Talk:Spin network

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This article may be too technical for a general audience. Please help improve this article by providing more context and better explanations of technical details to make it more accessible, without removing technical details.

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)

[edit] Exactly who is this article intended for?

'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)

[edit] 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)

[edit] 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).