Wen and Lloyd join emergent geometry bunch

[marcus]

I posted announcement of the August workshop at MIT on the announcement sticky.
there is a basic physics reason why emergent geometry is hot, probably several basic reasons. Let us know why you think it is. Here's my take.

We see an explosion of meetings now about emergent geometry.
The most immediate cause that triggered this is that Loll's group got deSitter spacetime to EMERGE as a feynmann path integral of random geometries

where they didn't put in any 4D manifold by hand. the deSitter arises from MICROSCOPIC PLANCKSCALE DEGREES OF FREEDOM that assemble themselves in chaotic fractally fashion at small scale but somehow manage to achieve a recognizable 4D geometry at larger scale.

The idea of emergent geometry (and matter) is that space time is an illusion and likewise particle fields are an illusion. There are more fundamental degrees of freedom which are busy interacting evolving at small scale according to their own dynamics, their own laws.

The game (Loll's game and the game of all these people coming to the workshop) is to find a way to MODEL these little atoms of pure existence, and their dynamics, so that you can put a bunch in the computer and have them swarm together like ants or bees so that a collective emerges that looks like space time and matter.

A word that some people use is "epiphenomenon" and an analogy is solidstate or condensed matter. There is the basic fundamental phenomenon and there is the "epi" stuff that arises from it---the larger scale processes that the microscopic stuff supports. Soundwaves are an "epi" supported by a host of bumping air molecules.

The thrust of this emergent geometry research is to go down to a deeper level.

There is a great variety of ideas, different mental pictures. Most of them won't appeal to everybody. Many of them don't appeal to me and i suspect most will turn out to be wrong.
But that's how it is supposed to work.

It is an active field and it is snowballing. That means a free-for-all bar-room brawl of ideas. So here comes this MIT conference to point this out. The actual title is Emergent Gravity but gravity is the geometry of spacetime so that is just a synonym. And matter interacts with geometry so it must arise from the same microscopic descriptors and be included too.

I will get the list of participants----many of them we have already discussed their work here at PF over the past 3 or 4 years. And I will get some links to a few papers mainly as a refresher----to remind us of the different approaches they take to emergent spacetime and matter.

 

[marcus]

Participants

David Finkelstein

Cohl Furey

Florian Girelli

Song He

Bei-Lok Hu

Ted Jacobson*

Seth Lloyd

Renate Loll

Fotini Markopoulou

Emil Mottola

Slava Mukhanov*

Daniele Oriti

Frederico Piazza

Jorge Pullin

Subir Sachdev

Lee Smolin

Silke Weinfurtner

Xiao-Gang Wen

Jan Zaanen

* to be confirmed

===================

it strikes me as a good thing that all these people are getting together and talking with each other for a few days 25-29 August

I posted about XG Wen back in 2004 when Dreyer's hep-th/0409048 came out. He approaches things from a condensed matter POV. (see Dreyer's references [3], [4], [5])
Smolin invited him to a workshop on Emergent Spacetime held November 2005 at Perimeter. The main other people were Renate Loll and Seth Lloyd, if I remember right. It was a small affair by comparison. Shows how this line of investigation has grown.

SetAI, a longtime PFer, has always been interested in Seth Lloyd's work deriving spacetime from computation. The fundamental atoms of existence are represented by something like an interconnected web of microprocessors---a network of automata.

Here's an illustrative Lloyd article:
http://arxiv.org/abs/quant-ph/0501135
A theory of quantum gravity based on quantum computation
Seth Lloyd
43 pages; 5 figures
(Submitted on 24 Jan 2005 (v1), last revised 26 Apr 2006 (this version, v8))

Abstract: This paper proposes a method of unifying quantum mechanics and gravity based on quantum computation. In this theory, fundamental processes are described in terms of pairwise interactions between quantum degrees of freedom. The geometry of space-time is a construct, derived from the underlying quantum information processing. The computation gives rise to a superposition of four-dimensional spacetimes, each of which obeys the Einstein-Regge equations. The theory makes explicit predictions for the back-reaction of the metric to computational `matter,' black-hole evaporation, holography, and quantum cosmology.


Here is an illustrative Xiao-Gang Wen paper
http://arxiv.org/abs/cond-mat/0407140
Photons and electrons as emergent phenomena
Michael Levin, Xiao-Gang Wen
9 pages, 12 figures
(Submitted on 6 Jul 2004)

Abstract: Recent advances in condensed matter theory have revealed that new and exotic phases of matter can exist in spin models (or more precisely, local bosonic models) via a simple physical mechanism, known as "string-net condensation." These new phases of matter have the unusual property that their collective excitations are gauge bosons and fermions. In some cases, the collective excitations can behave just like the photons, electrons, gluons, and quarks in our vacuum. This suggests that photons, electrons, and other elementary particles may have a unified origin -- string-net condensation in our vacuum. In addition, the string-net picture indicates how to make artificial photons, artificial electrons, and artificial quarks and gluons in condensed matter systems.

