# John Baez on Quantum Gravity (TWF 31 August)

1. Sep 1, 2005

### marcus

Last edited: Sep 1, 2005
2. Sep 1, 2005

### marcus

another bleak outlook on attempts at a quantum theory of gravity (nonperturbative geometric approaches especially) was recently posted by Jacques Distler

http://golem.ph.utexas.edu/~distler/blog/archives/000639.html

Distler called his blog entry "Motivation" and it serves as a pitch for learning string theory (he is teaching a course this term) as the only approach to QG with what he sees as a reasonable chance to succeed.

Haelfix on a tentatively more cheerful note offered this to Jacques
http://arxiv.org/abs/hep-th/0110021
Is Quantum Einstein Gravity Nonperturbatively Renormalizable?
O. Lauscher, M. Reuter
18 pages, 3 figures
Class.Quant.Grav. 19 (2002) 483-492

"We find considerable evidence supporting the conjecture that four-dimensional Quantum Einstein Gravity is asymptotically safe'' in Weinberg's sense. This would mean that the theory is likely to be nonperturbatively renormalizable and thus could be considered a fundamental (rather than merely effective) theory which is mathematically consistent and predictive down to arbitrarily small length scales. For a truncated version of the exact flow equation of the effective average action we establish the existence of a non-Gaussian renormalization group fixed point which is suitable for the construction of a nonperturbative infinite cutoff-limit. The truncation ansatz includes the Einstein-Hilbert action and a higher derivative term."

Jacques was not very expansive in his reply to Haelfix, who might also have suggested to Jacques the more recent article by the same authors that we have discussed in several PF threads this past week, including here

http://www.arxiv.org/abs/hep-th/0508202
Fractal Spacetime Structure in Asymptotically Safe Gravity
O. Lauscher, M. Reuter
20 pages
"Four-dimensional Quantum Einstein Gravity (QEG) is likely to be an asymptotically safe theory which is applicable at arbitrarily small distance scales. On sub-Planckian distances it predicts that spacetime is a fractal with an effective dimensionality of 2. The original argument leading to this result was based upon the anomalous dimension of Newton's constant. In the present paper we demonstrate that also the spectral dimension equals 2 microscopically, while it is equal to 4 on macroscopic scales. This result is an exact consequence of asymptotic safety and does not rely on any truncation. Contact is made with recent Monte Carlo simulations."

Last edited: Sep 1, 2005
3. Sep 2, 2005

### Juan R.

Unfortunately Baez "review" is rather distorted. Continue saying that string theory is a theory of everything when is (at least this week :rofl: ) almost a theory of nothing. Baez claims that LQG and related approaches are less ambitious than string theory which is not true. Baez would read last Smolin papers on unification with string theory or last advances in multidimensional LQG, links with SM, etc.

All is directly available on ArXiv with a pair of clicks. Even it is possible that today there are new preprints on the topic that i still unknow.

My favourite phrase is

Would not Baez explain to his readers that M-theory does not exist because nobody has formulated it still?

A more carefull and exact statement would be

Last edited: Sep 2, 2005
4. Sep 5, 2005

### john baez

M-theory

My readers, at least the devoted ones, already know this. In week158 I wrote:

Like lots of mathematicians these days, I'm trying to understand M-theory. It's a bit difficult, partially because the theory doesn't really *exist* yet. If it existed, it would explain lots of stuff: on that everyone agrees. But nobody knows how to formulate M-theory in a precise way, so you can't open up a paper and stare at "the fundamental equation of M-theory", or anything like that. There are some conjectures about what M-theory might be like, but no solid agreement.

And, these words are still true. My remark about "the marvelous unifying M-theory that we don't completely understand yet" was intended as a humorous way of saying this without wasting a lot of time on it.

5. Sep 5, 2005

### john baez

Rovelli's paper

If you're not yourself pessimistic about quantum gravity, especially loop quantum gravity, I strongly urge you to look at what Rovelli has done, because it's very cool. Among other things, he's figured out a reason why the huge contribution to the Barrett-Crane model due to degenerate 4-simplices should be cancelled out by an oscillating phase in the wavefunction for the Minkowski vacuum, at least when computing graviton propagators to the lowest order in perturbation theory.

