Spin Networks and Spin Foams

by dpa
Tags: foams, networks, spin
 P: 149 Hi all, Could anyone explain in very simple language, for lower UGrad standard, what spin foams and spin networks are? Thank You. SINCERELY DPA
 Astronomy Sci Advisor PF Gold P: 23,208 They are simple mathematical structures used in Loop quantum gravity. Loop is a theory of geometry---the grav. field is treated as geometry, not as force. It's quantum geometry, meaning that the angles between things are a bit fuzzy or uncertain. Likewise other geometric things you might imagine you or a very small being measuring. Little chunks of volume, areas between adjacent volumes where they press together. Fuzzy, uncertain. So how to REPRESENT these slightly uncertain geometric circumstances. Do you know what a GRAPH is. Something a bit like a room-filling spiderweb or a tinkertoy construction or a molecule model made with knobs and sticks. A spin network is a LABELED GRAPH that represents geometric information you gathered by measuring a volume (at each knob) and where two knobs are joined by a stick that means the two chunks of area are touching and you measured the area where they meet. You only get to make a finite number of measurements to determine a state of geometry, and remember that measurements involve uncertainty. The old rigid precise definite classical world isn't available. The spin network is a way of representing the quantum state of geometry of a 3d slice of spacetime. It may sound complicated but it's just about the simplest way to record the results of the finite number of geometric measurements that you are allowed to make. You can give the knobs names but you cannot locate them in space, they ARE space. Their relationships to each other defines location. You cannot say where they are except in relation to each other. They are "where". So a spin network is a "colored" ball and stick model like of a large molecule, where colors are measurements of area, volume etc . And that's the bare bones of what a quantum state of geometry is. All the spin networks are gathered into one big collection called "state space" and math tools are developed to work with them. Now we want a way to be able to calculate a probability-like number called an "amplitude" of evolving from one state to another. That's where spinfoams come in. A spinfoam is a diagram that shows how an initial (labeled) graph can evolve into a final (labeled) graph. It is like a Feynman diagram of particle interactions except it shows geometric changes. The appearance of a bit of volume here, the disappearance of another bit of volume over there. The scrunching together and stretching apart, that can change the amount of area between two things where they touch, or the volume, or the angle of one adjacency to another. A spinfoam is like a graph in one higher dimension, instead of just balls and sticks it has balls and sticks and flat pieces of plastic or tissue-paper stretched in between some adjacent sticks. So instead of a spiderweb it looks more like the foamy suds in the sink when you wash dishes. It is made of vertices, lines, and faces. It is the TRACK of one network changing into another. Its lines are where the network's knobs traveled. Its faces are where the network's sticks traveled. If they were "dragged thru time" leaving a streaky blur, the spinfoam would be the blur that they leave behind them. So the spinfoam sounds complicated but it really is about the simplest way you can depict a state of geometry changing into another. Where all the states are based on a finite quantity of geometric information.
 P: 149 thank you for the long post. Does lqg require higher dimensions and how well does it stand along string theory? Are string theory and lqg compatible at all? The fundamental difference is about background dependence right? Will experimental proof of lqg be death blow to string theory?
 Astronomy Sci Advisor PF Gold P: 23,208 Spin Networks and Spin Foams Dpa, there's no need to speculate about the future or to overdramatize. We can simply talk about what we have seen happen over the past 10 years. The String program has declined markedly in the past decade in terms of JOB prospects*, and in terms of CITATIONS to current string research. The number of times paper is cited by others is a rough measure of usefulness/value as seen by other string theorists. There are some tables here: http://physicsforums.com/showthread....60#post3813260. One of the tables tracks first-time faculty hires of HEP-theorists (particle theorists). On average around 2001 about HALF the theory jobs were going to string theorists. And by 2011 it was only about a TENTH or less. So it used to be if you wanted a high energy physics theory job it was a good thing to be a string theorist. Now it isn't so good, there are better areas to be in, like cosmology, astrophysics, lattice gauge theory, LHC phenomenology. It's interesting to watch this and try to figure out what could be causing it. But it's no big deal (unless you are a prospective PhD student choosing a specialty or otherwise directly involved.) Last year at the big annual string conference, Strings 2011, a number of the string theorists participating, including one of the organizers, commented that almost no one there was giving a paper that was actually about string theory. This got on video, in one of the recorded online presentations and was kind of amusing. We don't know the future. String has lost a some of its charisma (for various reasons) but who knows it might have a big comeback! We really do not know the future especially of research. And I don't know what a "death blow" would be. Nobody and nothing delivers a deathblow to a field like that---absent a comeback into fashion, the researchers who aren't smart or agile enough emigrate over into neighboring fields or who are diehard committed just have to keep on until they retire. *Usa and Canada universities, first-time faculty hires.
Astronomy
PF Gold
P: 23,208
 Quote by dpa Does lqg require higher dimensions...?
No, certainly not!

