13 October Abhay Ashtekar Gravity and the Quantum http://arxiv.org/gr-qc/0410054 ---quote from abstract--- A general review of quantum gravity addresed non-experts; for a special 2005 collection The goal of this article is to present a broad perspective on quantum gravity for non-experts. After a historical introduction, key physical problems of quantum gravity are illustrated. While there are a number of interesting and insightful approaches to address these issues, over the past two decades sustained progress has primarily occurred in two programs: string theory and loop quantum gravity. The first program is described in Horowitz's contribution while my article will focus on the second. The emphasis is on underlying ideas, conceptual issues and overall status of the program rather than mathematical details and associated technical subtleties.
This is a very clear and fair introduction. I would point to the section Quantum Dynamics, where he has a frank discussion of the present state of Hamiltonian Constraint research. It is clear that they have not yet settled on a specific Hamiltonian operator since there is un embarras du choix (similar to that in the string theory vacua?). Clearly Ashtekar does accept unitarity as a valid criterion for quantum gravity theories since he cites its lack as a reason for abandoning the high energy modification of naive quantum gravity, even specificallly mentioning non conservation of probability.
I am glad you have been reading Ashtekar's little essay! this could shed a bit of light on things. also I am glad you find Ashtekar's sketch of the current situation fair-minded---it is so important to have a few fair-minded recognized authorities present in a discussion. I see that next year (the centennial of Einstein's 3 papers on special rel and on the photovoltaic effect as well) is to be celebrated as the "year of science"------a kind of root year for both relativity and quantum physics. and my guess is that this "Gravity and the Quantum" talk is intended to be for some celebratory conference or commemorative volume of lectures. I see that it will be paired with a talk by Horowitz about String. It is a lot to hope for, but I nevertheless hope that whoever organizes things achieves the kind of balance which characterized the Potsdam MPI October 2003 conference "String meets Loop". I am going to scout around and see if I can find a preprint of Horowitz companion lecture. My guess is that it is not out yet, or I would have spotted it already.
Clearly Ashtekar does accept unitarity as a valid criterion for a certain type of quantum gravity theory. The part you refer to where unitarity is mentioned is on pages 5, 6, and 7, where he is contrasting two approaches to QG, one favored by particle theorists and one by relativists----the so-called "covariant" approach and the "canonical". Ashtekar mentions unitarity (unitary time evolution) three times in the paper but only in connection to the "covariant" approach. I suspect that we have both known about unitary operators on a hilbertspace and some reasons they are nice---and about the "probability preserving" feature of having unit vectors go to unit vectors---for roughly equally many years, since we are both mature people That is not the issue. The point is (as I think you can tell from Ashtekar) that the perturbative analysis of the "covariant" approach avoids the "problem of time" and comes up with a time-evolution operator----which of course should be probability-preserving but lets keep the language clean and say that it should be unitary. Obviously. The "canonical" approach has been worked on by relativists for about as long as the "covariant" approach and in the "canonical" approach there has always been the feature that instead of a familiar sort of hamiltonian you had a hamiltonian constraint. You have an operator that is clearly NOT unitary because it has to vanish on the physically relevant quantum states. Therefore Ashtekar recognizes unitarity as an appropriate criterion when he is discussing perturbative analysis connected with the "cov" approach, just on pages 5, 6, 7. And he mentions unitary three times! and by the same token he does not mention unitary or unitarity anywhere else in the paper! Most particularly he does not mention it, or give any indication of recognizing it as an appropriate criterion, in connection with the "can" approach---which is what he is mostly concerned with. BTW the timehonored terminologies "covariant" and "canonical" are mostly just accidents----Ashtekar has a footnote about "covariant" on page 5 where he points out that it is actually somewhat misleading. the "covariant" approach typically violates diffeomorphism covariance! So it isnt what the name makes it sound like. he explains the historical reason behind the name. We will never achieve clarity (or serenity either I fear) until we understand the deep split between these two approaches. At one point in his book, Rovelli says "this book is as much about time as it is about gravity". Rovelli tackles the problem of time somewhat more explicitly than Ashtekar, and I believe actually resolves it. Ashtekar is more wait-and-see regarding the issue.
