About a couple of years ago I received, to my surprise, an invitation to be the token string theorist in the annual conference “Loops 2007″. Over the years, especially during my long term stays at the Perimeter Institute, I befriended quite a few people from the loop community. Mexico is always a pleasure to visit, and there is practically no jet lag involved, so I could just fly in and out of there, in between getting a few days to go around with my camera and enjoy a picturesque colonial town. So, I thought to myself, why not?
Of course, there was also the small issue of what to talk about. Previous such talks involved string theorists reviewing recent developments in the field, and where progress has been made. Nothing is wrong with that, but I thought I’d go a different route. Years ago Lee Smolin asked me why I don’t work on LQG (Lee is a true believer, and a direct sort of guy, I respect that), so I thought I’d use my hour to give a detailed answer. Without being overly obnoxious, of course, I would not want people having the wrong impression of us string theorists…
Naturally, one hour is not enough for such a large topic, so I had to narrow it down to cover just one major issue, and I chose to talk about background independence. Among all the fundamental differences between different approaches to quantum gravity (including for example, what does it mean to quantize gravity), this to me seems like the one needing most clarification. It is the one expression most likely to be used as a mantra, or as the one answer fitting almost any question, so basic and primary that evidently no elaboration is needed.
So, I’ve done my part now, I have given the talk, which was a real pleasure, and I have now expanded it to this writeup. In the process I have learned that writing a polemic is not as easy as it looks…I hope someone enjoys reading this, and it provokes a few useful discussions. I’d be happy to answer questions if it is evident they are formed after reading what I wrote.
Update: I guess the link to the writeup is not going to be available till tomorrow, apologies for the bad planning. In the meantime anyone interested can play the traditional lunch-time game of trying to guess what is in a paper you haven’t read. Oftentimes you discover things more interesting than the actual paper, that may well be the case here.
Update (September 23rd): I am not sure how much I would trust someone who cannot manage to submit a simple PDF file to the arXiv, but here it is finally, knock yourselves out.
still password protected? looking forward to reading your writeup! i can’t say though I enjoyed Morelia, I had severe trouble breathing, probably a combination of the traffic and the high altitude.
Btw, nice you’ve joined the bloggers
The function you’ve requested for 0809.3804 requires that you be registered as an owner of 0809.3804. You (UncleAl) are not currently an owner of 0809.3804. You can become an owner by entering the paper password for 0809.3804.
One suspects things are not quite right with the link.
Does LQG require BRST invariance or the Equivalence Principle to unite the effects of a massive body and an accelerated coordinate system?
Apologies, did not cross my mind anyone would want to read it so urgently, a few more hours and the page will become accessible.
Bee: Morelia was a bit too large for my taste, but years of training in Aspen and one long visit to Mexico city prepared me for the two issues you mentioned. I’m still glad I got to go.
Note to self: LQG: Loop Quantum Gravity. As a layperson, I’m familiar with the concepts but sometimes I miss the abbreviations.
Am really enjoying your posts.
Oh yeah, sorry and thanks, in that order.
Moshe,
The wait is such a killer!
But, meanwhile, i’ll join Bee in welcoming you: “Finally!”
In any case, i went ahead and took a bite of your talk… and really like the way you “framed” the discussion, i.e., your choice of “topic selection” and how to connect them, echoed for me, we resonated.
I do plan to wait for your paper and i intend to read it more carefully before i start a “meatier” discussion… but, for now, i just want to point a few things:
• “Mathematical Topics between Classical and Quantum Mechanics”, http://www.amazon.com/Mathematical-Classical-Mechanics-Monographs-Mathematics/dp/038798318X/ : I thought that it was [at least] somewhat well known that the procedure we call “quantization” is *not* well defined, in the same sense that you pointed out in your talk: there are different systems that may yield the same “quantum system”. Why, or How, is string theory particularly illuminating in this case, i.e., why does one need to go to ST in order to find this out?
• In particular, the use of non-perturbative formulations seems to be quite important to me, e.g., for the mere reason that perturbative techniques cannot probe what we call symmetry breaking, in the sense that a perturbative model can only look at one particular sector of the theory, for it’s the same as asking that a series around “p = 1″ (where “p” is some parameter of the theory) gives results about the expansion around “p = -1″ — this will ultimately depend on the “radius of convergence” of these perturbative series… but, these series are not Taylor, but asymptotic in nature. See, for instance: http://arxiv.org/abs/0809.2778 , http://arxiv.org/abs/0710.1256 , http://arxiv.org/abs/hep-lat/0602013 . In this sense, what do you think of “String Field Theory”?
I don’t mean to come across as a “ST hater”, or “Devil’s advocate”, because neither is true; i actually just want to understand where this is all going… for it seems (from my reference frame) that there’s a convergence between languages nowadays…
Cheers.
Hey danieldf, to your questions:
1. I don’t think you need string theory to demonstrate the point, in fact I did talk about gauge theories to precisely emphasize this is nothing to do with quantum gravity as such.
2. String field theory is one attempt to get non-perturbative formulation of ST. In my mind it is too strongly tied to perturbation theory to be successful, but people smarter than myself disagree and choose to work on it.
One thing I hate about the moniker ‘background independance’ is that it can take on many different mathematical meanings, and its not clear what people are necessarily talking about when they discuss it. Physicists can usually understand the context, but it does one hell of a disservice to the layman.
For instance, I would be inclined to call lattice field theory, background dependant but other people call it background independant (say with regards to lattice gravity) and theres a sense in which both are correct.
Then theres a confusion between ‘manifest’ vs ‘nonmanifest’ BI, confusionns with diffeomorphism invariance, whether or not background independance means varying the metric tensor in the lagrangian or not, The existence of canonical 2forms, topological and quantum BI blah blah blah.
it’s accessible now.
There aren’t any references; the citations show up as question marks. I’m guessing a \bibliography line was omitted in the LaTeX source, or something like that.
Thanks, fixed.
The writeup was great, thanks. Maybe at some point you could talk in more detail about the question of what constitutes a gauge invariant observable in quantum gravity. I have trouble sorting out the arguments of the form “All the observables we can think of…” vs. “Here is a good reason why only these things are observables…”
(I hate it when people leave comments asking me to blog about something.)
Thanks Sean, I think I know what you mean, but maybe not precisely, could be fun to try to sort it out for myself. Maybe that what blogs are good for…
really interesting! now, when you are talking about ‘weak’ and ‘strong’ coupling limits in Seiberg dualities, you are slightly cheating, since now coupling constant are running (if I understand correctly). do you have a picture of what would happen to holography in a more realistic setting? I mean, is there some intuition on what holography would look like once you let the coupling constants run? does this question even make sense? probably the answer is buried somewhere in the literature, but I could never figure out exactly where. thx!
This is one of the points that is different in field theory or holographic dualities. In field theory dualities, where both theories are formulated on the same space, duality only makes precise sense when the coupling does not run. The case I discussed has (at low energies) a true coupling constant which does not run, and the duality is between strong and weak values of that coupling.
For holography both sides are not formulated on the same space, the gravitational side has an extra (radial) direction, which is roughly related to energy scale in the field theory. The running of coupling constants in the field theory is then encoded, in the gravitational picture, by some radial dependence of the appropriate field. There are many examples of that picture by now, see for example this classic paper by Klebanov and Strassler.
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