People intrigued by Wen's solid state physics metaphor for the universe may enjoy visiting his MIT website, which has lots of stuff to read and graphics to look at.
http://dao.mit.edu/~wen/

AFAIK neither approach has so far been especially fruitful (which doesn't mean it's wrong, simply that it hasn't yet produced a lot of follow-on and results) but both approaches are certainly intriguing and could link up with other lines of research. The field is changing unpredictably.

 

[marcus]

Right now I would say that Triangulations path integral (Loll's approach) and Braidmatter (represented by Song He and Lee Smolin at the conference) are in the limelight.

That doesn't mean that they are right and the other approaches are wrong. Maybe all the approaches are to some extent right--or on the right track.

All it means is that Triangulations and Braidmatter have both made important advances recently and gotten our attention.

This conference is like a test tube and we will see what happens when we add various things. Do they react and what happens when they react? Here are a couple of illustrative links for Loll

http://arxiv.org/abs/0712.2485
Planckian Birth of the Quantum de Sitter Universe
J. Ambjorn, A. Gorlich, J. Jurkiewicz, R. Loll
4 pages, 3 figures, published in Physical Revlew Letters
(Submitted on 17 Dec 2007)

Abstract: We show that the quantum universe emerging from a nonperturbative, Lorentzian sum-over-geometries can be described with high accuracy by a four-dimensional de Sitter spacetime. By a scaling analysis involving Newton's constant, we establish that the linear size of the quantum universes under study is in between 17 and 28 Planck lengths. Somewhat surprisingly, the measured quantum fluctuations around the de Sitter universe in this regime are to good approximation still describable semiclassically. The numerical evidence presented comes from a regularization of quantum gravity in terms of causal dynamical triangulations.


http://arxiv.org/abs/0711.0273
The Emergence of Spacetime, or, Quantum Gravity on Your Desktop
R. Loll
22 pages, 11 figures, to appear in Classical and Quantum Gravity
(Submitted on 2 Nov 2007)

Abstract: Is there an approach to quantum gravity which is conceptually simple, relies on very few fundamental physical principles and ingredients, emphasizes geometric (as opposed to algebraic) properties, comes with a definite numerical approximation scheme, and produces robust results, which go beyond showing mere internal consistency of the formalism? The answer is a resounding yes: it is the attempt to construct a nonperturbative theory of quantum gravity, valid on all scales, with the technique of so-called Causal Dynamical Triangulations. Despite its conceptual simplicity, the results obtained up to now are far from trivial. Most remarkable at this stage is perhaps the fully dynamical emergence of a classical background (and solution to the Einstein equations) from a nonperturbative sum over geometries, without putting in any preferred geometric background at the outset. In addition, there is concrete evidence for the presence of a fractal spacetime foam on Planckian distance scales. The availability of a computational framework provides built-in reality checks of the approach, whose importance can hardly be overestimated.

An illustrative paper from the braid-matter group is

http://arxiv.org/abs/0805.1265
C, P, and T of Braid Excitations in Quantum Gravity
Song He, Yidun Wan
28 pages, 5 figures
(Submitted on 9 May 2008)

Abstract: We study the discrete transformations of four-valent braid excitations of framed spin networks embedded in a topological three-manifold. We show that four-valent braids allow seven and only seven discrete transformations. These transformations can be uniquely mapped to C, P, T, and their products. Each CPT multiplet of actively-interacting braids is found to be uniquely characterized by a non-negative integer. Finally, braid interactions turn out to be invariant under C, P, and T.

My thought is that what we need to do is put this all together and get an overview of where the whole thing is going.

 

[gorgos]

Any connection between emergent phenomena and Prof. Robert Laughlin,"Emergent Relativity"?

ftp://large.stanford.edu/publications/2005/p01apr05/p01apr05.pdf[/URL]

Laughlin, for example, argued that if you try to write down all the interactions of a single electron in a conductor, no matter how many electrons you add up in your interactions, you will NEVER recover the superconductivity phenomenon. Superconductivity is an emergest phenomenon that is a result of a many-body interaction. The starting point in describing such a phenomenon MUST start not from a single particle scenario, but from a many-body ground state scenario. This effect emergers out of a many-body interaction and will simply disappears if one tries to take it apart to a single-particle level.

