Time Dependence in Quantum Gravity: Recent Bojowald Paper

[marcus]

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:

want to read together this recent Bojowald paper?
Time Dependence in Quantum Gravity
http://arxiv.org/gr-qc/0408094

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

 

[marcus]

Whoa! we were just talking about Partial Observable concept
edgar1813 had some words about it in this thread
and now today a paper by Bianca Dittrich is posted.
She is at AEI-Gölm and was just giving a paper at perimeter a couple of days ago

---Bianca abstract---
We will pick up the concepts of partial and complete observables introduced by Rovelli in order to construct Dirac observables in gauge systems. We will generalize these ideas to an arbitrary number of gauge degrees of freedom. Different methods to calculate such Dirac observables are developed. For background independent field theories we will show that partial and complete observables can be related to Kuchar's Bubble Time Formalism. Moreover one can define a non-trivial gauge action on the space of complete observables and also state the Poisson brackets of these functions.

Additionally we will investigate, whether it is possible to calculate Dirac observables starting with partially invariant partial observables, for instance functions, which are invariant under the spatial diffeomorphism group.
---end quote---

B. Dittrich (Max Planck Institute, Potsdam and Perimeter Institute)
Partial and Complete Observables for Hamiltonian Constrained Systems
http://arxiv.org/gr-qc/0411013

 

[selfAdjoint]

Wow! I thought I understood Hamiltonian systems, but this is terrific. I'll have to return to it tomorrow (tracking election results tonight).

 

[marcus]

Wow! I thought I understood Hamiltonian systems, but this is terrific. I'll have to return to it tomorrow (tracking election results tonight).

Bianca is just a grad student (or maybe now a postdoc).
Not to expect anything too revolutionary.
I was struck by the coincidence that we had just been discussing partial observables and the next day there is an article about them. But
who knows if it is the right way to go.
I have the impression that if one does as GP suggest
and discretizes time and then applies LQG methods to the spatial slice,
then (if turns out to work as GP say) one does not need to stress this
distinction of partial/complete observable. GP do relational time but I don't see them talking about partial observable.
this is all deliciously unclear to me at the moment.

BTW does anyone remember the paper of Padmanabhan from a month or two back?
From Gravitons to Gravity: Myths and Reality [gr-qc/0409089].
now Padmanabhan has posted a new paper
astro-ph/0411044
I am impressed with him. he seems like a world class cosmologist
he lives at Ganeshkhind, in Pune (used to be spelled Poona)

 

[selfAdjoint]

Still, I think her version of time is not far from GP, modulo the discretization, even though she winds up with an infinite number of clocks in her analytical version. Which is, after all, only reasonable. Unless you focus down on just one special observer, or test particle, or whatever, then you have to consider all possible ones.

The partial observable idea is so neat, I don't WANT to work around it! But CD is neat too! So many marvels, so little time!

 

[marcus]

Here is a snap of Bianca Dittrich talking to R. Gambini
(May 2004)
http://perimeterinstitute.ca/images/marseille/marseille010.JPG

Here is a much earlier snap (spring 1999) of Bianca
when she won some science prize for students at Uni Potsdam.
http://www.uni-potsdam.de/u/putz/sept99/19.htm

Maybe no one but me thinks it helps to have some pix of the
real people to go with the scholarly papers. But just in case.

 

[edgar1813]

Hey,

Nice pictures, btw have you seen GPP mentioned in her paper? or any of Rovelli's ones besides that one with Mike?
Interesting they were discussing in May04 isn't it?
There has been another paper recently I'm not sure you have seen by Dolby and the Page-Wotters approach. That papers turns out doesn't look right but attempts have been made and the relational approach is by now considered the right track, in different fashions, by almost everybody.
I disagree with Marcus that grad students can't provide revolutionary ideas or fundamental insights. Look at Frank W wand David P, btw congratulations to them and the other David G for the nobel prize 2004.

 

[marcus]

Wow! I thought I understood Hamiltonian systems, but this is terrific. I'll have to return to it tomorrow (tracking election results tonight).

I disagree with Marcus that grad students can't provide revolutionary ideas or fundamental insights. Look at Frank W wand David P,...

well I have to concede that I underestimated graduate students. selfAdjoint and edgar1813 are right on this point. Or at least I misjudged in the Bianca Dittrich case.

As for who should get credit for realizing the possibilities of relational time---I can't say about that. I am not going to worry too much about that.
But I hope Dittrich is friends with Gambini and will always be able to get ideas from discussions with him (regardless of citations and acknowledgments) since he seems to have very good ideas.

