Talk:Spin network

Recursion

Recursion, see Recursion. String-net directs here, yet the only place where string-nets are mentioned is in a link to string-nets. I am going to break the redirect and hope that someone with more in depth knowledge of string-nets can make a more specific article. Hillgiant 20:32, 15 March 2007 (UTC)

Exactly who is this article intended for?

Resolved

'A spin network, immersed into a manifold, can be used to define a functional on the space of connections on this manifold. One simply computes holonomies of the connection along every link of the graph, determines representation matrices corresponding to every link, multiplies all matrices and intertwiners together, and contracts indices in a prescribed way. A remarkable feature of the resulting functional is that it is invariant under local gauge transformations.'

Clear as mud and twice as thick. Is it any wonder that other scientists think that theoretical physicists are getting up to nothing of any relevance to the scientific community, let alone the real world outside academia?

This fragment assumes that the reader is familiar with terms "manifold", "functional", "connection", and "local gauge transformation". In other words, familiar with GR and QFT. It is possible in principle to describe spin networks without making any statements that require knowledge of GR and QFT, but it would not do justice to the subject (and would not make sense in a quantum gravity related article). --Itinerant1 11:30, 30 June 2007 (UTC)

" It is possible in principle to describe spin networks without making any statements that require knowledge of GR and QFT, but it would not do justice to the subject (and would not make sense in a quantum gravity related article). "

Rubbish. It would be perfectly easy to write a Wikipedia article that would do justice to the subject and didn't drag in quantum field theory or general relativity to any over-techical degree. See Scientific American, January 2004 if you don't believe me. Also, to imply that talking less technically doesn't make sense to those who understand quantum gravity, totally ignores the vast percentage of the readership who don't understand it but would like to. I don't see how a sentence composed almost totally of jargon does justice to any subject, to be honest. Deadlyvices 16:27, 30 June 2007 (UTC)

Agreed. This article, and others like it, should, among other things, start with an introduction that includes a statement as to what the everyday meaning of the subject-matter is, that is, what does it mean in simple terms to a person who is not a specialist in the field. Tmangray 07:50, 6 November 2007 (UTC)

Note: technical tag is removed and section marked as resolved. The article seems vastly improved from its state in late 2007. --C S (talk) 07:36, 27 April 2009 (UTC)

Suggestion for figure and definition

Suggestion: use Figure 2 in http://math.ucr.edu/home/baez/penrose/Penrose-AngularMomentum.pdf for an illustration. Also, base a definition of spin network on that article. —Preceding unsigned comment added by 66.245.58.135 (talk) 05:07, 3 February 2008 (UTC)

For example:

A spin network (as described in Penrose 1971) is a kind of diagram in which each line segment represents the world line of a "unit" (either an elementary particle or a compound system). Three line segments join at each vertex. A vertex may be interpreted as an event, in which either a single unit splits into two, or two units collide and join into a single unit. Time may be viewed as going in one direction, such as from the bottom to the top of the diagram, but the direction of time is irrelevant to calculations.

Each line segment is labeled with an integer called a spin number. A unit with spin number n is called an n-unit and has angular momentum n times half of ℏ(the reduced Planck constant). For bosons, such as photons and gluons, n is an even number. For fermions, such as electrons and quarks, n is odd.

Given any spin network, a non-negative integer can be calculated which is called the norm of the spin network. Norms can be used to calculate the probabilities of various spin values. A network whose norm is zero has zero probability of occurrence. The rules (defined by Penrose 1971) for calculating norms and probabilities are beyond the scope of this article. Their consequences include the following. If a vertex joins three units with spin numbers a, b, and c, then a spin network containing the vertex will have zero norm (zero probability), unless two requirements are satisfied. First, a+b+c must be greater than or equal to twice the maximum of a, b, and c. (This requirement is called the triangle inequality.) Second, a+b+c must be an even number. (This requirement is called fermion conservation.) For example, a=3, b=4, c=5 is possible since 3+4+5=12 is even and greater than 2*5=10. However, a=3, b=4, c=6 is impossible since 3+4+6=13 is odd. And, a=3, b=4, c=9 is impossible since 3+4+9=16 is less than 2*9=18. —Preceding unsigned comment added by 66.245.43.7 (talk) 09:44, 3 February 2008 (UTC)

I think this is nice as an elementary introduction. But I have a few comments. I think the spin network norm is defined only if the spin network is closed. Also, I'm not sure adding in the conditions on integer labels is beneficial since it doesn't really relate to anything else that is discussed, so it may appear to the uninitiated as an arbitrary set of rules. From the mathematical POV, this is the Clebsch-Gordan formula. Perhaps it could be phrased as relating to the permissible interactions between particles. A nice way to state the rule is that a,b,c must be permissible as integer side lengths of a Euclidean triangle. —Preceding unsigned comment added by Triathematician (talk • contribs) 20:39, 3 February 2008 (UTC)

Image

Would Scientific American or Lee Smolin let us use one of the picures from their article (The one in the 2006 special edition)? *Max* (talk) 03:30, 22 February 2008 (UTC).

