Quantum gravity confusion redux

by I.Vecchi
Tags: confusion, gravity, quantum, redux
 P: n/a Googling around I recently ended up on a beautiful old spr thread ([1]) about QG, which I found extremely interesting both for its scientific content and for the hopeful mood it conveys (the overall mood in QG is not really hopeful these days, is it? My perception is that it changed quite suddenly around one year ago). The thread also contains a vivid exemplification of the semantic problems arising in GR ([2],cf.[3]), which I like to juxtappose to the following recent Zeilinger ([4]) quote: "Physics will in the future put less emphasis on equations and mathematics but more on verbal understanding". Scary, huh? IV [1] http://groups.google.com/group/sci.p...520204717c753c [2] http://groups.google.com/group/sci.p...a0bb6897aa8ccc "... there might be two U. C. Riversides with clock towers, or U. C. Riversides with dubious entities that we might or might not consider a clock tower." [3] http://groups.google.com/group/sci.p...ece53891b06e6d [4] http://xxx.lanl.gov/abs/quant-ph/0505187 , quoted by Peter Zoller.
 P: n/a In article <1131438756.304268.219710@g43g2000cwa.googlegroups.com>, I.Vecchi wrote: >Googling around I recently ended up on a beautiful old spr thread >([1]) about QG, which I found extremely interesting both for its >scientific content and for the hopeful mood it conveys (the overall >mood in QG is not really hopeful these days, is it? My perception is >that it changed quite suddenly around one year ago). I remember the thread you mention: http://groups.google.com/group/sci.p...520204717c753c and it was indeed a lot of fun. It concerned a key conceptual problem of quantum gravity: the problem of describing quantum systems without using a fixed background metric on spacetime. This conceptual problem is largely ignored in string theory, but people working on other approaches to quantum gravity have thought about it for many years: A. Ashtekar and J. Stachel, Editors; conceptual Problems of Quantum Gravity. Proceedings of the 1988 Osgood Hill Conference (Birkhauser, N. Y., 1991), 602 pages. and eventually a good rough understanding was worked out. The problem was then to take this understanding and use it to come up with a specific theory of quantum gravity! All attempts to do this raise difficult "technical" challenges - "technical" in the sense that they involve a bit less verbal reasoning, and a lot more detailed math. Loop quantum gravity was the first theory to meet a bunch of these technical challenges. It did so starting in the late 1980s, and into the mid 1990s. This is perhaps responsible for the optimistic mood you detect. Loop quantum gravity moved on to the next stage: the problem of "getting the right semiclassical limit". This means showing the theory gives results that match those of general relativity at length scales far larger than the Planck scale. Doing this is a really crucial basic test for any theory of quantum gravity. It's preliminary to the really fun part: getting *new* predictions. This is where things bogged down and people became less optimistic: http://math.ucr.edu/home/baez/dynamics/ The story in string theory is very different: they made progress on different questions and became bogged down in different ways. The mood in string theory is also not very optimistic these days. But that's another story. People in modern urban societies tend to be very impatient. They think of 10 or 20 years as a long time. So, they find it upsetting to imagine that it might take a century or more to solve the problem of quantum gravity. I think it's good to relax a bit. The problem of quantum gravity is not going away; the only danger is that we'll destroy ourselves or lose interest in science before we solve this problem. If we manage to keep our society going and stay interested in science, I feel sure we'll make serious progress on quantum gravity - eventually. And even if *we* don't, *someone* probably will: there's lots of room out there. So, when I get myself in a sufficiently high-level frame of mind, surveying the whole history of the universe and imagining its immensity, I'm very optimistic about the problem of quantum gravity. We (the people reading this now) probably won't be around to see it solved, but at least we can have fun trying. That should be enough.
P: n/a

Quantum gravity confusion redux

Eugene Stefanovich wrote:

> If there is one lesson we can learn from quantum mechanics this lesson
> should be: "never ask questions about something you are not measuring"
> (e.g., whether the electron passed through the left slit or through the
> right slit?). Since spacetime curvature is something we cannot directly
> observe, I think our life would be much easier if we just abandon the
> attempts to describe how the spacetime "looks like", and focus
> instead on directly measurable observables of real particles or
> systems of particles.
>

The mass of a particle can be taken as a direct measure of the "curvature of
spacetime" due to that particle. Using the tired old rubber sheet analogy
the deeper a dent a particle is in the harder it will be to move, it will
have more inertia. Mass is a measure of inertia and a curvature tensor is
a mathematical expression of inertia.

