Monday, April 07, 2008

Group Field Theory and Emergent Space-Time

This paper by Daniele Oriti includes some ambitious ideas toward a theory of quantum gravity. In its first sections, he introduces his preferred formalism, called Group Field Theory (GFT). He shows how this formalism offers a framework general enough to incorporate aspects of other quantum gravity approaches. He then draws some lessons from these other approaches to suggest a path toward a successful theory by which space-time may be seen to emerge from a discrete quantum micro-structure using a GFT. Interestingly, in light of my last QG post, he takes inspiration from condensed matter theory in advocating his ideas. (My thanks to the anonymous commenter who suggested I look at this paper).

I had come across Oriti’s work before, and my first casual impression was that if GFT was a generalization of quantum field theory which hoped to incorporate gravity, then it might not be too interesting. I had taken to heart the criticisms that approaches which start by extending QFT (like the original string theory) were flawed by not being “background-independent”. Field theory is formulated against a flat space-time background, so how can you get space-time back out of it? As Oriti describes the formalism, while it is a true species of QFT, the way he uses it can be interpreted as modeling pre-geometric discrete quantum gravity elements. If so, then the QFT origin of the mathematical structure may not be an issue. In any case, I’m in no position to make judgments about the merits of the formalism, so I’ll just try to summarize here some the interesting ideas which arise as Oriti explores this framework.

He says the GFT can describe a quantum field in terms of fundamental variables which can be represented either as spin network vertices or elementary (d-1) simplices. Therefore he can draw connections to both the loop quantum gravity/spin foam and dynamical triangulations research programs. He says while there are open issues here, it appears that the GFT formalism can be seen to incorporate enough of these theories (and quantum Regge calculus as well) that he can draw some new lessons from examining certain features of these models from within the GFT framework.

Let me try to see if I can relate what he says the main lesson is (section 3.4 of the paper). These theories have tried to get dynamics from path integrals of the discrete structures they start with. Oriti says what results are the physics of (only) “few-particles”; these approaches lack a way to get interesting large –scale “many-particle” physics which would offer a chance to reveal an emergent space-time “continuum”. GFT offers a way to do a second quantization and field-theoretic analysis of the same starting structures in order to study the complex features which come in the many-particle regime. It is in this regime where we would hope to find an approximation of the continuum space-time described by General Relativity.

One exception to these perceived limitations of the other theories is the Causal version of Dynamical Triangulations (my post on this is here). In this approach, the micro-variables are stripped down to include only causally ordered ones, and the resulting path integral analysis has given interesting results in terms of an emergent four dimensional structure. Oriti suspects, though, that the strict limitations put imposed in CDT may lead one to again prefer analyzing the more general results which can come from using the GFT approach.

Oriti says that condensed matter physics shows the usefulness of field-theoretic and 2nd quantization approaches to studying the collective behavior and statistical properties of many-particle physics. He thinks we should consider quantum space-time as a condensed matter system, with the discrete structures of the GFT formalism as the atoms of space-time, and the continuum space-time as an emergent collective regime. General Relativity would be a hydrodynamic effective description of a quantum space-time fluid. Condensed matter techniques, themselves based on QFT, can point the way for how to research this possibility within GFT. Toward the end of the paper, Oriti offers a speculation that the Bose-Einstein condensate may be the specific analogue to look at (section 7 of the paper). His outline for how this would work is hard for me to follow. Some of the choices one makes in setting the terms in the GFT model seem important, but I can’t offer any opinions on this.

As I’ve said before, I like the idea of having a theory where a discrete quantum micro-physics leads to the space-time of GR in an emergent regime. So Oriti’s work is one I will try to follow as I have the other programs which have this feature. I also like that he wants to incorporate condensed matter physics as a guide to how this works. The parallels between condensed matter physics and fundamental physics are so suggestive that this link should be pursued. I still have a residual worry about the use of a field-theoretic approach which has space and time coordinates in the configuration of the micro-theory. I have this idea that a causal network of elementary quantum systems with absolutely no space-like metric would be a philosophically more appealing starting point. But perhaps this will turn out to be an unfounded worry. I look forward to reading more from Oriti in the future.

Emergent Quantum Gravity Research Series (in chronological order):

What’s New in Quantum Gravity
A section of Lee Smolin’s recent book discusses new approaches.

Causality First
Rafael Sorkin’s Causal Sets and Fotini Markopoulou’s Quantum Causal Histories.

Emerging From the Noise
More on Markopoulou’s approach.

Caution: Universe under Construction
The Causal Dynamical Triangulation program.

More papers from Markopoulou and colleagues.

In the Beginning was the Qubit
Seth Lloyd’s quantum computing-inspired take on quantum gravity.

Dreyer's Internal Relativity
Olaf Dreyer's approach to finding emergent gravity from a quantum mechanical base.

The Superfluid Universe
Grigory Volovik looks for the answers to fundamental physics in the surprising phenomena displayed in condensed matter physics.


Mike Wiest said...


Interesting. I was going to complain that I was denied access to the paper at the link you gave, but on reading your description I think I'm happy to take your word about it rather than get a few hours older trying to glean something from the paper.

