Quantum Gravity and Specific GR Tests

[inflector]

In another forum that I frequent, I have been having a discussion where the state of quantum gravity research came up. Another poster claimed that one of the first thing that any gravity scientist checks for the theory is the theory's prediction for the precession of Mercury's perihelion.

Now for cosmological extensions to GR like, MOND, TeVeS or STVG, I can see where this might make sense. But I can't see how this poster's claim holds for quantum-gravity theories that haven't been able to establish that they reproduce GR in the continuum limit.

So I feel like I'm either missing something important about quantum gravity theories, in general, or the poster's comment only applies to gravity modifications designed as an alternative to dark matter and not quantum gravity theories. Or perhaps a little of each.

How, for instance, would one compute the precession of Mercury's perihelion using CDT, or Rovelli et al.'s spin-foam version of LQG? It may be that the dynamics of any object are implied in the spacetime microstructure, I don't understand the math well enough yet to follow the implications to know if this is true. But how can you compute the orbit of a planet when you require mass and fermions in order to have a sun and a planet like Mercury?

I noted the recent paper Dec. 21 paper where the Marseille LQG group claims to incorporate Fermions, so my question applies to research prior to this event, not that going forward.

 

[marcus]

But how can you compute the orbit of a planet when you require mass and fermions in order to have a sun and a planet like Mercury?

I noted the recent paper Dec. 21 paper where the Marseille LQG group claims to incorporate Fermions, so my question applies to research prior to this event, not that going forward.

started trying to answer and got interrupted, have to go.
Present inclusion of fermions is preliminary. No definite way to include mass, very much just a start. No way to compute orbits yet, which would be a classical application anyway. Some years more development needed.

 

[Careful]

In another forum that I frequent, I have been having a discussion where the state of quantum gravity research came up. Another poster claimed that one of the first thing that any gravity scientist checks for the theory is the theory's prediction for the precession of Mercury's perihelion.

Now for cosmological extensions to GR like, MOND, TeVeS or STVG, I can see where this might make sense. But I can't see how this poster's claim holds for quantum-gravity theories that haven't been able to establish that they reproduce GR in the continuum limit.

So I feel like I'm either missing something important about quantum gravity theories, in general, or the poster's comment only applies to gravity modifications designed as an alternative to dark matter and not quantum gravity theories. Or perhaps a little of each.

How, for instance, would one compute the precession of Mercury's perihelion using CDT, or Rovelli et al.'s spin-foam version of LQG? It may be that the dynamics of any object are implied in the spacetime microstructure, I don't understand the math well enough yet to follow the implications to know if this is true. But how can you compute the orbit of a planet when you require mass and fermions in order to have a sun and a planet like Mercury?

I noted the recent paper Dec. 21 paper where the Marseille LQG group claims to incorporate Fermions, so my question applies to research prior to this event, not that going forward.

The only scheme which can do you want it to do and which is available at the moment is semiclassical quantum gravity.

Careful

 

[genneth]

In another forum that I frequent, I have been having a discussion where the state of quantum gravity research came up. Another poster claimed that one of the first thing that any gravity scientist checks for the theory is the theory's prediction for the precession of Mercury's perihelion.

Now for cosmological extensions to GR like, MOND, TeVeS or STVG, I can see where this might make sense. But I can't see how this poster's claim holds for quantum-gravity theories that haven't been able to establish that they reproduce GR in the continuum limit.

So I feel like I'm either missing something important about quantum gravity theories, in general, or the poster's comment only applies to gravity modifications designed as an alternative to dark matter and not quantum gravity theories. Or perhaps a little of each.

How, for instance, would one compute the precession of Mercury's perihelion using CDT, or Rovelli et al.'s spin-foam version of LQG? It may be that the dynamics of any object are implied in the spacetime microstructure, I don't understand the math well enough yet to follow the implications to know if this is true. But how can you compute the orbit of a planet when you require mass and fermions in order to have a sun and a planet like Mercury?