Please note that the image has an error, in that one of the line segments does not have a number associated with it: the line that connects the 2 most-connected vertices at the upper left and center. For a supposedly fundamental science how can such sloppiness get this far unnoticed? 75.144.250.170 (talk) 19:13, 21 February 2009 (UTC)

Basic information needs to be added

This article really confuses me. I'm not a physicist but I don't like to think of myself as completely ignorant, either.

• Spin networks are described as the world lines of particles that come together in threes. But the illustration shows a network of triangles - so I assume the vertices in the text are actually the centers? of the triangles in the illustration.

• Two rules are given for the numbers in spin networks, but making the above assumption, the illustration still breaks both of them. For example 4, 2, and 1 on the second triangle up on the right edge.

• The article on loop quantum gravity says "In this context, spin networks arose as a generalization of Wilson loops necessary to deal with mutually intersecting loops. Mathematically, spin networks are related to group representation theory and can be used to construct knot invariants such as the Jones polynomial." This at least should be incorporated, and preferably... explained.

• Please explain in very simple terms: do the axes on this graph represent physical dimensions? Is, say, up at a later time? Does the left-right axis represent the movement of particles in one dimension? Or is the map only conceptual, and does the mention of knot invariants mean that somehow these networks can encode knot patterns in higher dimensions?

This article is a node between several unapproachable articles; yet the simple diagram gives the impression that it is a topic that can be understood by a novice without great sophistication. Wnt (talk) 03:19, 25 March 2009 (UTC)

What should "ladder symmetry" link to? If anything - is this yet another thing that cannot be understood without a proper background in GR and QFT? Lee Smolin says in his book "Three Roads to Quantum Gravity" that he envisions a (very optimistic) future where LQG is proven to be "true" (whatever that really means), string theory is shown to be something that "sits on top of it" (my words not his), a reformulation of QM and the (weak) holographic principle based on "information transfer" is created, and "the quantum theory of gravity will be taught to high-school students around the world" (emphasis mine) (p. 211) Based on this article I'm thinking, yeah right.. :) Jimw338 (talk) 18:45, 15 April 2017 (UTC)

How the definition relates to the figure?

I see a number of apparent inconsistencies between the figure and the definition given in the current page. I am not familiar with the subject so I cannot judge whether it is due to a confusing wording in the definition(s), a problem with the figure, or something else. Yet it would be nice if someone knowledgeable could address this. The problems include:

1. The "formal definition" states the graph is directed, the figure shows an undirected graph. (The "directed" word is in parenthesis but the meaning of the parenthesis is unclear).

2. The "Penrose's original definition" states that exactly three segments join at each vertex; if this is not true for a general definition (as the figure suggests) it should be stated explicitly.

3. Again, "Penrose's original definition" includes a "triangle inequality", violated even for those vertices in the figure for which it is defined (e.g. 4 > 2+1), and undefined for all the vertices joining more than three lines. Would be nice to explain this.

4. More generally, the "formal definition" may be hard to understand even to a person familiar with the basic ideas like Lie groups etc. Thus, if the conditions implied by that definition are less restrictive than those stated in the "Penrose's original definition", this should be commented upon. —Preceding unsigned comment added by 128.97.82.220 (talk) 02:11, 29 July 2009 (UTC)

Here we are 13 years later and as far as I can tell not one of these inconsistencies has been addressed. This article needs serious pruning until someone can replace it with a consistent account. — Cheers, Steelpillow (Talk) 18:23, 21 June 2022 (UTC)

(Another) confused reader

I thought I would add to the previous mentions that the diagram is pretty, but confusing, since it is inconsistent with the article definitions. I'm sure the diagram is simply a more advanced development, but the article needs to connect these, or the diagram detracts from the overall message. Oh, and for the record, mad props to Roger Penrose! 70.247.164.231 (talk) 03:26, 28 August 2010 (UTC)

I'll add myself to the list of readers who would like to see a clear connnection between the picture and the text defining spin networks. I'll aslo add another question:

• In Penrose's original definition, it is stated that spin networks are diagram with an integer attached to each edge. Then the section on the Formal definition states that general spin networks have irreducible representations of compact Lie Groups attached to each edge. What is the link between the two definitions? Is it that in Penrose's definition, the compact Lie group is U(1) so that its set of irreducible representations can be identified with the set of natural numbers? --sebastien 09:52, 2 January 2011 (UTC) —Preceding unsigned comment added by 78.86.9.216 (talk)

"Connection" linked to "Levi-Civita connection" - correct?

In the Formal Defintion section where it says "can be used to define a functional on the space of connections on this manifold", I linked "connection" to "Levi-Civita connection". Is this correct? 18:05, 15 April 2017 (UTC)