> GR regarding light bending or binary pulsars. However, successful
> predictions of QM and QFT are much broader in scope and few orders
> of magnitude more accurate. So, I would place my bet on QM rather than
> on GR.
>

GR is a classical theory of course it is going to be less precise. There is
no argument that QM is more fundamental. That QM is more fundamental is
the reason a theory of quantum gravity is so sought after.

> Eugene.
>
> P.S. I have zero credentials in quantum gravity research, so my
> thoughts can be safely ignored.

--
"...we advanced from the telegraph to telephones to e-mail?" -Mr ef'n
conductor- George Carlin. www.geocities.com/hontasfx

 P: n/a I.Vecchi skrev: > Googling around I recently ended up on a beautiful old spr thread > ([1]) about QG, which I found extremely interesting both for its > scientific content and for the hopeful mood it conveys (the overall > mood in QG is not really hopeful these days, is it? My perception is > that it changed quite suddenly around one year ago). > My own heretical idea is that you can learn something about QG in 4D by trying to generalize the key aspects of QG in 2D, which are well understood. Actually, 2D QG proper is quite boring, because the Einstein action in 2D is a topological invariant - the Euler characteristic. However, we are really interested in QG coupled to other fields, e.g. the standard model. The D-dimensional free bosonic string in the Polyakov formulation is nothing but 2D gravity coupled to scalar fields, and thus it may be regarded as the simplest possible toy model of gravity. To me, the key lesson from 2D gravity is something that both string theory and LQG has missed: ______________________________________________________ | | | Some gauge components of the metric become physical | | after quantization. | |______________________________________________________| In classical 2D gravity, the metric is purely gauge, because it has 3 components and there are 3 gauge symmetries, 2 diffeomorphisms and 1 Weyl rescaling of the metric. But after quantization, the trace of the metric becomes physical. Depending on your formalism, this phenomenon manifests itself in different ways. In lightcone quantization, the physical Hilbert space becomes unexpectedly large, because you cannot factor out the conformal symmetry unless the number of scalar fields D = 26, due to the conformal anomaly. Provided that D < 26, the theory is consistent in spite of the anomaly, because the Hilbert space has a positive-definite inner product (the spectrum is ghost-free). Alternatively, one can introduce the trace of the metric as a dynamical field already at the classical level; it is then known as the Liouville field. The parameters can be fine-tuned so that the Liouville field has central charge c = 26 - D, cancelling the matter and ghost contributions, and proper conformal invariance is restored. However, the physical Hilbert space is still larger than expected classically, because it now includes the Liouville field. The moral is that a field which is classically a pure gauge becomes physical after quantization, due to a gauge (conformal) anomaly. This shows that, contrary to popular belief, some (not all) gauge anomalies are indeed consistent, and that the quantum theory as a result has more degrees of freedom than its classical limit. In particular, this does happen in 2D gravity, which strongly suggests that it will happen in 4D gravity as well. Gravity is not Weyl invariant except in 2D, so the conformal anomaly does not directly generalize to higher dimensions. However, if you start by gauge-fixing Weyl symmetry rather than diffeomorphisms, the conformal anomaly reappears as a diffeomorphism anomaly instead, see e.g. http://www.arxiv.org/abs/hep-th/9501016 . This immediately suggests what is missing from all approaches to QG: _________________________________________________________ | | | Just as Weyl/diffeomorphism anomalies make the trace | | of the metric physical in 2D gravity, diffeomorphism | | anomalies make gauge components of the metric (beyond | | the two graviton polarizations) physical in 4D gravity. | |_________________________________________________________| | In order to implement this program, I discovered how to generalize the Virasoro algebra beyond 1D and how to build quantum representations. Not alone, but as the only one who contributed to this discovery with a motivation from physics. Note that the existence of a multi-dimensional Virasoro algebra is not a priori obvious, in view of two no-go theorems: 1. The diffeomorphism algebra has no central extension except in 1D. 2. In field theory, there are no gravitational anomalies in 4D. However, it turns out that these theorems, although correct, depend on unnecessarily strong assumptions. The Virasoro extension is not central (commutes with everything) except in 1D, and one has to go slightly beyond field theory proper, by introducing and quantizing the observer's trajectory, in order to formulate the extension. Of course, the discovery of the multi-dimensional Virasoro algebra is by itself not enough to quantize gravity, just as the discovery of the