I noted the recent paper Dec. 21 paper where the Marseille LQG group claims to incorporate Fermions, so my question applies to research prior to this event, not that going forward.

I don't think you're missing anything ;-)

I would actually like to tack on a question of my own:

As you noted, the precession of Mercury's perihelion is not quantum at all --- it's a purely classical effect. Thus the check would be to reproduce GR in the classical limit. LQG can almost show this for pure gravity. Can string theory? As I understand it, there is something like a theorem which states that spin-2 particles have to be gravitons (?) so does that mean everything is okay in the perturbative/effective theory limit, or does it imply quite some more?

 

[Careful]

As you noted, the precession of Mercury's perihelion is not quantum at all --- it's a purely classical effect.

Isn't the world quantum mechanical ? So what do you mean by a classical effect?

Thus the check would be to reproduce GR in the classical limit. LQG can almost show this for pure gravity.

Could you please cite paper, date and author ?

 

[inflector]

I don't think you're missing anything ;-)

I didn't think so. It would have meant that I really had a deep hole in my understanding somewhere for this to have been true.

As you noted, the precession of Mercury's perihelion is not quantum at all --- it's a purely classical effect. Thus the check would be to reproduce GR in the classical limit. LQG can almost show this for pure gravity.

I tried to argue this specific point, that reproducing GR was the first check, and that once you could do that, you automatically get Mercury's perihelion computations. But this idea seemed to fall on deaf ears.

That's one of the problems with forums, especially when you are new. There can be members with lots of experience in the forum (posts and years) who don't know as much as they think, and there can be very smart experienced members—even professional scientists—who don't know as much as you do in a specific domain where you as a relative beginner have studied more than they have. It makes it hard when someone disagrees with you because you are in the process of learning yourself and can't really judge others' opinions objectively. At least here in Physics Forums, I know who tends to know what they are talking about for the topics of interest to me.

Thus the check would be to reproduce GR in the classical limit. LQG can almost show this for pure gravity. Can string theory? As I understand it, there is something like a theorem which states that spin-2 particles have to be gravitons (?) so does that mean everything is okay in the perturbative/effective theory limit, or does it imply quite some more?

Good question. It might be good to post a separate thread. My understanding of string theory is so limited that I can't even begin to answer your question adequately. From what I have read about the graviton-based reproduction of GR in string theory, they have only shown GR in Minkowski space without dipheomorphism invariance.

 

[Careful]

I tried to argue this specific point, that reproducing GR was the first check, and that once you could do that, you automatically get Mercury's perihelion computations. But this idea seemed to fall on deaf ears.

Please, could you define precisely what you mean by reproducing GR from a theory of quantum gravity. That might substiantially help any further discussion.

Careful

 

[genneth]

Please, could you define precisely what you mean by reproducing GR from a theory of quantum gravity. That might substiantially help any further discussion.

Careful

I think both I and the OP (who should correct me if otherwise) think of this as writing down an expansion of the theory, order by order, in \hbar. Now, such a procedure is probably not going to produce a convergent series (but maybe an asymptotic one?), but it would still be good if the zero-th order theory yields GR (or at least after taking some more limits, such as not-too-strong field, etc.)

As far as the state of the art in LQG, marcus should be the one to pipe up, but my personal favourite review at the moment: is http://arxiv.org/abs/1012.4707

I believe (from memory as opposed to quoting) that the state "LQG reproduces GR in the semiclassical limit" is more technically "using only 5-valent vertices in spin-foams, to zeroth order in \hbar, the action of LQG is that of Regge theory (a discretised GR, which has already been shown to give GR in the limit that lattice spacing goes to zero)". (Again, quotes are not literal quotes!)

 

[Careful]

I think both I and the OP (who should correct me if otherwise) think of this as writing down an expansion of the theory, order by order, in \hbar. Now, such a procedure is probably not going to produce a convergent series (but maybe an asymptotic one?), but it would still be good if the zero-th order theory yields GR (or at least after taking some more limits, such as not-too-strong field, etc.)

