Talk:Symmetry (physics)/Archive 1

Major rewrite
This is my version of the symmetry in physics article. I plan a major rewrite. I've started this by including some examples at the start. The third example needs a few more careful words of explanation. I plan to include a section on Symmetry groups, briefly describing some symmetry groups in physics with links shooting off to more technical articles. A discussion of spacetime and internal symmetries is essential here (there is an article on the former, but I don't think there is an article on the latter). A mention of continuous and discrete symmetries is needed too. I plan not to dispose of the earlier work in the article, but just to reorganise it so that the article reads a lot better; the skeleton of the article is there, but just needs a little 'fleshing out'. MP  (talk) 11:31, 28 December 2005 (UTC)


 * Fleshed out the article somewhat. Still need to:


 * Mention examples of local and global symmetries.


 * Mention the eightfold way, SU(3), SU(2) and U(1) (and electroweak gauge group).


 * Give symmetries of Maxwell's equations (or link to an existing article) - especially completion of Maxwell's equations to include magnetic monopoles (+ a discussion of pros and cons of this completion).


 * Include symmetry in relativity (principle of relativity).


 * Lagrangians.


 * Of course, other stuff needs to be mentioned too. MP  (talk) 14:52, 1 January 2006 (UTC)


 * The old material has not been eliminated; it contains a lengthy discussion of isometries, so I created a new article isometries in physics into which the old material has been accommodated. This new article still needs to be cleaned up considerably, but has the potential to become a very good article. MP  (talk) 10:32, 2 January 2006 (UTC)

Changes to article
Hi Patrick.

Regarding the deletion of the 'time translation' part you made, let it be said that that symmetry should definitely be in this article. It was in the wrong section, I'll give you that; when rewriting the article, I was copying and pasting a lot and must have placed the 2 time symmetries in the wrong places. Please don't just delete chunks because they are in the wrong place; put them in the right place. Thanks. MP  (talk) 08:29, 3 January 2006 (UTC)


 * Normally I would fix instead of delete, but it was not even clear whether you tried to explain a system constant with time, or a periodic system.--Patrick 11:03, 3 January 2006 (UTC)


 * ...a system constant with time, or a periodic system. is vague. I described time translation symmetry accurately by giving the precise definition. Specific examples may or may not exhibit time translation symmetry. In fact, 'for all real values a' is unrealistic, and will be changed accordingly. MP   (talk) 11:26, 3 January 2006 (UTC)


 * A formulation like "invariance under the transformation $$t \, \rightarrow t + a $$" if applied to a physical state is a difficult way of simply saying independence of time. It becomes useful if applied to physical laws, so that we can compare some variation with time in time interval [b,c] with that in time interval [d,e], both within a larger interval in which the property applies. For example, if I drop an object now or a minute later, the process of falling is the same except for the time-shift.--Patrick 13:29, 3 January 2006 (UTC)


 * Also, "invariance under the transformation $$t \, \rightarrow t + a $$" applied to a physical state is a useful formulation if we are talking about a fixed a: then we have a periodic system.--Patrick 13:34, 3 January 2006 (UTC)


 * Added stubby section tags to some sections. When I feel up to it, I may contribute a little to those. MP  (talk) 10:02, 12 April 2006 (UTC)

This article needs a lot more work
The nexus symmetry-invariance-conservation law captures a great deal of the beauty of theoretical physics. This article has a long way to go before it does justice to that beauty. It at least cites the work of Brading, Castellani, and Van Fraassen. I am not qualified to improve it.

I knew Emma Noether's grand-niece in grad school. She, to her everlasting credit, never boasted of her blood tie. (She did not hide it either: she once explained a 10 day absence in the middle of the term, saying that the German government was paying her expenses to attend the dedication of a new girl's high school named in honour of her great-aunt.) I will never forget the day when I mentioned this fact to a bartender in the campus pub I knew (he had done a Ph.D. in math). He quickly replied that Noether's theorem, connecting mathematical symmetry and physical conservation law, was the greatest result ever found by a woman mathematician. That was the first time I had ever heard of that theorem, one I did not encounter again until I discovered Wiki 25 years later.202.36.179.65 14:37, 18 April 2006 (UTC)

Huge omission: irreducible representations
One of the most important theorems regarding symmetry in physics is that the eigenfunctions of an operator with some symmetries (i.e. the operator commutes with the operations of the symmetry group) can be chosen as partner functions of irreducible representations of the group.

This is the basic reason for everything from Bloch's theorem (for periodic systems: discrete translational symmetry) to the fact that wavefunctions in a spherically-symmetric potential have their angular dependence given by spherical harmonics (corresponding to the irreducible representations of the rotation group). The simplest example is that, if you have a mirror symmetry, the eigenfunctions must be either even or odd.

See for example, Tinkham, Group Theory and Quantum Mechanics (or many other books of this sort).

(This also gives rise to something like Noether's theorem: the irreducible representation is conserved over time in a linear symmetric system. If you start at one time with a state that is a partner function of an irrep, then the state at all future times will be a partner function of that irrep.   For example, if you have a mirror symmetry, and start with an odd state, whether or not it is an eigenstate the solution at all future times will also be odd.)

—Steven G. Johnson (talk) 00:34, 19 March 2009 (UTC)