 

[Coin]

Hm, so let me see. It seems like emergent gravity [emergent geometry] is basically an umbrella category that incorporates the common elements of
1. The Spin network/spinfoam models of LQG
2. Loll's Triangulations/Lego path stuff
3. Any similar models yet to be imagined wherein spacetime is an emergent side-effect of the behavior of some underlying structure.

Do I understand this correctly?

Something that I notice: It seems like all attempts thus far to construct what could be described as an "emergent geometry" have all produced pictures of reality where the geometry of spacetime which emerges is fundamentally discrete. Is this correct? If so, is this just a coincidence of those attempts to the problem which have been tried so far? Or might there be some reason to think emergent geometry implies discrete geometry by necessity?

 

[marcus]

Hm, so let me see. It seems like emergent gravity [emergent geometry] is basically an umbrella category that incorporates the common elements of
1. The Spin network/spinfoam models of LQG
2. Loll's Triangulations/Lego path stuff
3. Any similar models yet to be imagined wherein spacetime is an emergent side-effect of the behavior of some underlying structure.

Do I understand this correctly?

Coin you are asking good questions. I think there are several different ways to understand the term. And I understand it different from you. I think most of all that emergent spacetime geometry is a HOPE that a lot of people share. We can't make a paradigm for it by just looking at some overlaps of what we have now.

And this MIT conference is not necessarily a satisfactory representation. It is just one attempt to gather a conference about this widely shared hope.
http://www.rle.mit.edu/emergent/participants.htm

I think the hope is that you can find some deep fundamental degrees of freedom and some dynamical laws governing them, from which space, time, and matter will arise. You want to find that space (which is geometrical relationships) and matter are fundamentally the same thing, which is why matter and geomtry interact with each other.

I've heard David Gross several times express this hope. "We need some new idea. Maybe we need a new idea of what space and time are." It sounds plaintive when he says it (like at the final talk of an international conference.)

I have to go. I will try to respond more to what you said later. This part is also interesting but I don't have time to reply now:

Something that I notice: It seems like all attempts thus far to construct what could be described as an "emergent geometry" have all produced pictures of reality where the geometry of spacetime which emerges is fundamentally discrete. Is this correct? If so, is this just a coincidence of those attempts to the problem which have been tried so far? Or might there be some reason to think emergent geometry implies discrete geometry by necessity?

 

[marcus]

Coin I had to go to supper and now I'm back. There's something else I'd like to say. Emergent space time and matter (from a single set of d.o.f.) is not just a hope, I think it is a REASONABLE hope. Because it seems to be happening.

At the moment the only approach that delivers the goods, even partially, is Renate Loll's triangulations. Because it starts from microscopic elements that are totally other than a smooth continuum, and out of that emerges a familiar (macroscopically smooth) 4D continuum--the deSitter universe.

The microscopic elements she starts with could easily coagulate into ugly stuff with the wrong dimension or even no well-defined dimensionality---in earlier research that is what kept happening.

And indeed the quantum geometries that are produced and then averaged together in the path integral do have depleted dimensionality at very small scale---they are only 4D at larger scale. the aren't the conventional differentiable manifolds we are used to.

So as I see it that is real emergence. And I would hope that matter could arise from the same stew of fundamental d.o.f. but it hasn't yet. So Loll's group is the only one that has really delivered.

Several of the other approaches have very interesting results and may be farther ahead in other ways----like application to cosmology for example. But they haven't shown me deSitter space arising out of Planckscale chaos. Yet.
===============================

Coin you are generalizing from a limited set of approaches, when you say in effect "all these approaches are in some way discrete, so can I conclude that the answer will be a discrete approach?"

We both see that this is risky guesswork because there is nothing guaranteed valid about the set of approaches being pursued now. So your guess is as good as mine.

I would make a different guess, of the same sort. I would say that whatever ultimately succeeds will necessarily be a BACKGROUND INDEPENDENT approach, where no continuum with a pre-defined geometry is put in at the beginning.

I am making a risky generalization too, because I see that all the approaches which are making progress now are, in fact, background independent. And this makes me imagine that the ultimately successful one (which we may not have seen yet) may also be that.

And maybe background independence is conducive to approaches that are somehow combinatorial or graph-theoretical, I don't know that it is, but it might be. Combinatorial graphy things have a discrete aspect. So in that case our two guesses would be close relatives.

I try to keep an eye on the whole pack and avoid picking favorites, at this point. As long as an approach is plainly and manifestly background independent, and as long as it is trying to incorporate both quantum geometry and matter, then I think it's worth keeping track of.

You'll doubtless have your own way of watching the same events which is fine and I like to get your insights.