But the problem here is what background are you writing your expansion around ? If you take Minkowski, you would have to reproduce the Newtonian potential as a condensate of virtual gravitons. I haven't seen anybody doing that yet, all one does is to study S-matrices for graviton scattering at asymptotic infinity (where the Newtonian potential is switched off). The point being is that your background should also be dynamically determined and this is merely words in LQG so far. And what does such expansion mean ? The only thing you can study is correlation functions. How would this translate to a planet moving around the sun?

the action of LQG is that of Regge theory (a discretised GR, which has already been shown to give GR in the limit that lattice spacing goes to zero)". (Again, quotes are not literal quotes!)

Regge theory is a classical theory and it is indeed well defined. The question is whether it's quantum ancestors like CDT/LQG are in the same category.

 

[marcus]

...

As far as the state of the art in LQG, marcus should be the one to pipe up, but my personal favourite review at the moment: is http://arxiv.org/abs/1012.4707

Mine too. The "December 4707" is a good review article, with history, motivation, intuition, and lots of citations to recent papers.

I believe (from memory as opposed to quoting) that the state "LQG reproduces GR in the semiclassical limit" is more technically "using only 5-valent vertices in spin-foams, to zeroth order in \hbar, the action of LQG is that of Regge theory (a discretised GR, which has already been shown to give GR in the limit that lattice spacing goes to zero)". (Again, quotes are not literal quotes!)

I think the "LQG reproduces GR" result is a beast gradually crawling up out of the mud of confusion. I see how it's going, even though I don't yet see the final result clean and clear.

 

[Careful]

Mine too. The "December 4707" is a good review article, with history, motivation, intuition, and lots of citations to recent papers.

Of course, it means everything that 25 years of ''progress'' can be summarized on 24 pages, that is 0,96 useful pages/year

 

[genneth]

Of course, it means everything that 25 years of ''progress'' can be summarized on 24 pages, that is 0,96 useful pages/year

Better than my batting average in research...? (Can I claim to have even written one useful page? I doubt it...)

 

[genneth]

But the problem here is what background are you writing your expansion around ? If you take Minkowski, you would have to reproduce the Newtonian potential as a condensate of virtual gravitons. I haven't seen anybody doing that yet, all one does is to study S-matrices for graviton scattering at asymptotic infinity (where the Newtonian potential is switched off). The point being is that your background should also be dynamically determined and this is merely words in LQG so far. And what does such expansion mean ? The only thing you can study is correlation functions. How would this translate to a planet moving around the sun?


Regge theory is a classical theory and it is indeed well defined. The question is whether it's quantum ancestors like CDT/LQG are in the same category.

Isn't the Regge action also independent of background? Isn't GR? I don't see why you have to expand around a fixed background at all. Classical GR is not a theory of scattering, and no background is necessary.

 

[MathematicalPhysicist]

Of course, it means everything that 25 years of ''progress'' can be summarized on 24 pages, that is 0,96 useful pages/year

It's almost 1 useful pages/year, what more can you ask for?!

 

[marcus]

One thing I get from Inflector's posts is an interest in testing. This could become more important than the gradual progress one sees being made on the "reproduce GR" front.

Someone to watch in this regard is Wen Zhao (Cardiff). In a recent paper of his he had two co-authors at the KICC---Kavili Institute for Cosmology Cambridge.
Yin-Zhe Ma and Michael Brown

The way I see it, interest and credibility in the eyes of young unknown astro-phenomenology postdocs at a place like KICC has an almost "make or break" significance. These are people I have never heard of, in a first-rate place, who either are or are not willing to invest career-time in seeing how to test an early universe QG model. Who may or may not take the LQG picture seriously. Who are not biased either way as to the outcome.

So we'll see.