I have to agree with your nagging concern that emergent spacetime is not as impressive when it is built into the micro-Monads. That concern seems similar to your concern about building time into the "Causal Dynamical Triangulation" scheme. I haven't read about it...but would a similar concern hold for the causal histories picture?

Dmitri Nanopoulos has a string field theory scheme in which he claims space and time AND an arrow of time emerge from nonspacetime variables. Some part of the story is even described in popular form in "As Time Goes By." I never quite grasped how it worked though (so far).

He happens to be the same guy who has a quantum string model of brain microtubules to explain consciousness and the psychological arrow of time. Fun for the whole family!

Steve said...

Hi Mike.
(Did the PDF download in the upper right not work?)

Right - I have this preference that we want is to get the spacetime of GR to emerge as a limit of an underlying system of quantum micro-monads, preferably without the monad's themselves existing on a background spacetime.
Field theories have this (flat, special relativistic) background.

The issues for LQG and CDT are a little more subtle. LQG and CDT are "background independent" in the above sense, but they start with an abstract graph that is a direct quantum encoding of the spacetime geometry of GR. Then, they look to take a path integral of all of the possible spacetime configurations and get 4D GR back out. This seems a little circular also.

CDT only uses causally ordered options in its path integral - this aspect I'm good with. My concern about the time element in CDT was not that time was part of the background, but that the simulation used globallly synchronized time-steps (if I read it right). This struck me vaguely as artifical. Time should be local.

The Quantum Causal histories program lacks any of these concerns, but of course they haven't got GR as an emergent feature yet either. I like Sorkin's causal set theory, but in his case the last I read it wasn't yet available in a truly quantum mechanical form yet.

Honestly, when I read Nanopoulos before my quick conclusion was that he was a bit "out there" -- but I should probably revisit to see if I'm being fair.

Mike Wiest said...

Hi Steve,

The pdf link works today. But I'm still not going to read the paper. I used up my time-wasting allotment for today reading Schwitzgebel (Erik's link from the Periphery post).

Thanks for the brief clarifications about the different QG programs.

Nanopoulos is out there. There is no getting around that. And he comes off a bit like a used car salesman. On the other hand, he's apparently a real string theorist and one of the most highly cited living physicists, so he may know his physics. So, even if his story about the arrow of time and consciousness are fraudulent, I find them exciting because he is outlining solutions to basic problems that are barely acknowledged by most. I mean, if you think about the arrow of time, and get past the bullshit 2nd law of thermo explanation of it, you might come to the conclusion (with Kant and Schopenhauer) that the arrow is in our heads, and/or it needs some physical explantion. Then you need a physical explanation for how this arrow arises in our head (and in the objective world if you believe in that--Nanopoulos does). Nan describes a model he claims does that. And, although he's an atheist, his (quantum-gravity, Penrose-like) story gives the only inkling I've come across for how there could be some truth or at least MEANING behind the claims of mystics that we can perceive some kind of eternal reality. Another way to see his theory is as a concrete instantiation of the kind of theory that Penrose proposed in a vague manner.

So he's out there, but hey, you're a panpsychist: so are you! And the truth is out there too...

Which thing of his did you look at? The "Time" one or the "String Theory of Brains" one?

Steve said...

"So he's out there, but hey, you're a panpsychist: so are you!"


The paper I read was the "Theory of Brain Function, Quantum Mechanics and Superstrings." But I really don't remember much about it. Clearly Nanopoulous is publishing a ton of string theory work and this brain work was an added side interest of his. The "time" paper I don't remember seeing, let me know if you know the full title or have a link.

With regard to the arrow of time, though, one of the nice possibilities of the emergent space-time programs is that they appear to allow for the following possibility: the arrow could be the function of the micro-level causal structure, even though the emergent level degrees of freedom (the basis of our current GR and QFT theories) lack an arrow.

Mike Wiest said...

The time paper is "As Time Goes By..." which is here:

It's about his solution to the collapse of the wave function problem, which gives him a microscopic arrow of time. There's nothing about consciousness or the brain in this one. I haven't read it in years but I can confess to finding it frankly inspirational when I read in grad school (around 1996). But there are a lot of exclamation points. You can feel that as the excitement of the author or you can feel it as the author's attempt to pull the wool over your eyes...

Re: emergent space-time programs with micro-arrow and no macro-arrow--my gut feeling these days about the lack of arrow in GR and (for the most part) QFT is to regard it as a FAULT of those theories, rather than a datum to be reproduced by other candidate theories. I mean, we are macro, and we experience an arrow. The wavefunction collapse seems like a natural place for an arrow to come in that will be consistent with the empirical data that support GR and QFT. But I know Brain Greene is at least one (string) expert who doesn't believe there's really any wave function collapse or associated arrow....


Steve said...

I was hoping we could have it both ways. The micro-level is the realm of causally ordered interactions among quantum systems (these interactions are measurement events=wave function collapses). Despite our being macro-sized, our biology and neurology allows us to leverage this fundamental reality into time-ordered experience at our level. Yet out there in the world, the collection of very small interactions self-organizes into the world approximately described by present day physics.

Here's hoping nature is kind enough to conform to my philosophical preferences.