Nor do several other non-perturbative or no-prior-geometry approaches which you've probably heard of (or should have) like Triangulations, AsymptoticSafety, Horava-Lifgarbagez. They're all mainly suited to 4D.

You asked a question related to testing. I think the kind of observational testing that are practical at least in the near future are more likely to DISPROVE some variant or other of LQG and force the theory to change.

You shouldn't have such great expectations, or you will just be disappointed. There is a real ability to test, but it is more an ability to CONSTRAIN or NARROW DOWN the range of variation of theory. Nothing is going to immediately "kill off" or to disprove some approach in totality. It would be great just to narrow the quantum geometry field down some!

That applies to the other quantum geometry initiatives as well. If observation can be brought to bear on them, like on AsymSafe QG. But this is a Loop thread ("Spin Networks and Spin Foams") so we can focus on Loop. If you are interested in the options for testing I can get some links to papers on the subject.

Just passing one observational test does not automatically prove a theory is right. One may have to pass quite a few tests to gain acceptance.

I'm probably not saying anything you don't know already.
 Sci Advisor P: 5,437 We had a similar discussion some time ago and we decided compile a section for the Wikipedia article: http://en.wikipedia.org/wiki/Loop_qu...verview_of_LQG
 P: 247 Keep in mind that all those mathematical models are classical interpatations, and nothing else. Although they are very usefull to work with i envison. Where do we go from here (spin networks and spinfoams) ?.. It's a sort of metaphorical conceptualization at best !..
P: 149
 Keep in mind that all those mathematical models are classical interpatations, and nothing else. Although they are very usefull to work with i envison. Where do we go from here (spin networks and spinfoams) ?.. It's a sort of metaphorical conceptualization at best !..
sorry, could you clarify that?
P: 247
 Quote by dpa sorry, could you clarify that?
Hello dpa. Yes you are right i have to clarify..

In my humble ideas about the world we envision, mathematical construction are important to describe the world as constructed by our brains !.. that sounds weired but is nothing else but to saY that mathematical construction ar useful to concretize or handle information proces fabricated in and by the brain.. This is way off topic of course

But what i really mean is that String theory, LQC and LQG are theories that trie to describe geometry in spinfoams networks etc strings and so on in a classical way. By the way foams strings knots braids and so on are classical macroscopic products. But the lesson from Quantum mechanics is more open and non classical. There lies the open question for physics, there is no quantum world to describe
P: 407
 Quote by John86 But what i really mean is that String theory, LQC and LQG are theories that trie to describe geometry in spinfoams networks etc strings and so on in a classical way.
Not at all! These theories are quantum from the ground up, and the whole point of using mathematics is to get rid off misleading intuition from the human brain.
 P: 247 But Suprised But you could also interped this way of thought as saying mathematis is a generalizing tool to overcome misconceptionalizing. you can't separate te two of them
P: 149
i thought marcus pointed about non classical/quantum geometry when he said:
 That applies to the other quantum geometry initiatives as well. If observation can be brought to bear on them, like on AsymSafe QG.That applies to the other quantum geometry initiatives as well. If observation can be brought to bear on them, like on AsymSafe QG.
Astronomy
PF Gold
P: 23,208
 Quote by dpa i thought marcus pointed about non classical/quantum geometry...
Dpa thanks for emphasizing that point. There is a group of QG approaches where the central mathematical object that you study and deal with is a representation of the 4D geometry of the universe (or an evolving 3D slice of same.) The primary object you focus on is the whole geometry of space, not on some wiggling particle
And where there is no fixed prior geometry.