Here are some Wen Zhao papers. This is exactly the sort of person you want to be interested in whether there was a bounce:

2. arXiv:1009.5243 [pdf, ps, other]
Relic gravitational waves: latest revisions and preparations for new data
Wen Zhao, L. P. Grishchuk
Comments: 11 pages, 4 figures, 3 tables; v.2: modifications, improvements, additional references; accepted for publication in Phys. Rev. D
Subjects: Cosmology and Extragalactic Astrophysics (astro-ph.CO); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th)

4. arXiv:1009.0206 [pdf, ps, other]
Determination of Dark Energy by the Einstein Telescope: Comparing with CMB, BAO and SNIa Observations
W. Zhao, C. Van Den Broeck, D. Baskaran, T.G.F. Li
Comments: 28 pages, 5 figures, 5 tables; v.2: modifications, improvements, additional references; accepted for publication in Phys. Rev. D
Subjects: Cosmology and Extragalactic Astrophysics (astro-ph.CO); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th)

5. arXiv:1007.2396 [pdf, ps, other]
Constraints on standard and non-standard early Universe models from CMB B-mode polarization
Yin-Zhe Ma, Wen Zhao, Michael L. Brown
Comments: 41 pages, 23 figures, JCAP in Press
Journal-ref: JCAP 10 (2010) 007
Subjects: Cosmology and Extragalactic Astrophysics (astro-ph.CO)

6. arXiv:1005.4549 [pdf, ps, other]
Relic gravitational waves in the light of 7-year Wilkinson Microwave Anisotropy Probe data and improved prospects for the Planck mission
W. Zhao, D. Baskaran, L. P. Grishchuk
Comments: 27 pages, 12 (colour) figures. Published in Phys. Rev. D. V.3: modifications made to reflect the published version
Journal-ref: Phys.Rev.D82:043003,2010
Subjects: General Relativity and Quantum Cosmology (gr-qc); Cosmology and Extragalactic Astrophysics (astro-ph.CO); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th)

7. arXiv:1005.1201 [pdf, ps, other]
Separating E and B types of polarization on an incomplete sky
Wen Zhao, Deepak Baskaran
Comments: 43 pages, 15 figures, 1 table. The finial version, will appear in PRD
Journal-ref: Phys.Rev.D 82, 023001 (2010)
Subjects: Cosmology and Extragalactic Astrophysics (astro-ph.CO); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th)

8. arXiv:1004.0804 [pdf, ps, other]
Primordial Gravitational Waves and Cosmic Microwave Background Radiation
D. Baskaran, L. P. Grishchuk, W. Zhao
Comments: A summary of presentations delivered at the OC1 parallel session "Primordial Gravitational Waves and the CMB" of the 12th Marcel Grossmann Meeting on General Relativity (Paris, 12-18 July 2009). To be published in the Proceedings of the MG12. 18 pages, 8 (colour) figures.
Subjects: General Relativity and Quantum Cosmology (gr-qc); Cosmology and Extragalactic Astrophysics (astro-ph.CO); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th)

 

[Careful]

Isn't the Regge action also independent of background? Isn't GR? I don't see why you have to expand around a fixed background at all. Classical GR is not a theory of scattering, and no background is necessary.

Well, Regge action still requires a nice piecewise linear manifold with fixed topology, a background if you want to. GR has the same kind of background dependence. LQG has not. I don't know if you are aware, but all kind of observables we use in relativity are gauge dependent. When we calculate perihelion shift of Mercury we assume a flat Minkowski background, when we speak about orbits of planets we do the same... Dirac observables are almost never ever computed in GR and doing so in quantum gravity would be ''almost'' impossible.

Moreover, if you want to define perturbation series in $\hbar$, you always have to split the system in free part and interaction and the linearization of the system always depends upon the background metric. Equivalently, in LQG, you will have to import a preferred basis which is not related to the total Hamiltonian, otherwise you won't be able to set up a perturbation series.

Careful

 

[Careful]

It's almost 1 useful pages/year, what more can you ask for?!

Indeed, from such intellectual giants

 

[marcus]

Well, Regge action still requires a nice piecewise linear manifold with fixed topology, a background if you want to. GR has the same kind of background dependence. LQG has not...

?

In the LQG community "background independence" refers to to theories where the development does not require a background metric--a pre-arranged geometry.

