Quantum Gravity and Specific GR Tests

[atyy]

In LQG, we actually sum over all combinations of the combinatorial structure; in principle there is no limit (unless I have not understood the papers correctly --- always possible, even likely) to what the underlying graph actually is. I expect that we would find topologically non-trivial configurations to simply be massively unfavourable in the sum-over-spin-foams, but nevertheless be represented. Perhaps someone who actually does these computations can weigh in and answer in detail? There's only so much information an amateur can bring to the table...

There is some commentary on this on pages 60 and 61 of http://arxiv.org/abs/1007.0402 .

 

[atyy]

I think it's important to separate Rovelli the philosopher from the LQG theorist. The former will make strong statements about relational views on quantum mechanics and the importance of general covariance. The latter produces concrete, novel physical theories which are scrutinised to the usual level of rigour. Of course, the former may have guided the latter, and the latter occasionally extols the virtues of LQG with the moral viewpoint of the former, but we can still take the physics and leave the interpretation up to personal preference. *IF* it turns out that LQG really does reduce (at zero-th order in \hbar) to Regge theory then it doesn't really matter how and why the philosophy works --- we should indeed rebuild the philosophical understanding after the fact.

I agree almost completely. I dislike Rovellian philosophy and the relativists are so conceptually superior to particle physicist talk. I do find many areas of LQG - GFT especially- interesting and worth investigating, even if it does not produce a candidate QG theory.

The part I'm not sure I agree with is surely we need a candidate QG theory to produce GR in the classical limit, not Regge?

 

[genneth]

The part I'm not sure I agree with is surely we need a candidate QG theory to produce GR in the classical limit, not Regge?

I agree that this is debatable.

For LQG it makes more sense to compare to Regge theory because both are fundamentally discrete, rather than continuous; nothing much is lost, since Regge theory converges to normal GR as the lattice spacing goes to zero, and presumably the lattice spacing for LQG-Regge is order Planck length (specifically, whatever the lowest eigenvalue of the volume operator is, converted to length), which would make no difference experimentally at the moment (after all, the whole point about reproducing GR isn't that GR is magic, just that it is experimentally validated).

For other theories I agree that directly going to GR might make much more sense.

 

[atyy]

I agree that this is debatable.

For LQG it makes more sense to compare to Regge theory because both are fundamentally discrete, rather than continuous; nothing much is lost, since Regge theory converges to normal GR as the lattice spacing goes to zero, and presumably the lattice spacing for LQG-Regge is order Planck length (specifically, whatever the lowest eigenvalue of the volume operator is, converted to length), which would make no difference experimentally at the moment (after all, the whole point about reproducing GR isn't that GR is magic, just that it is experimentally validated).

For other theories I agree that directly going to GR might make much more sense.

I vacillate between this idea and the other which is that if we take Planck's constant to zero, then the lattice spacing should already be zero, so there shouldn't be any discreteness left over. However, I guess there are enough free parameters left over that one can keep the lattice spacing non-zero in the classical limit, and then we just set that parameter small enough. But in which case, have we gained anything than just putting a cutoff in the EH action?

For string, how about AdS/CFT as a non-perturbative definition of quantum gravity? It probably doesn't match observed cosmology and matter, but it does give AdS GR in the classical limit.

 

[marcus]

... in LQG the system under study actually allows *greater* change than GR proper. In GR, the topology is fixed, and only the metric is allowed to vary. Similarly, in Regge theory we build a combinatoric structure of flat 4-simplices glued together, and this structure is fixed, but the "creases" at the gluing edges are allowed to vary. In LQG, we actually sum over all combinations of the combinatorial structure; ...

The Marseille group does seem to be mostly studying the combinatorial version now. It isn't clear how that will go. It is *manifoldless* which as you point out is more than just being independent of a prior metric geometry background.

It's good to raise the issue and get clear about it. Rovelli hasn't burned bridges---just look at the April survey 1004.1780. He says he is going to choose the "combinatorial" way of formulating and presenting the theory, and that it is not derived from GR. But he also talks about other ways to derive and formulate LQG, which are to some extent equivalent. One can argue back and forth connecting the different versions.