 

[gorgos]

By Wikipedia http://en.wikipedia.org/wiki/Induced_gravity
Sakharov "Induced gravity" also the kind of Emergent gravity.

 

[marcus]

Gorgos, does it strike you that some of the stuff presented at this Emergent meeting is likely to be wild and wacky? It does me.
If everybody on the list shows up then there will certainly be some solid research results discussed but there will also be some ideas presented that frankly I find bewildering. I don't know what your tolerance of "far out" ideas is. Mine is limited.

 

[marcus]

Something that I notice: It seems like all attempts thus far to construct what could be described as an "emergent geometry" have all produced pictures of reality where the geometry of spacetime which emerges is fundamentally discrete. Is this correct? If so, is this just a coincidence of those attempts to the problem which have been tried so far? Or might there be some reason to think emergent geometry implies discrete geometry by necessity?

One thing that this thread helps emphasize is the ambiguity in the word "emergent".
It is both deep and superficial. On the one hand I think it is a signpost pointing in the right direction, and on the other hand it is a fashionable buzzword.

It might help clarify to have a look at the statement on Loll's main webpage that describes the main direction of her and her co-workers' research, as she sees it:

"...developing a theory of quantum gravity, reconciling the beautiful geometric description of space and time laid out in Einstein's theory of General Relativity with the insight that all of physics at its most fundamental level must be described by quantum laws of motion. ... a new approach to the nonperturbative quantization of gravity, that of Causal Dynamical Triangulations which recently has produced a number of remarkable results. These include a dynamical derivation of the fact that space-time is four-dimensional (something that can be taken for granted only in classical gravity) and that it has the shape of a de Sitter Universe (like our own universe in the absence of matter), and of the so-called wave function of the universe which plays an important role in understanding the quantum behaviour of the very early universe. Remarkably, one also finds that the dimensionality of spacetime reduces smoothly to two at short distances, indicative of a highly nonclassical behaviour of spacetime geometry near the Planck scale. These results are obtained by superposing elementary quantum excitations of geometry which have a notion of causality ("cause preceding effect") built into them at the very smallest scale..."
http://www.phys.uu.nl/~loll/Web/title/title.html

Coin you asked about the continuous vs discrete issue. Probably we have to be prepared for a TENSION between these ideas analogous to the wave vs. particle tension.
In a very real way, Loll's approach is NOT DISCRETE. Because it has no minimal length and it does not view spacetime as constructed from small components. It approximates with simplices but then takes the limit as their size goes to zero. That is why she can say that the dimensionality as a quantum observable depending on scale is 4D at large scale and reduces smoothly to 2D as you zoom in at smaller scale with a higher magnification microscope.

The picture is of something that is NOT made of little building blocks, but on the other hand it is not a normal diffy manifold like what Riemann gave us and Einstein used to build General Relativity. It is not a normal continuum as in traditional mathematics. So there is a paradox. Geometrical features like dimensionality are quantum observables, they depend on scale, we can use a discrete language of simplicial complexes to talk about them to an excellent approximation, and yet the overall result also has aspects of a continuum (just not a normal one.) So there is a tension.

And I would not try to look at the whole field and find the common thread. I would take Loll's approach as a paradigm of what emergent gravity or emergent geometry is about. And then I would go out from that paradigm and expect to find other approaches which have some family resemblances to CDT.

The reason is that Loll CDT has achieved the emergence of 4D de Sitter space as a quantum average---or path integral. CDT may not be the RIGHT way and may not be what eventually solves all the problems, but it is farthest along the emergent geometry road. So that is where I would look for my checklist of common features to look for, or family resemblances, in the other approaches.

Loop cosmology has been getting great results, but it is in a sense applied Quantum Gravity. It is so successful in cosmology that I suspect that it might be potentially more complete or righter. But I don't think anyone has yet set up a spinfoam model in a computer and have deSitter universe emerge from it, whole hog so to speak. Maybe I am wrong but I don't think this has happened. What happens is a few instants after the big bang the LQC model converges to the corresponding classic FRW model with whatever parameters were put in. And LQC is symmetry reduced, like FRW. Isotropic. So you are not seeing a world arise out of complete quantum chaos. Here is another sign https://www.physicsforums.com/showthread.php?t=236946 that LQC could eventually be right even though CDT is currently further along the road to emergent spacetime.

the one thing I don't see in CDT is matter.

and I frequently wonder what would happen if Loll in her model allowed some twisting and crossing as the simplexes were being glued together or were being allowed to rearrange themselves in their Monte Carlo dance. they might need more computer power to get matter to appear in CDT