Regge GR and the original formulation of LQG are more or less on the same footing. They all assumed a manifold at the start. Indeed with LQG there is a fixed topology, as in other cases.

The manifold simply did not have a background metric defined on it at the start. The metric arises dynamically. Traditionally this is what the relevant researchers have always meant by "background independence".

So what you said there was potentially confusing.

 

[Careful]

?

In the LQG community "background independence" refers to to theories where the development does not require a background metric--a pre-arranged geometry.

Regge GR and the original formulation of LQG are more or less on the same footing. They all assumed a manifold at the start. Indeed with LQG there is a fixed topology, as in other cases.

That was the case in the original formulation and required to give meaning to things like knotting of spin networks. But things have evolved now, and people start to think more in the causal set way. This is another example of a fact I once mentioned to you, LQG says A and not A, and it's practitioners demand I can only use classical logic

The manifold simply did not have a background metric defined on it at the start. The metric arises dynamically. Traditionally this is what the relevant researchers have always meant by "background independence".

So what you said there was potentially confusing.

No, it was not, certainly not in the modern way of thinking about it.

Careful

 

[marcus]

That was the case in the original formulation and required to give meaning to things like knotting of spin networks. But things have evolved now, and people start to think more in the causal set way. This is another example of a fact I once mentioned to you, LQG says A and not A, and it's practitioners demand I can only use classical logic


No, it was not, certainly not in the modern way of thinking about it.

Careful

Heh heh, now you are getting even more confusing. The meaning of "background independence" has not changed. It still means the theory does not use a prearranged background metric.

Lqg, including the most recent formulation, shares this property with GR and Regge etc.

 

[Careful]

Heh heh, now you are getting even more confusing. The meaning of "background independence" has not changed. It still means the theory does not use a prearranged background metric.

Lqg, including the most recent formulation, shares this property with GR and Regge etc.

Sure it has been. If you want to, I will even cite a paper of SMOLIN proving that it has been so ! Smolin has been taking about many different kinds of background independence going from kinematical objects such as the manifold, the differentiable structure, the dimension to objects we think of as dynamical such as the metric.

Careful

 

[Careful]

For example, see http://arxiv.org/PS_cache/hep-th/pdf/0507/0507235v1.pdf page 20, third bullet. Other references needed ?

Careful

 

[marcus]

I thought you might try to cite Smolin's "The case for background independence."

Smolin is not a representative LQG researcher---more of an outlier. That was a 2005 paper where he tried to expand the discussion, and generalize on B.I. It did not catch on. For most of the LQG community, B.I. just means B.I. That one 2005 paper did not change how 50 other Loop researchers talk.

Smolin's paper explicitly argued that it would be fruitful to talk about degrees of background independence, put it on a scale, so you could say something was more or less background independent. The term has a special meaning within the context of the paper.

 

[atyy]

But Smolin is the one who started all the fuss with his popular anti-string book.

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"?

 

[atyy]

Maybe Weinberg would say that the fewer pages per year the better - isn't the dream of of a TOE to have everything on 1 line?

genneth is a condensed matter guy, I think, so his aim would be different?

 

[marcus]

But Smolin is the one who started all the fuss with his popular anti-string book.
...

Atyy I suspect you are just joking. There are serious issues involving QG and "tests" as mentioned by the O.P. Inflector---issues involving the background independence of GR and newer theories (e.g. Witten papers on B.I. going back to 1992, 1993 as I recall.)

Whether or not there was some "fuss" is largely irrelevant to the substantive issues that we care about.

Also the "fuss" I think you refer to was already in full cry in 2003! on Usenet sci.physics.research. I was particularly struck by the posts of Motl and Baez but there were many others. I don't remember much from Lee Smolin at the time. And his book did not appear until Fall of 2006! Back in 2003 there was this Usenet thread called "String theory crack up?" and all this stuff was hotly debated. Susskind had come out with the "anthropic string landscape" in summer 2003.