He makes it clear that focusing on the "combinatorial" or manifoldless version is a personal choice. As I recall, other senior people such as Ashtekar and Lewandowski have not entirely gone along with this. Thiemann may have anticipated Rovelli in exploring a combinatorial approach (I don't recall for sure) but I don't think he is as consistently focused along those lines.

If the manifoldless approach doesn't work out, I expect the roughly 10-20 researchers seriously pursuing it will have ways to retreat back to manifold (taking many if not all of their insights and results with them.) LQG has always been anarchic with different formulations joined by never-quite-complete logical equivalence. So they are used to running back and forth between canonical and covariant and embedded spinfoam (of several sorts) and combinatorial.

But my personal hunch, for what it's worth, is that the manifoldless LQG will outlive the manifoldy LQG. I've watched C.R. since 2003 and haven't seen him make a wrong jump.
He tends to move deliberately and then not have to retrace steps. Just a vague impression.

I like the "combi" or manifoldless version myself because to me a spin network symbolizes our FINITE GEOMETRICAL INFORMATION about the world based on a finite number of measurments of area, volume, angle, etc which in a sense prepare the experiment.

I don't believe that spacetime exists any more than the classical trajectory of a particle exists. All we have is finite info about where the particle was detected etc. etc. There are no "world-lines" in the real world. There is no manifold.

These things are extremely useful idealizations. But one always has mental reservations about useful idealizations.

I do not think topology can exist at very small scale---what use or meaning has the homotopy idea of "simply connected" or the idea of a knot, when one cannot measure below a certain scale. The idea of dimension---a relation between radii, areas, volumes so small that one cannot even in principle measure them? Heh heh.

Quantum gravity is quantum geometry (and how it interacts with matter). Quantum geometry concerns geometrical INFORMATION and its uncertainty. How nature responds to geometrical measurement, including time I guess.

So the spacetime manifold is a bit too rich for my taste, as it presumes an uncountable infinity of measurements and statements. (On the other hand I must admit to fondness for the Lie group---a manifold of the mind---and for group field theories based on G^N group manifolds---but that is something else. Let us have all the mental manifolds we wish, just refrain from imputing that structure to spacetime.)

Given that inclination, I'm happy to see people working on the combinatorial formulation of LQG. And maybe that's more than enough about my own private attitude!

This is interesting too, but i have to go out and will have to comment later on it:

...Rovelli the philosopher from the LQG theorist. The former will make strong statements about relational views on quantum mechanics and the importance of general covariance. The latter produces concrete, novel physical theories which are scrutinised to the usual level of rigour. Of course, the former may have guided the latter, and the latter occasionally extols the virtues of LQG with the moral viewpoint of the former, but we can still take the physics and leave the interpretation up to personal preference. *IF* it turns out that LQG really does reduce (at zero-th order in \hbar) to Regge theory then it doesn't really matter how and why the philosophy works --- we should indeed rebuild the philosophical understanding after the fact...

 

[marcus]

Right. It is important to distinguish between those two different facets or aspects. There is the philosophical analysis of concepts: what is space what is time what is the operational meaning of distance or area or dimension or the operational meaning of a loop being contractible to a point. Einstein was good at that, how does an observer actually measure a distance to something--he sends a flash of light, OK let's look at the light...

So there is the conceptual analyst side (the "philosopher") and also the physical theorist side---the person who constructs and explores mathematical models comparable to our experience of nature.

I suppose that C.R. is not so unusual in having these two sides, and in having the analysis of concepts serve as an heuristic guide to the mathematical modeling. Many other good theoretical physicists must, like him, be asking questions like "what does this mathematical object actually stand for?" and "how in principle might we determine if this condition is actually satisfied?"

Nice thing about empirical science is that if some philosophical investigation guides you heuristically to some physical theory, and then the theory turns out not to work, then you can realize the philosophy was wrong! At least I think you can. There's a way of discovering that some line of thought was on the wrong track---if you follow through rigorously on it.
One reason I think QG research is exciting to follow.