This characterizes classical GR too---so this bunch of non-string QG approaches carries along the most distinguishing features of the 1915 GR theory.

Whatever we say about "spin networks and spin foams" QG could often apply as well to several other non-string QG programs (Triangulations, AsymSafe, Horava...) They too aim at some type of quantum geometry, geometry interacting dynamcally with matter, no fixed prior, 4D as we experience it. It's good to keep this group of QG approaches in mind while we're talking about Loop in particular.

Loop is exceptionally fast-developing, so hard to keep up with. The person usually asked to provide an overview of Loop (in conference, or wide-audience lectures, or review articles) is Carlo Rovelli. So the simplest thing to do is just refer to whatever his latest definition of the theory is. He is also good at identifying and discussing the open problems still to be addressed.

Since Loop has "revolutions" on a fairly frequent---wild guess would be roughly 3-5 year---basis, I find it a real convenience to stick to recent research papers almost entirely, and to keep an eye out for summary/overview/outlook papers by Rovelli. (Also for the more specialized application to cosmology Abhay Ashteker is a leading senior authority.)

A nice coincidence for this thread is that Rovelli is giving a colloquium talk in just two weeks from today, at Perimeter institute! Colloquium talks are for wider audience, people not necessarily in your own specialty. So it should have some more accessible less technical parts (than say a seminar talk). And Perimeter normally posts online VIDEO of its colloquium talks.

So we are apt to have a definitive hourlong presentation in a couple of weeks of what Loop (or as you say "Spin Network and Spin Foam") quantum geometry is, and where it is going, what progress has been made towards its main goals, and what problems remain to be worked around or resolved.

When the talk has been given, on 4 April, after a day or so we can expect the video to be posted online at:
http://pirsa.org/12040059
If it's not a definitive overview of the Loop research program to date, I'll be surprised.

He goes on to give another talk (or two) at Princeton, Institute for Advanced Studies a couple of weeks later. Those talks will not be recorded and put online, I think. Perimeter is good that way.
P: 149
 If you are interested in the options for testing I can get some links to papers on the subject.
 (PhysOrg.com) -- As a quantum theory of gravity, loop quantum gravity could potentially solve one of the biggest problems in physics: reconciling general relativity and quantum mechanics. But like all tentative theories of quantum gravity, loop quantum gravity has never been experimentally tested. Now in a new study, scientists have found that, when black holes evaporate, the radiation they emit could potentially reveal “footprints” of loop quantum gravity, distinct from the usual Hawking radiation that black holes are expected to emit.
It would be kind of you to provide link to some papers.
 P: 149 it was the first one i know for sure.
 Sci Advisor P: 5,437 Regarding the classical picture: we wrote in the LQG Wikipedia article: A spin network is not a mechanical object which comprises spacetime. Instead, quantized spacetime is a superposition of an infinite number of spin networks. This is very well known in quantum mechanics: there is no reason why an atom should be in a "certain state". In principle, a single atom can be in an arbitrary complex quantum state, a phenomenon which has been described as a superposition of "an atom sitting here, an atom moving in a certain direction over there, an atom moving in this or that direction, ...". Therefore, classical spacetime is recovered by two averaging processes: First, there seems to be a regime where the superposition of spin networks is peaked around a single classical spacetime (i.e. where one single spin network dominates the superposition of infinitely many spin networks) Secondly, from this single spin network, one can reconstruct spacetime in the same sense as one can reconstruct the "water surface" from the individual atoms That means that we do not have a classical picture of spacetime but a full dynamical one. I am not an expert about the detailed picture in string theory but again it should be fully quantum mechanical. The fuzzball picture of a black hole in string theory is not a single string solution but a quantum mechanical superposition of all (infinitly many?) black hole quantum states with certain classical properties.
Astronomy
PF Gold
P: 23,208
Tom raises an interesting point. For continuity I will recap the discussion with Dpa of testing Loop (black hole radiation/cosmology) and also quote Tom's post. We have (at least) two worthwhile topics going in this thread!