Peter Woit today, in connection with a memorial to his late friend Hide Yamagishi, links to a 1997 paper by Yamagishi and Zahed which discusses covariant and canonical, and BRST, quantizations of QCD. In the body of the paper they ask the question "Can unitarily equivalent Hamiltonians produce different physics?". And they answer it with a yes. If such things can happen with a well established system like QCD, we must not be overhasty in accepting long intricate quantizations of new theories at face value.
Hi, The paper by Horowitz is gr-qc/0410049. It is written for the volume edited by Pullin and Price. http://www.iop.org/EJ/journal/-page=extra.wypfocus/1367-2630/1
Thanks! So the volume edited by Jorge Pullin and Richard Price is Spacetime 100 Years Later described here http://www.iop.org/EJ/journal/-page=extra.spacetime/1367-2630/1 It will be a (january?) 2005 'focus' issue of the IOP New Journal of Physics and I suppose it could appear separately as a book, and it will include the Gary Horowitz paper http://arxiv.org/gr-qc/0410049 Also it might have something by Ashtekar, which could (very likely will) be the paper this thread is about: "Gravity and the Quantum" Pullin's newsletter "Matters of Gravity" has been a big help (you called our attention to it IIRC, as you have to several other things, some months back) and I also have been finding the Gambini/Pullin papers interesting. Pullin is a smart editor IMHO and this could be an important book. It is supposed to come out in january 2005. It seems it could have a balance between various things---theory/experiment, loop/string---and could be very up-to-date. Hope so. Here is the blurb for Spacetime 100 Years Later: --quote-- Among the remarkable new ideas that Einstein introduced into physics in 1905 was the revision of our concept of space and time. His special theory of relativity quickly became incorporated into all of physics. This cannot be said of his later general relativity, the ultimate outgrowth of his original insight 100 years ago. In the general theory, curvature of Einsteinian spacetime was introduced to represent gravitation. For many years the general theory remained an intellectual and aesthetic triumph with little connection to the rest of physics. This has now all changed dramatically, and the broader physics community may not be aware of the extent of the change. The general theory is at the centre of new modes of astronomical observation; it is being tested in laboratories and on large scales; it is crucial to understanding some of the most exciting astrophysical discoveries; it presents a frustrating challenge to computational scientists; it is indispensable for constructing a new understanding of cosmology from our present quandary. This celebratory Focus Issue in New Journal of Physics will attempt to give a glimpse of the current status of what Einstein wrought in 1905, as well as a historical perspective on how ideas about spacetime have evolved since then. Richard Price, University of Texas at Brownsville, USA Jorge Pullin, Louisiana State University, Baton Rouge, USA --endquote--
I see, Ashtekar says about Gravity and the Quantum http://arxiv.org/abs/gr-qc/0410054 that it is intended for a "special 2005 collection" and he mentions a companion paper by Gary Horowitz (one doing QG and Loop in particular, the other doing String) and Horowitz for his part, says that his essay is to appear in “Spacetime 100 Years Later”, eds J. Pullin and R. Price(2005). Horowitz paper is "Spacetime in String Theory" http://arxiv.org/gr-qc/0410049 and the abstract is: ---quote--- We give a brief overview of the nature of spacetime emerging from string theory. This is radically different from the familiar spacetime of Einstein's relativity. At a perturbative level, the spacetime metric appears as "coupling constants" in a two dimensional quantum field theory. Nonperturbatively (with certain boundary conditions), spacetime is not fundamental but must be reconstructed from a holographic, dual theory. --end quote-- the concept of locality seems to be getting trampled as if by a stampede of scholars. maybe it deserved this. I wonder if Jorge Pullin will have someone write an essay about what is happening to the theme of locality at the hands of quantum gravitist and stringist.