...*IF* it turns out that LQG really does reduce (at zero-th order in \hbar) to Regge theory then it doesn't really matter how and why the philosophy works --- we should indeed rebuild the philosophical understanding after the fact...

Philosophy and physics aid each other, sometimes essentially. Philosophy can guide innovative theory, as a kind of heuristic, and in turn get feedback from physics. If the physics works, it validates the concepts, but if the physics fails empirical test, then go back and re-work the philosophy. Didn't people around 1650-1750 call it "natural philosophy". Maybe they had the right idea.

 

[Fra]

And how can Rovell's "relational" arguments in his QG book make sense if there is a background metric? Do you think Rovelli meant only no background 4D spacetime metric - ie. not everything is relational?

Did you think LQG researchers understand "background independence" to mean "no background 4D spacetime metric" or "no background metric"?

I was dissapointed by rovelli's reasoning on these points. IMHO he has undoubtedly several excellent points, but to make it short this is how I characterize his reasoning on relational thinking(and I don't like it):

Rovelli tries to argue that there is not objective background information at all. Each observer simply views everything from it's own subjective "context" - OK.

Also, there are no objective predetermined absolute relations between these contexts, the only way level them in any way is for two observes to interact/communicate - OK.

But as Rovelli's is not questioning or analysing QM as such, here he just assumes that the "communication" between two observers, somehow obey the Rules of Quantum Mechanics. This is where he lost me because QM also requires a background context. Not a metric background, but a encoding structure and system for computing expectations. But he also declared that this is as far as his anzats goes, and he simply didn't aim to revise QM or counting problematics, just put it in what he thinks is the right view.

> If Rovellian LQG's insistence that all physics should be relational means that there is no
> background metric, it is wrong. There can be a background metric which does not have
> the meaning of spacetime, so that the emergent classical spacetime is still dynamical.

I sort of agree, it could be any abstract information space metric. Information can be recoded, so as far as I'm concerned it's irrelevant to principles here which information carriers we talk about. Spacetime manifolds, theory manifolds are all information carriers.

So I think it doesn't end there. I think that ANY background information (metric or something else) that is assume absolute and eternal smells. Ie. I do not think that we can assume a observer invariant structure on any theory space itself.

I personally think the only reasonable conclusion is to accept that information evolves. Any attempt to cast in stone, theory spaces or background metrics or whatever are IMHO conceptually incoherent and thus misguiding if one is to have some respect for what I think is the core of science and inference. Because why would certain information carriers be excepted from the inference requirement? The only excuse I'm aware of is that the history is erased or overwritten and you just know where you are but not how you got there.

As I see it this must have implications also for the RG work. Somehow, I can't help but insist that theory space must be the one and same as what defines the population of observers in the universe. This IS the REAL theory space, isn't it?

/Fredrik

 

[atyy]

Regarding what genneth and I were discussing, there is an interesting comment in http://arxiv.org/abs/1011.2149 . Spinfoams are being pushed in 3 different directions, and it is not clear how they are related (i) Rovellian spinfoams (ii) GFT (iii) KKL . This paper tries to see what relationship there might be between (i) and (iii): "The geometrical interpretation in terms of tetrahedra (and now polyhedra) has raised a lively discussion and it is sometimes unpalatable to the more canonical oriented part if the community. Part of this discussion is based on a misunderstanding. The precise claim ... truncated Hibert space has a classical limit ... naturally interpreted as describing a collection of polyhedra ... classical general relativity admits truncations ... where the geometry is discretized."

 

[marcus]

Regarding what genneth and I were discussing, there is an interesting comment in http://arxiv.org/abs/1011.2149 . Spinfoams are being pushed in 3 different directions, and it is not clear how they are related (i) Rovellian spinfoams (ii) GFT (iii) KKL . This paper tries to see what relationship there might be between (i) and (iii): "The geometrical interpretation in terms of tetrahedra (and now polyhedra) has raised a lively discussion and it is sometimes unpalatable to the more canonical oriented part if the community. Part of this discussion is based on a misunderstanding. The precise claim ... truncated Hibert space has a classical limit ... naturally interpreted as describing a collection of polyhedra ... classical general relativity admits truncations ... where the geometry is discretized."