There are some hand-waving approximations that need to be checked, but still - interesting stuff.

6. Sep 6, 2005

### marcus

What a pleasure to have a visit from you, John Baez!

Indeed I am not pessimistic about QG at all! to me it looks like things are progressing well! but I remember the empty worried feeling a couple of years back when computer studies (Dan Christensen, you, Greg Egan) showed trouble with the Barrett-Crane model. Now (based on the little I have read in the new Rovelli paper) it seems that the degeneracies are whirled away by an oscillating phase.
http://www.arxiv.org/abs/gr-qc/0508124

I will take a more careful look, as you suggest.

You said over at Peter's that you were going to Marseille in February (lucky!) and would be talking about this paper with Rovelli.

----quote rovelli---
The physical correctness of these theories has been questioned because in the low–energy limit their interaction vertex(10j symbol, or Barrett-Crane vertex amplitude) has been shown to include–beside the “good” term approximating the exponential of the Einstein-Hilbert action [18]–, also two “bad” terms: an exponential with opposite sign, giving the cosine of Regge action[18] (analogous to the cosine in the Ponzano–Regge model) and a dominant term that depends on the existence of degenerate four-simplices[19, 20]( reference [19] is the christensen baez egan computer study). We show that only the “good” term contributes to the propagator. The others are suppressed by the rapidly oscillating phase in the vacuum state that picks the state on its correct extrinsic geometry.
---end quote---

I looked up that reference [19] it is
http://www.arxiv.org/abs/gr-qc/0208010
Asymptotics of 10j symbols
John C. Baez, J. Daniel Christensen, Greg Egan
25 pages, 8 figures
Class.Quant.Grav. 19 (2002) 6489
"The Riemannian 10j symbols are spin networks that assign an amplitude to each 4-simplex in the Barrett-Crane model of Riemannian quantum gravity. This amplitude is a function of the areas of the 10 faces of the 4-simplex, and Barrett and Williams have shown that one contribution to its asymptotics comes from the Regge action for all non-degenerate 4-simplices with the specified face areas. However, we show numerically that the dominant contribution comes from degenerate 4-simplices...."

I recall in 2003 there was a certain amount of triumphal gloating and schadenfreude on the part of detractors, on sci.physics.research, based on this. "Spin foam will never work because look, the 4-simplex is overwhelmingly degenerate..." or words to that effect.

but perhaps now rovelli has dispelled that discomfort.
the key steps seem to be on rovelli page 5, equations (15) and (19).
I'm sleepy now but it does not look too hard, and perhaps tomorrow I can get clear about it. It seems to turn on a simple matter of two differentt signs in the exponent, the good term has a minus sign which cancels with an overall exp factor and paralyzes the whirling, so the good term counts, but the bad term has a plus sign and reinforces the overall "rapidly oscillating phase" exp factor so it gets whirled into oblivion.
may all our bad terms be hypnotized by a dizzy phase, and fade into nothing

Last edited: Sep 6, 2005
7. Sep 6, 2005

### Kea

I find this pessimism a bit confusing. It seems to me that the 'maths' that John is working on now is more physically relevant than most LQG stuff. Even if you don't buy all the abstract nonsense (category theory) there's the obvious connection to String theory, which a lot of physicists take seriously.

Cheers
Kea

8. Sep 6, 2005

### Chronos

I'm not convinced they are intractable, but I've had issues since this:

Lack of observational evidence for quantum structure of space-time at Planck scales
http://www.arxiv.org/abs/astro-ph/0303043

9. Sep 6, 2005

### Juan R.

Well, since many inexpert readers can see your post it would be more exact to explain to them that M-theory is just an undeveloped idea. M-theory is, strictly speaking, a misnomer. M-hyphotesis?

