🚀 go-pugleaf

aankrom@nyx.cs.du.edu (Anthony Ankrom) writes:

> I have never read this group so I have no idea if it has been sloshed
>around before, butI would like to know, in a nutshell, just what
>Spontaneous SymmetryBreaking is. I read an article in a quantum chemistry
>journal that discussed SSB in the visual cortex in relationship to viual
>hallucinations. (I can provide a reference if it would be handy. I have
>studied verylitlle quantum mechanics, but feel free to use technical
>terms...) This would put an interesting perspective on my study of
>neurology.

SSB is a very simple idea, and not necessarily a quantum mechanical one.
The following examples are swiped from Physics Today (the pencil) and
Sidney Coleman (the ferromagnet):

Imagine that you have a pencil lying on a flat table.  The laws of
physics for this system are completely rotationally invariant; the
pencil behaves the same way no matter how you point it.  However, the
lowest-energy configuration (in which the pencil is lying on the table,
rather than, say, standing on its point) is not rotationally symmetric.
The pencil has to point in *some* direction.  This is a very simple
example of SSB; though the physics is rotationally symmetric, the ground
state is not.  The rotational symmetry is "spontaneously broken."

The same thing happens in, for instance, a ferromagnet.  The spins of
adjoining atoms are all aligned in the lowest-energy configuration.  So
even though the laws of physics are rotationally invariant, in the ground
state the ferromagnet has a net magnetization in some direction.  If
you lived inside the ferromagnet, it would be hard for you to tell that
the underlying symmetry existed unless you heated the magnet beyond its
Curie point.

The spontaneously broken symmetries spoken of by particle physicists are
usually not of spatial rotations but of rotations in some "internal" space
of components of the field value.  It's the same basic idea, though.
The laws of physics possess a symmetry that the possible ground states 
(which particle physicists call the vacua) do not.  With a sufficiently
enormous particle accelerator or a Big Bang,  one might be able to do the
equivalent of heating the ferromagnet, and see the underlying symmetry.
-- 
Matt McIrvin, posting nonsense again