Atyy, I went and looked through the Ding Han Rovelli paper and, on page 7, I found the passage you quoted. Is there a way I could use google or some other search to find a passage in the context of a given article? Sometimes that would be a real help, especially when you quote from longer papers and don't give a page. Tell how you do a keyword search within an article, if you know, please!

The passage on page 7 is interesting. Here is the paragraph in full:

==quote Ding Han Rovelli==
The geometrical interpretation in terms of tetrahedra (and now polyhedra) has raised a lively discussion and it is sometimes unpalatable to the more canonical-oriented part of the community. Part of this discussion is based on misunderstanding. The precise claim here is that if we take the diff--invariant Hilbert space of the theory and we truncate it to a finite graph (so that the observable algebra is also truncated), then the truncated Hilbert space (with its observables algebra) has a classical limit, and this classical limit can be naturally interpreted as describing a collection of polyhedra. This is well consistent with classical general relativity, because classical general relativity as well admits truncations where the geometry is discretized. Also, this is not inconsistent with the continuous picture for the same reason for which the fact that the truncation of Fock space to an n particle Hilbert space describes discrete particles, is not inconsistent with the fact that Fock space itself describes a (quantized) field.
==endquote==

I'm not sure what you mean by "Rovellian" spinfoams, since spinfoam formulation has changed so much since 2007.
I don't see any permanent barriers between what Rovelli is now doing and the KKL. (Lewandowski's version of spinfoam with vertex valence greater than 5). Just generalizing from less-general to more-general polyhedra.
My idea of Lqg is a gradual evolution---it is easier to see steady directions of progress than to specify exact location at any given moment.
Especially since so many people are working on it and so much has been happening lately.

But definitely yes! they are exploring the connection between what you call (i) and what you call (iii), just as you say. I would expect some kind of coming together there----likewise probably with GFT ---your item (ii).

Convergence has been a common theme in LQG research since 2007 and probably before---convergence of different lines of investigation, approaches---it is a good guess that the trend will continue. Convergence, after all, was what the original KKL paper was about.

 

[marcus]

Here's part of an introductory overview of the Ding Han Rovelli results, from page one of their paper. I think it helps to understand:

==quote page 1 of "Generalized Spinfoams" http://arxiv.org/abs/1011.2149 ==
The relation with LQG, however, is limited by the fact that the simplicial-spinfoam boundary states include only four-valent spin networks. This is a drastic reduction of the LQG state space. In [20], Kaminski, Kisielowski, and Lewandowski (KKL) have considered a generaliza- tion of the spinfoam formalism to spin networks of arbi- trary valence, and have constructed a corresponding vertex amplitude. This generalization provides truncated transition amplitudes between any two LQG states [1], thus correcting the limitation of the relation between the model and LQG. This generalization, on the other hand, gives rise to several questions. The KKL vertex is obtained via a “natural” mathematical generalization of the simplicial Euclidean vertex amplitude. Is the resulting vertex amplitude still related to constrained BF theory (and therefore to GR)? In particular, do KKL states satisfy the simplicity constraint? Can we associate to these states a geometrical interpretation similar to the one of the simplicial case? Can the construction be extended to the physically relevant Lorentzian case?

Here we answer several of these questions. We show that it is possible to start form a discretization of BF theory on a general 2-cell complex, and impose the same boundary constraints that one impose in the simplicial case (simplicity and closure). Remarkably, on the one hand, they reduce the BF vertex amplitude to a (generalization of) the KKL vertex amplitude, in the Euclidean case studied by KKL. On the other hand, a theorem by Minkowski [21] garantees that these constraints are precisely those needed to equip the classical limit of each truncation of the boundary state space to a finite graph, with a geometrical interpretation, which turns out to be in terms of polyedra [22].
==endquote==