gravity
It is from page 29 of his recent review paper Gravity and the Quantum
http://arxiv.org/gr-qc/0410054
and I quoted it at length here
https://www.physicsforums.com/showthread.php?p=359374#post359374
What I want to focus on is where he is talking about the 4 main ways being explored to include dynamics in the theory. In fact what he says is somewhat more general, he poses two main issues for the future of LQG----(1)quantum geometry and (2)quantum einstein equation----and he says at bottom of page 28 "To address these core issues, at least four different avenues are being pursued..." The four he lists are:
1. Thiemann master constraint
2. Gambini et al knot invariants
3. spinfoam---various people
4. Gambini et al. CD
first note that in Ashtekar perspective, two of the four important avenues to explore are ones opened by Gambini et al. this gives Gambini et al good marks for having creative, possibly fertile, ideas----as I believe Ashtekar would see it.
Now here is the relevant Ashtekar quote
---quote---
In the fourth approach, also due to Gambini and Pullin, one first constructs consistent discrete theories at the classical level and then quantizes them [42]. In this program, there are no constraints; they are solved classically to find lapse and shift fields. This strategy has already been applied successfully to gauge theories and certain cosmological models. An added bonus here is that one can revive a certain proposal made by Page and Wootters to address the difficult issues of interpretation of quantum mechanics which become especially acute in quantum cosmology, and more generally in the absence of a background physical geometry...
---end quote---
the reference [42] which he cites is to
Gambini/Pullin
Consistent Discretizations and Quantum Gravity
http://arxiv.org/gr-qc/0408025
So this CD approach is quite new (first proposed by Gambini and Pullin in 2002) and looks promising---is appealing because obviates the constraint business---and it has a kind of "official Abhay stamp of approval" as being a good direction to look in. Also it puts the wind back into Page Wootter sails, puts new life into an old (1983) idea.
this thread started with a paper of Bojowald.
I said:
and then edgar1813 came in and showed that, as far as being relevant to the topic of Time in Quantum Gravity, this work of Gambini Pullin and others is highly on-target. It looks well worth keeping an eye on and gradually understanding more about it.
In Rovelli's book, chapter on Mechanics, he says that
(1) Nonrelativistic mechanics is about evolution in time.
(2) Relativistic mechanics is about correlation between partial observables.
In the preface he warns that when he says "relativity" he means GENERAL relativity----he says that if you always have to say general it can begin to sound like a Frenchman discussing Charles de Gaulle. So the thing is to mean gen rel when you say rel, so for Rovelli "nonrelativistic" includes 1905 special rel.
What Rovelli says about Mechanics goes back to the 1983 idea of Page Wootters, and what makes Gambini-team's CD approach especially interesting to me is that it implements Page Wootters idea for the first time.
(when they proposed it in 1983, Kuchar blocked it by pointing to the 'miltonian constraint, which now CD bypasses)
I guess this means we have to look at Kuchar which is online, just to better understand the context.
http://www.phys.lsu.edu/faculty/pullin/kvk.pdf
BTW this looks like a scan of a xerox, you have to allow some time for it to download, like over half an hour, as if it were a hundred low-resolution black and white photographs
Pullin gave the first talk Saturday morning 30 October at Perimeter
Americas LQG conference:
Jorge Pullin: Semi-discrete solution to the dynamics of loop quantum gravity
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