In some sense none of this matters. GR is still background independent---in the usual sense of having dimension and topology specified, but no background metric (no prior geometry). GR is still general covariant--thus no physical meaning to points in space. Manifold used in formulation but ultimately modded out---solutions are equivalence classes belonging to no particular manifold.

So either the rest of physics needs to catch up with GR, and reach a general covariant formulation (continuum does not physically exist) or it has to find some reason not to take the principles of GR seriously---some crucial flaw or limitation.

It doesn't matter if there is fuss or no-fuss. These issues persist on the agenda.

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"?

Unfortunately I don't understand the questions. You could elaborate and explain why you think the questions are important.

I think it is assumed that there is no background metric, and so the premise of your question "how can...make sense?" does not seem to hold.

In case you want to look into them here are some Witten papers on B.I.---I don't know what he meant by B.I. back in 1992-1993, exactly, but here they are for what it's worth:3. arXiv:hep-th/9306122 [pdf, ps, other]
Quantum Background Independence In String Theory
Edward Witten
Comments: 20 pp
Subjects: High Energy Physics - Theory (hep-th)

4. arXiv:hep-th/9210065 [pdf, ps, other]
Some Computations in Background Independent Open-String Field Theory
Edward Witten
Comments: 14 pp
Journal-ref: Phys.Rev.D47:3405-3410,1993
Subjects: High Energy Physics - Theory (hep-th)

5. arXiv:hep-th/9208027 [pdf, ps, other]
On Background Independent Open-String Field Theory
Edward Witten
Comments: 18 pp
Journal-ref: Phys.Rev.D46:5467-5473,1992
Subjects: High Energy Physics - Theory (hep-th)

 

[marcus]

Maybe Weinberg would say that the fewer pages per year the better - isn't the dream of of a TOE to have everything on 1 line?

genneth is a condensed matter guy, I think, so his aim would be different?

Yes I agree! Some of the great landmark papers in physics have been just a couple of pages, or a halfdozen, or so I'm told. It's sometimes a good sign when something is so concise.

Why do you think Genneth specialty is condensed matter? I have that impression too but don't remember where I got it. Did he say something to that effect in another thread?

In any case it is refreshing to meet someone with lively interest in some field (like QG) but no stake in this or that approach

 

[genneth]

All this speculation about me is a bit embarrassing... I am a condensed matter theorist by training, but have now almost left physics entirely for biology. Ironically, this has perhaps led me to really think about where theoretical physics sits in the grand scheme of things, especially with respect to experiments.

Back to the topic at hand, I find Careful's words intriguing. I'm not 100% certain I understand what his point was, but my interpretation is that he is asking about what the "background" is, rather in the style of the Smolin article Marcus linked to. This I believe is a perfectly good question. However, I think the answer is that 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; 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...

 

[atyy]

Yes, a viable theory of quantum gravity should have GR as its classical limit, and thus have no prior 4D spacetime geometry in that limit. However, I don't see the relationship between that and Rovellian LQG's tremendous stress on general covariance and relational physics.

One can have generally covariant flat spacetime theories, so Rovellian LQG's concentration on general covariance may have nothing to do with no prior 4D spacetime geometry.

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.

 

[genneth]

Yes, a viable theory of quantum gravity should have GR as its classical limit, and thus have no prior 4D spacetime geometry in that limit. However, I don't see the relationship between that and Rovellian LQG's tremendous stress on general covariance and relational physics.

One can have generally covariant flat spacetime theories, so Rovellian LQG's concentration on general covariance may have nothing to do with no prior 4D spacetime geometry.

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 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.

All this current discussion was based around my original assertion (why may have been worded too strongly) that LQG does indeed reduce to Regge theory (kinda --- I had already clarified to what extent I believe this to be true (belief here meaning what I understand, rather than what I personally believe...)). The question I asked still stands: to what extent can a similar program be achieved with the state of the art in string theory? I have no doubt that string theory can produce sensible scattering amplitudes in the perturbative regime --- but that was the case some 15/20 years ago --- what's the status now? (Review papers would be excellent, but I don't know the literature in the same way as I do for LQG).

 

[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==