Ok! If you want say it without waste your time writting large posts, simple to compare your phrase

with my proposal

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10. Sep 6, 2005

### john baez

Wink

Seriously, I'm not sure what's "more physically relevant" than what. The big difference is between:

1) trying to build specific physical theories and do calculations to see if they give results that match what little we know of what quantum gravity should be like,

and

2) "going with the flow" - following where mathematics naturally leads, not worrying whether it has a quick payoff in physics, trusting that good ideas will eventually get applied.

For about 10 years I worked on strategy one, first trying to make loop quantum gravity rigorous, developing the theory of spin networks and then spin foams, and finally doing a bunch of calculations with Greg Egan and Dan Christensen to study the behavior of a specific spin foam model: the Barrett-Crane model. This was very nerve-racking because it was never clear - and it still isn't clear - whether all this activity was converging on a model which met the basic criteria any theory of quantum gravity should satisfy. It wore me out.

For the last 3 years I've switched to a different strategy: have fun doing math. I've been spending a lot of time learning stuff, especially topology and number theory. When it comes to writing papers, I've mainly been working on higher gauge theory: a theory that describes the parallel transport of 1-dimensional extended objects (loops or strings) intead of 0-dimensional point particles.

I'd have an ulcer by now if I'd been trying to find a specific Lagrangian for a higher gauge theory "theory of everything". Instead, it was much more pleasant and sane to take my time and make the math nice: first categorifying the theory of groups, then the theory of Lie algebras, then classifying Lie 2-algebras and figuring out their Lie 2-groups, then categorifying the theory of bundles and connections....

Of course I did this with a whole gang of grad students and postdocs: I would never have overcome all the obstacles just thinking alone in my attic. We had a lot of fun. And, we came up with a lot of nice stuff, which may or may not be good for physics, but is definitely solid math, since it's tightly related to things that are obviously important: n-categories, Lie algebra and group cohomology, central extensions of loop groups, gerbes, and so on.

Right: one spinoff of the above project was to discover that the most interesting Lie 2-groups are those related to central extensions of loop groups. This means that the most interesting higher gauge theories are inherently related to the math behind string theory!

This isn't supposed to be shocking: we did, after all, start with the goal of developing a theory of parallel transport for 1-dimensional extended objects.... okay, so they're a lot like strings! But, it's great to see how it works in detail.

And, it's great not to be fighting the loop/string battles, with all their unpleasant rhetoric and partisanship.

Last edited by a moderator: May 2, 2017
11. Sep 6, 2005

### john baez

saved by a whirling phase?

Thanks! Last night I started looking around to see if anyone had responded to
"week220", so I peeked at Woit's blog and Physics Forums.

Right. We did that 3 years ago, and I felt completely stuck and burnt out at the time, so I switched to "pure math" - actually higher gauge theory.

Right. Doubtless written by people who had no understanding of our calculation and what it meant - people more interested in battles and rhetoric than actual science. I knew at the time that there could be all sorts of different ways around this problem. I never felt it would be a death blow to spin foam models. I just couldn't see which way around the problem was worth studying. Studying these things takes a lot of time and effort, and I didn't want to put another year or two into some direction that might be a waste of time.

Luckily Carlo Rovelli marched ahead, pretty much ignoring the problem, and figured out how to perturbatively compute the graviton propagator starting from the Barrett-Crane model and a choice of boundary conditions representing Minkowski spacetime! It took him 3 years but now he has done it.

There are lots of approximations being made in his paper, and it's only 1st-order perturbation theory, so there are millions of things that could still go wrong. It would still be incredibly nerve-racking if I had my heart set on the success of this specific model.

But, it's definitely progress, and he has come up with a quite convincing
reason why the "problem" might not be a problem... at least to 1st order in perturbation theory.

Excellent summary of the key idea. Note that this all comes from the boundary conditions describing Minkowski spacetime.

12. Sep 6, 2005

### marcus

great tribute to Carlo

your hunches have been a compass by which (I think) a lot of us have navigated, so this assessment (not that it works but that it might) counts extra