usual Virasoro algebra was not enough to quantize the free string. But it is a quite non-trivial, and IMO crucial, step. Besides, it is undoubtedly the discovery of my life-time. 2D gravity permits an unrelated but interesting observation. The Liouville field can be viewed as a Goldstone boson for the conformal symmetry. So what in lightcone quantization looks like anomalous symmetry breaking, looks like spontanous symmetry breaking in Liouville theory. Without having thought too much about it, I think that this suggests an interesting idea: _______________________________________________________ | | | Anomalous and spontanous breaking of gauge symmetries | | are closely related, perhaps different sides of the | | same coin. | |_______________________________________________________| In particular, the algebra of gauge transformations in 4D admits an extension which makes it into a higher- dimensional analog of affine Kac-Moody algebra. This is a kind of gauge anomaly, but not a conventional one because it is proportional to the second rather than to the third Casimir operator. It is tempting to speculate that the symmetry breaking induced by these gauge anomalies is related to the Higgs effect, much like conformal anomalies are related to the Liouville field. Finally, let me point out that my key observation, that infinite-dimensional constraint algebras generically acquire anomalies at the quantum level, has passed the most stringent test conceivable: it was repeated approvingly by Lubos Motl at http://motls.blogspot.com/2005/09/wh...nstein-ii.html Alas, I suspect that Motl didn't realize from whom the formulation originated, see my comment at http://www.haloscan.com/comments/lum...0241393188648/
 P: n/a "Ilja Schmelzer" wrote in message news:dl9k03$onq$1@tamarack.fernuni-hagen.de... > > Since spacetime curvature is something we cannot directly > > observe, > > At least in principle spacetime curvature is easily observable. > We measure the radius and circumsphere of a circle, and > if u = 2 pi r does not hold we have measured curvature. My point was that the "circle" we are measuring is made of some "real stuff", i.e., particles interacting (or not interacting) with each other. Quantum mechanically, our measurements refer to expectation values of the position operators of these particles in the Hilbert space. So, in order to describe these measurements you just need the Hilbert space of the system, the operators of observables (e.g., position) of particles belonging to the system, and the unitary representation of the Poincare group in the Hilbert space which expresses the properties of invariance for measurements made from different reference frames. This is sufficient for a complete description of the system (circle) and all possible measurements that we can make there, including the circumference-to-radius ratio. In this description, the space-time continuum does not play any role at all. If we found, for example, that the ratio u/r is different from 2 pi, I would rather attribute it to some pecularities of interparticle interactions in the circle, than to "curvature" of some mysterious spacetime that evades direct observation. Eugene.
 P: n/a Eugene Stefanovich wrote: > "Ilja Schmelzer" wrote in message > news:dl9k03$onq$1@tamarack.fernuni-hagen.de... > > At least in principle spacetime curvature is easily observable. > > We measure the radius and circumsphere of a circle, and > > if u = 2 pi r does not hold we have measured curvature. > > My point was that the "circle" we are measuring is made of some "real > stuff", i.e., particles interacting (or not interacting) with each > other. Quantum mechanically, our measurements refer to expectation > values of the position operators of these particles in the Hilbert > space. So, in order to describe these measurements you just need the > Hilbert space of the system, the operators of observables (e.g., > position) of particles belonging to the system, and the unitary > representation of the Poincare group in the Hilbert space which > expresses the properties of invariance for measurements made from > different reference frames. Space-time is not Poincare symmetric. That is what our telescopes tell us. That is what our satelites tell us. That is what the cosmic microwave background tells us. > This is sufficient for a complete description of the system (circle) and > all possible measurements that we can make there, including the > circumference-to-radius ratio. In this description, the space-time > continuum does not play any role at all. If we found, for example, that > the ratio u/r is different from 2 pi, I would rather attribute it to > some pecularities of interparticle interactions in the circle, than to > "curvature" of some mysterious spacetime that evades direct observation. You are free to choose an interpretation of experimental data, and so is everyone else. The tough part is predicting what the outcome of the next experiment will be, where the circle will be moved, tilted, rotated, or the particle will go faster, slower, be of different species, etc. Success in theoretical physics is not measured by interpretation. Igor