Causal Dynamical Triangulations

[BenTheMan]

First, a disclaimer: please don't link me to a list of abstracts from arXiv. I can do the literature search myself.

Now, a question.

I was reading in Scientific American June 2008 issue about this new approach to quantum gravity, called Causal Dynamical Triangulations. The author(s) of the article state that they assume a positive cosmological constant, and are led to a deSitter space-time. Was it ever a question that a positive cosmological constant would give a deSitter space-time?

 

[Haelfix]

Yea. For instance the whole spacetime could crumple up or yield junk (which indeed happened ubiquitously in early attempts at trying to stick gravity on a lattice). So its rather nontrivial that they get something that is approaching a nice continuum and it seems resilient relative to changes in lambda (they get minkowski for lambda = 0 I think).

Still they're very far from proving that indeed that is *the* continuum limit (lattice theory is notorious for 'close but not quite'), much less that its unique and/or stable relative to addition of matter and other nasties. The best they can do is to refine their algorithms, add more computing power and hope for someone else to give some sort of analytic result. Alas they'll never be able to make the lattice spacing on the right order to probe microscopic quantum gravity effects.

People hope that as times go on, those sorts of models will help to give some sort of intuition for various processes that might take place in nice spacetimes (so for instance it could be useful for analyzing inflation and the like).

 

[BenTheMan]

For instance the whole spacetime could crumple up or yield junk

Ahh ok.

So it's more or less Lattice QG, is what I got from it. This formulation also isn't Lorentz invariant, right? That is, Lorentz invariance is an emergent idea, not a fundamental one? Also, how can they extrapolate a continuum limit which they trust? I seem to recall that lattice QCD people have to use something like Chiral Perturbation theory. What's the analogy here?

 

[nrqed]

Ahh ok.

So it's more or less Lattice QG, is what I got from it. This formulation also isn't Lorentz invariant, right? That is, Lorentz invariance is an emergent idea, not a fundamental one? Also, how can they extrapolate a continuum limit which they trust? I seem to recall that lattice QCD people have to use something like Chiral Perturbation theory. What's the analogy here?

As far as I understand it, no there is no Lorenrz invariance built in. However, they do impose a causal structure from the start. I don't know exactly what that means and how it's implemented but apparently they only include triangulations respecting causality. (I think older approaches to summing over triangulations did not impose this condition and were yielding bad results).

Chiral perturbation theory has nothing to do with lattice QCD per se. ChPT is a continuum effective field theory using different degrees of freedom than quarks (it basically use directly the symmetries of QCD to build an EFT in terms of the observed mesons).


In lattice QCD they simply work with finer and finer grids and then extrapolate to the continuum.

 

[BenTheMan]

Chiral perturbation theory has nothing to do with lattice QCD per se. ChPT is a continuum effective field theory using different degrees of freedom than quarks (it basically use directly the symmetries of QCD to build an EFT in terms of the observed mesons).

In lattice QCD they simply work with finer and finer grids and then extrapolate to the continuum.

Well, they can only work on grids that are a certain size. At some point, the problem becomes computationaly too difficult, and they have to extrapolate. From listening to Lattice talks, I get the impression that they do a garbageload of simulations at smaller and smaller lattice spacings, and then use those results to extrapolate down to the physical result. And I know it's not as easy as just drawing a line, or something. (I know because I asked the speaker at a lattice talk, and everyone laughed.)

So there MUST be some consistent way to get from a finite lattice spacing to an infinitessimal one, because I don't think it's possible to work at 0 lattice spacing, and I don't think it's as easy as just drawing a line.

 

[jal]

And I know it's not as easy as just drawing a line, or something. (I know because I asked the speaker at a lattice talk, and everyone laughed.)

Did anyone suggest a paper that justify the inserting of points and lines. In other words, not putting them in by hand.
I'd like to read it.
jal

 

[BenTheMan]

I think that the justification is just that it works.

It's like assuming that the fundamental degree of freedom is a string, and not a point particle.

You always have to start SOMEwhere.

 

[Haelfix]

"So there MUST be some consistent way to get from a finite lattice spacing to an infinitessimal one"

Well that's sort of the million dollar question from a foundational stand point. QFT is perfectly consistent mathematically as a lattice theory. Its well defined all the way up to the continuum limit, where all hell breaks loose and all the subtleties and mathematical problems with field theory creep in.

Some field theories are better behaved than others in that regard, QCD (we think) for instance is pretty well under control on the lattice (minus fermions, which are still touchy), but lattice QED for instance is a complete mess: One expects all sorts of phase transitions to take place (for instance a transition from a confining theory to a nonconfining theory), and certain known dynamics are unbelievably sensitive to lattice spacing and details of the procedure.

In a sense, physics are as sensitive to that limit, as they are to the limit where perturbation theory becomes strongly coupled. Strange things happen, that may or may not be invisible at the particular lattice spacing or even to *any* order of lattice spacing.

 

[BenTheMan]

Well that's sort of the million dollar question from a foundational stand point. QFT is perfectly consistent mathematically as a lattice theory. Its well defined all the way up to the continuum limit, where all hell breaks loose and all the subtleties and mathematical problems with field theory creep in.

Agreed. But this seems to anchor all of the claims of the Loll et al. people. The claim seems to be that the continuum limit IS well defined, and that one ends up with nice, smooth, causal 4d space times.

 

[BenTheMan]

Ok, from this presentation: http://echo.maths.nottingham.ac.uk/qg/wiki/images/1/1e/GoerlichAndrzej1214824381.pdf (which marcus seems to be pretty high on), on page 30 it looks like they actually DO apply a simple linear fit to get the continuum limit.

This seems rather dubious because the main conclusion that they find (i.e. that the approach gives four dimensions) is entirely based on this fit, in spite of the fact that in the other lattice theory that people work with (QCD), this approach doesn't work.