Talk:Spontaneous symmetry breaking

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[edit] Quantum Vacuum Collapse

QVC redirects to this page. A more explicit explanation of why would be nice.

[edit] vacuum states

This article uses the term vacuum state that is inconsistent with the definition at Vacuum state: a vacuum state is supposed to not contain any particles. Wouldn't it be more appropriate to speak of the energy minimum or the ground state? --141.154.205.61 21:47, 13 November 2006 (UTC)

[edit] langrangians

A Lagrangian isn't even necessary for the process of spontaneous symmetry breaking. Neither is a vacuum. What's necessary is simply a solution to symmetric dynamical equations which isn't invariant under the same symmetries. Phys 19:04, 20 Feb 2004 (UTC)

I have, as may be obvious, only an amateur interest in physics, so I'm sorry for my somewhat loose explanation. I put in the Lagrangian bit so that I could provide a more concrete example of spontaneous symmetry breaking, and also because this is how I learned about it. I have reworded the article ("one way of seeing" instead of "is accomplished by") in order to be more accurate. If you have further suggestions for restating it, I definitely welcome them. Thanks for the input. Jcobb 05:12, Feb 21, 2004 (UTC)

Is it supposed to be the lagrangian or the lagrangian density? The lagrangian is generally not lorentz invariant. JeffBobFrank 23:43, 19 Mar 2004 (UTC)

Technically you are correct that it is more accurately described as the Lagrangian density. However, as can be seen in the Lagrangian article itself, many different entities end up being called just the plain Lagrangian (for another example the n-form L dx^0 wedge dx^1 wedge ... wedge dx^n is also commonly described as the Lagrangian even though it is something slightly different). In the context of this article, I don't think it is necessary to make the distinction between Lagrangian and Lagrangian density. Jcobb 07:53, Mar 21, 2004 (UTC)

What's wrong with my example on the Earth's gravitational field? It's not a scalar field, but it's still an example, one everyone is familiar with. Phys 00:20, 15 Aug 2004 (UTC)

What's the example with Earth's field? Wilgamesh 21:14, 17 Sep 2004 (UTC)

Well, you know, you've been around WP long enough to catch on to the requirements of the articles. It may have had a point to make, but it certainly didn't make it clearly. Please don't add chat to articles when it really belongs to the talk page. Charles Matthews 08:33, 15 Aug 2004 (UTC)

Hi! I added another example I think is worthwhile because it's easily imaginable/testable, and yet still non-intuitive (like the ruler example). I may have made a mistake, but I think it's right, I remember seeing it in an undergraduate mechanics class with the pot cover, drill and marble, and it was fantastic! Jesse 12:58 2 Apr 2004 (Paris Time?)


the article says: In this state the Lagrangian has a U(1) symmetry. However, once it falls into a specific stable vacuum state (corresponding to a choice of θ) this symmetry will be lost or spontaneously broken.

but is this correct ? the lagrangian is U(1) symmetric independent of the state what is probably meant is the symmetry of the state itself and not of the lagrangian

so I would suggest: In this state the system has a U(1) symmetry. However, once it falls into a specific vacuum state (corresponding to a choice of θ) this symmetry will be lost or spontaneously broken.



[edit] Mexican hat potential

Shouldn't there be a little more explanation of how/why it's called that? At very least, a link to the Mexican hat wavelet? - JustinWick 16:46, 6 December 2005 (UTC)

It sounds clear enough to me. Penrose's picture looks more like a hat though. David R. Ingham 01:14, 26 August 2006 (UTC)

Well, it was not clear enough to me. Sure, it was clear why it was called "Mexican hat" (it does _sort_ of look like a Mexican hat), but what is not clear is the axes. Please label the axes, and/or which angle is Phi, which Theta, what coordinates _are_ you using, anyway? —Preceding unsigned comment added by 204.119.233.229 (talk) 19:04, 13 February 2008 (UTC)

[edit] ferromagnetic materials

It is not mentioned that the lowest energy configuration must also minimize the magnetic field energy. I am not sure that that is needed in such a brief mention of this example.

Perhaps because he started as a mathematician, Roger Penrose got that wrong in The Road to Reality. Soft iron can be easily magnetized but spontaneously loses most of its magnetization when taken out of the magnetic field. For an isolated ferromagnetic material, the stable configurations have the magnetization of the domains pointed around in small closed loops, so that the field energy is nowhere great. Small iron particles are "super-paramagnetic" with the whole particle having the same direction, but they are not good examples of topologically stable grain boundaries either. He should have used a different type of crystal with only short range interactions. David R. Ingham 01:14, 26 August 2006 (UTC)

[edit] Why does it matter?

Symmetry is a fairly intuitive concept. What has always puzzled me (as a non-physicist) is why symmetry breaking is considered so significant. Of course a ball rolling off the top of a symmetric mound is no longer in a position to roll in any direction. And of course a pencil, once balanced on its tip but now fallen over, is no longer in a position to fall in any direction. That's common sense. Why is that so important to physicists? And perhaps more to the point, what mathematical or theoretical leverage does symmetry breaking provide? RussAbbott (talk) 04:23, 12 June 2008 (UTC)

[edit] Isn't symmetry added also?

This may seem like a foolish question, so I apologize in advance.

When water vapor condenses to liquid or when (liquid) water freezes to ice, symmetry is broken. (Right?) There are fewer possibilities after the state transition than before. It's like the pencil falling down.

But symmetry is added also, isn't it? In the case of ice there is a new symmetry that characterizes how the atoms in the ice crystal relate to each other. They are always in a fixed relationship, no matter how the ice is moved around in space. So isn't that an additional symmetry that is added when the symmetry going from water to ice is lost?

Or is that better expressed as a new "conservation law?" The new conservation law states that the atoms in the ice crystal will retain the same mutual relationship no matter how the ice crystal itself moves. If symmetry is invariance under a transformation, isn't this "conservation law" an example of symmetry?

Or am I completely confused? If so, would you tell me why. RussAbbott (talk) 05:25, 12 June 2008 (UTC)

[edit] Article quality

Since I'm not a physicist, I hesitate to edit the actual article. But I'm surprised that this article is rated A. I came to this page because I wanted to understand symmetery in physics and symmetry breaking. This article didn't help. The overview and the first section are not useful to someone who doesn't already understand the concept. The examples are useful, but they are incomplete. So I looked further and found a couple of other interesting articles: The Future of Language: Symmetry or Broken Symmetry? and The Symmetry-Breaking Paradigm by Jim Coplien. These are where I came to understand that symmetry is invariance under a transformation. RussAbbott (talk) 05:42, 12 June 2008 (UTC)