# Symmetry breaking

Symmetry breaking in physics describes a phenomenon where (infinitesimally) small fluctuations acting on a system which is crossing a critical point decide the system's fate, by determining which branch of a bifurcation is taken. To an outside observer unaware of the fluctuations (or "noise"), the choice will appear arbitrary. This process is called symmetry "breaking", because such transitions usually bring the system from a symmetric but disorderly state into one or more definite states. Symmetry breaking is supposed to play a major role in pattern formation.

Symmetry breaking is distinguished into two types as:

In 1972, Nobel laureate P.W. Anderson used the idea of symmetry breaking to show some of the drawbacks of Reductionism in his paper titled "More is different" in Science.1

## Examples

Symmetry breaking can cover any of the following scenarios:2

• The breaking of an exact symmetry of the underlying laws of physics by the random formation of some structure;
• A situation in physics in which a minimal energy state has less symmetry than the system itself;
• Situations where the actual state of the system does not reflect the underlying symmetries of the dynamics because the manifestly symmetric state is unstable (stability is gained at the cost of local asymmetry);
• Situations where the equations of a theory may have certain symmetries, though their solutions may not (the symmetries are "hidden").

One of the first cases of broken symmetry discussed in the physics literature is related to the form taken by a uniformly rotating body of incompressible fluid in gravitational and hydrostatic equilibrium. Jacobi3 and soon later Liouville,4 in 1834, discussed the fact that a tri-axial ellipsoid was an equilibrium solution for this problem when the kinetic energy compared to the gravitational energy of the rotating body exceeded a certain critical value. The axial symmetry presented by the McLaurin spheroids is broken at this bifurcation point. Furthermore, above this bifurcation point, and for constant angular momentum, the solutions that minimize the kinetic energy are the non-axially symmetric Jacobi ellipsoids instead of the Maclaurin spheroids.

## References

1. ^ Anderson, P.W. (1972). "More is Different". Science 177 (4047): 393–396. Bibcode:1972Sci...177..393A. doi:10.1126/science.177.4047.393. PMID 17796623.
2. ^ http://www.angelfire.com/stars5/astroinfo/gloss/s.html
3. ^ Jacobi, C.G.J. (1834). "Über die figur des gleichgewichts". Annalen der Physik und Chemie (33): 229–238.
4. ^ Liouville, J. (1834). "Sur la figure d'une masse fluide homogène, en équilibre et douée d'un mouvement de rotation". Journal de l'École Polytechnique (14): 289–296.

 HPTS - Area Progetti - Edu-Soft - JavaEdu - N.Saperi - Ass.Scuola.. - TS BCTV - TS VideoRes - TSODP - TRTWE TSE-Wiki - Blog Lavoro - InterAzioni- NormaScuola - Editoriali - Job Search - DownFree !
 TerritorioScuola. Some rights reserved. Informazioni d'uso ☞