It looks to be that Thiemann is excited and hopeful about the progress he as been able to make with the help of this dittrich paper and the partial observable idea.

 

[marcus]

this paper was the topic for post #1 of the thread

...
Time Dependence in Quantum Gravity
http://arxiv.org/gr-qc/0408094

Bojowald is at Albert Einstein Institute (AEI)...
... the other two authors are
Pamapreet Singh (IGPG-Penn State) and
Aureliano Skirzewski (AEI).
...

the paper has been revised
and has a slightly different title
Coordinate Time Dependence in Quantum Gravity

the paper has been accepted for publication in Physical Review Series D

I don't know of anything changed besides the title. I'll have a look and see.

 

[vasudevshyam]

Yes, I find it interesting that he brings in relational time, and then (it seems to me regretfully) rejects it because it can't be fitted into the math. What do you think about his next statements, that in the canonical approach where the Hamiltonian is a second class constraint, time is just a gauge degreee of freedom? The implication is that if you fix the gauge, as one does, you get no time.

Nice question. We know that in Quantum gravity we find that the scalar Hamiltonian constraint on quantization leads to the Einstein-Schrodinger or Wheeler DeWitt equation
$\hat{H} \Psi = \left( \hat{ G_{ijkl} } \frac{\delta} { \delta \gamma_{ij} } \frac{ \delta } { \delta \gamma_{kl} }+\gamma^{1/2} R \right) \Psi = 0$ . Now let us consider the dynamics of the theory. the field operator here woud be $\gamma_{ij}\left(t,x\right)$ where t represents the label time of an arbitrary Cauchy hypersurface. its realtion with the t=0 hypersurface is given by: $\gamma_{ij} \left( t,x \right) = e^{iHt} \gamma_{ij} \left(0,x\right) e^{-iHt}$ but on application of the Wheeler DeWitt equation, we see that this yeilds: $\Psi^{*}\gamma_{ij}\left(t,x\right)\Psi=\Psi^{*} \gamma_{ij} \left(0,x\right)\Psi$ Which would mean that in this thery there exists no dynamics at all, or in other words, the universe is completely static. In order to circumvent his we say that the Wheeler DeWitt equation doesn't quite describe a static universe but instead it tells us that the co ordinate labels (t,x) are truly irrelevant, and so it is but a constraint that annihilates non physical field modes from the field. Thus time is but a gauge degree of freedom.

 

[marcus]

Vasu, I hope you will post more here in BtSM forum. For some reason I missed seeing this December 2011 post of yours.

I appreciated your response to the current "MIP" poll which pointed out the interest of Shape Dynamics (e.g. work of Sean Gryb et al).
https://www.physicsforums.com/showthread.php?t=681598

http://arxiv.org/abs/1303.7139
Symmetry and Evolution in Quantum Gravity
Sean Gryb, Karim Thebault

Nice question. We know that in Quantum gravity we find that the scalar Hamiltonian constraint on quantization leads to the Einstein-Schrodinger or Wheeler DeWitt equation
$\hat{H} \Psi = \left( \hat{ G_{ijkl} } \frac{\delta} { \delta \gamma_{ij} } \frac{ \delta } { \delta \gamma_{kl} }+\gamma^{1/2} R \right) \Psi = 0$ . Now let us consider the dynamics of the theory. the field operator here woud be $\gamma_{ij}\left(t,x\right)$ where t represents the label time of an arbitrary Cauchy hypersurface. its realtion with the t=0 hypersurface is given by: $\gamma_{ij} \left( t,x \right) = e^{iHt} \gamma_{ij} \left(0,x\right) e^{-iHt}$ but on application of the Wheeler DeWitt equation, we see that this yeilds: $\Psi^{*}\gamma_{ij}\left(t,x\right)\Psi=\Psi^{*} \gamma_{ij} \left(0,x\right)\Psi$ Which would mean that in this thery there exists no dynamics at all, or in other words, the universe is completely static. In order to circumvent his we say that the Wheeler DeWitt equation doesn't quite describe a static universe but instead it tells us that the co ordinate labels (t,x) are truly irrelevant, and so it is but a constraint that annihilates non physical field modes from the field. Thus time is but a gauge degree of freedom.

 

[Salman2]

...the problem is with the poverty of our language----there are many implementations of the notion of causal ordering and temporal evolution, but we have very few word-tags for them. One way is to have time advance in little roughly-planck-scale steps.

I have a question. Would it not be more appropriate to have moments in time advance in roughly Planck scale steps...well, better yet, let the duration of each moment in time be Planck scale ? I do not see time as anything that advances, objects advance, time measures the advancement process intermediate between moments within time? What am I missing ?