Quote by dpa
 If you are interested in the options for testing I can get some links to papers on the subject.

... provide link to some papers.
 Quote by marcus I didn't see the PhysOrg article. Is it about this? http://physicsforums.com/showthread....32#post3815732 http://arxiv.org/abs/1109.4239 Probing Loop Quantum Gravity with Evaporating Black Holes Aurelien Barrau, Xiangyu Cao, Jacobo Diaz-Polo, Julien Grain, Thomas Cailleteau (Submitted on 20 Sep 2011) This letter aims at showing that the observation of evaporating black holes should allow distinguishing between the usual Hawking behavior and Loop Quantum Gravity (LQG) expectations. We present a full Monte-Carlo simulation of the evaporation in LQG and statistical tests that discriminate between competing models. We conclude that contrarily to what was commonly thought, the discreteness of the area in LQG leads to characteristic features that qualify evaporating black holes as objects that could reveal quantum gravity footprints. 5 pages, 3 figures. Published in Physical Review Letters 107, 251301 (2011) Barrau Cailleteau and Grain are well-known in this area. They have published a number of papers with ideas for testing Loop using astronomical observations. Mostly it is observations of ancient light showing features of big bounce or of inflation. This is the first paper by them with an idea for Loop "footprint" in black hole radiation. ... If astronomers look for the predicted radiation and do not find it that would at least disprove a variant of LQG, or constrain the theory. I don't know that the whole program is staked on this prediction though. It's new to me. I don't understand this black hole radiation spectrum stuff at all thoroughly. Maybe someone else can help. I'll find some other LQG testing links where I understand better what they are doing. The tests proposed have to do with further refined mapping of the cosmic microwave background. They go back several years, at least to 2008. Barrau and Grain have written extensively about that. Might not get around to this until tomorrow though.
 Quote by dpa it was the first one i know for sure.
 Quote by tom.stoer Regarding the classical picture: we wrote in the LQG Wikipedia article: A spin network is not a mechanical object which comprises spacetime. Instead, quantized spacetime is a superposition of an infinite number of spin networks. This is very well known in quantum mechanics: there is no reason why an atom should be in a "certain state". In principle, a single atom can be in an arbitrary complex quantum state, a phenomenon which has been described as a superposition of "an atom sitting here, an atom moving in a certain direction over there, an atom moving in this or that direction, ...". Therefore, classical spacetime is recovered by two averaging processes: First, there seems to be a regime where the superposition of spin networks is peaked around a single classical spacetime (i.e. where one single spin network dominates the superposition of infinitely many spin networks) Secondly, from this single spin network, one can reconstruct spacetime in the same sense as one can reconstruct the "water surface" from the individual atoms ...
Dpa, I won't forget to fetch some links to papers exploring Loop "footprints" to look for in the CMB and other testing options.

Meanwhile however, the "water surface" analogy that you bring up, Tom, is intriguing. It's definitely something to think about.

At first sight I don't altogether understand. A spin network is a quantum state of the geometry of a 3D slice of the whole universe, or else it could be the 3D boundary of some particular 4D region.

If you have a superposition of many spin networks, I think it would be a mistake to imagine them as being in "different places" spread all around like the water molecules defining the surface of a pool.
So they do not seem to me to be analogous to many atoms or molecules. Probably this was not what you were suggesting.

Each individual spin network represents a possible geometry of the world.

Each is intended to be the stage on which matter fields are defined.

I suppose what is analogous to the molecules would be the the *nodes* that make up one individual spin network. These symbolize possible volume measurements (imagined as chunks of volume) in various relations to each other---a web of angles, distances, contact areas relating the nodes.

I think of a spin network as telling the story of trying to sketch the geometry of the whole, but being limited to only a finite number of uncertain measurements. The spirit of quantum mechanics has always been about limitations of knowledge. We do not know what IS, we only know how it responds to measurement, and our ability to measure is finite.

However the analogy of the water surface being abstracted from the presence of countless separate molecules is in some ways very pertinent! It is a perfect analogy to use for thermodynamic quantities like temperature and pressure! We should keep it in mind here too.

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