# Spin Networks and Spin Foams

1. Mar 20, 2012

### dpa

Hi all,
:shy:
Could anyone explain in very simple language, for lower UGrad standard, what spin foams and spin networks are?

Thank You.

SINCERELY
DPA

2. Mar 20, 2012

### marcus

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.

Last edited: Mar 20, 2012
3. Mar 20, 2012

### dpa

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?

4. Mar 21, 2012

### marcus

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:
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.

Last edited: Mar 21, 2012
5. Mar 21, 2012

### marcus

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.

Last edited: Mar 21, 2012
6. Mar 21, 2012

### tom.stoer

7. Mar 21, 2012

### John86

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 !..

8. Mar 21, 2012

### dpa

sorry, could you clarify that?

9. Mar 21, 2012

### John86

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

Last edited: Mar 21, 2012
10. Mar 21, 2012

### suprised

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.

11. Mar 21, 2012

### John86

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

12. Mar 21, 2012

### dpa

i thought marcus pointed about non classical/quantum geometry when he said:

13. Mar 21, 2012

### marcus

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.

Last edited: Mar 21, 2012
14. Mar 21, 2012

### dpa

It would be kind of you to provide link to some papers.

15. Mar 21, 2012

### marcus

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.

The PhysOrg news item could also be about a paper by Hossenfelder Modesto and Prémont-Schwarz.If you give me the link to the news item I will poke around a bit. Here is the Hossenfelder paper
http://arxiv.org/abs/1202.0412
Emission spectra of self-dual black holes
Sabine Hossenfelder, Leonardo Modesto, Isabeau Prémont-Schwarz
(Submitted on 2 Feb 2012)
We calculate the particle spectra of evaporating self-dual black holes that are potential dark matter candidates. We first estimate the relevant mass and temperature range and find that the masses are below the Planck mass, and the temperature of the black holes is small compared to their mass. In this limit, we then derive the number-density of the primary emission particles, and, by studying the wave-equation of a scalar field in the background metric of the black hole, show that we can use the low energy approximation for the greybody factors. We finally arrive at the expression for the spectrum of secondary particle emission from a dark matter halo constituted of self-dual black holes.
15 pages, 6 figures

This paper is also based on Loop, which according to the authors allows for long-lived microscopic black holes. THEY have a distinctive radiation that is different from the others that were analyzed in the other paper.
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.

Last edited: Mar 21, 2012
16. Mar 22, 2012

### dpa

it was the first one i know for sure.

17. Mar 22, 2012

### 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

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.

18. Mar 22, 2012

### marcus

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!

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.

Last edited: Mar 22, 2012
19. Mar 23, 2012

### marcus

Thanks for being patient, I've been slow in responding. I had offered (then temporarily forgot) to get some papers having to do with QG phenomenology, that is studying ways to TEST quantum gravity theories.
A few posts back we mentioned some that had to do with observing radiation from black holes. Those are interesting but not typical. Most of the QG phenomenology papers I've seen (at least in the past 3 years or so) have been about looking for "footprint" features in the cosmic microwave background.

Here, this search turns up 49 papers that appeared 2008 or later:
http://inspirehep.net/search?ln=en&...Search&sf=&so=d&rm=citation&rg=100&sc=0&of=hb
I asked it to rank them by the number of citations to the paper. The papers most-cited by other research are listed first. Just to take an example, the top one on the list is by Grain and Barrau two people especially active in early universe phenomenology, testing QG cosmology models and such like stuff. Their paper on "Footprints of LQG" was cited by 45 others.

http://inspirehep.net/record/812301?ln=en
Cosmological footprints of loop quantum gravity.
J. Grain (APC, Paris & Paris, Inst. Astrophys.), A. Barrau (LPSC, Grenoble & IHES, Bures-sur-Yvette).
Feb 2009
7 pp. Phys.Rev.Lett. 102 (2009) 081301
e-Print: arXiv:0902.0145 [gr-qc]
Abstract: The primordial spectrum of cosmological tensor perturbations is considered as a possible probe of quantum gravity effects. Together with string theory, loop quantum gravity is one of the most promising frameworks to study quantum effects in the early universe. We show that the associated holonomy correction should modify the potential seen by gravitational waves during the inflationary amplification. The resulting power spectrum should exhibit a characteristic tilt. This opens a new window for cosmological tests of quantum gravity.

You can look down the list and click on other papers that the search finds and see what they are about. They vary in how relevant but they all tend to be about some observable feature of the early universe that offers a possibility for testing LQG cosmology.

Last edited: Mar 24, 2012
20. Apr 4, 2012

### marcus

On the general topic of "Spin Networks and Spin Foams"
there is a third type of combinatorial structure called SN-diagram or spin network diagram which looks roughly like a small number of spin networks connected to each other by dashed or dotted lines showing how to glue them together to recover a spin foam.

The SN-diagram was introduced by Marcin, Jerzy and Jacek of the Warsaw group. Polish first names are easier to remember and to say than are the last names---I don't intend undue familiarity.

You can think of an SN-diagram as a spin foam sliced and the slices laid out flat
together with dashed or dotted memories of how to put them back on top of one another so as to reconstruct the SF.

It appears to be an important mathematical innovation because SN-diagrams are finite combinatorial things (finite abstract sets of elements connected by relations) which a computer can generate and readily thereof calculate the AMPLITUDE and readily thereto find the conventional spin network that is its BOUNDARY.

Marcin Jerzy Jacek posted their paper in July 2011 and it was on our third quarter MIP (most important paper) poll and it only got one vote https://www.physicsforums.com/showthread.php?t=535170
Only one out of the 30 votes cast in that poll, by the 13 people who took part.

No matter. I think perhaps it was the most important Loop paper of that year or a close second to the February paper 1102.3660 Zakopane Lectures. That was about surveying, taking stock, teaching, and identifying the next problems to work on. The July paper was about something entirely new.

A new kind of combinatorial structure corresponding approximately one-one with the spin foams.

A graph is a finite abstract set S of elements connected by a subset of SxS called a "relation", a set of ordered pairs (x,y) of elements of S. A SN is a labeled graph. The Warsaw group label with operators, essentially with matrices, which is nice.

A SN represents a finite number of geometric measurements (which you can think of as before during after some process of geometry change). It is the role of a SF to be ENCLOSED by a SN and to serve as one instance of a process or history that effects the change specified by the SN. The SF is one possible history how the change observed in the SN could have occurred. Think of adding up the amplitudes of the histories.

So given a SN the possible SFs it can bound tell the transition amplitudes of the possible processes that produce it. In a way it is like writing down all the Feynman diagrams that lead from some initial to some final state of QED. The Warsaw people have shown how to enumerate all the "Feynman diagrams" on a flat piece of paper, and get the amplitude for each one.

There is no ORIGAMI---no 3D modeling. It is all plain flat diagrams. For better or for worse. Who knows how this will turn out? Whatever it is, whether helpful or not, it is non-trivial. It is the kind of thing a strong mathematician often ends up doing, can even be expected to do in some situations, regardless, which may be the reason we have them.

So google "puchta feynman arxiv" (since puchta's name is the shortest) and see.
Now we no longer have just SNs and SFs. We have also SN-diagrams, whose "points" so to speak are SNs and whose dotted/dashed connections are a kind of "higher" link. Graphs of graphs.
http://arxiv.org/abs/1107.5185
Categorical goings-on here it seems.

Wow! Rovelli's talk is online at PIRSA already, it was just over. I'll watch it now:
http://pirsa.org/12040059

Last edited: Apr 4, 2012