**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 disorderly state into one of two definite states. Symmetry breaking is supposed to play a major role in pattern formation.

Symmetry breaking is distinguished into two types as:

- Explicit symmetry breaking where the laws describing a system are themselves not invariant under the symmetry in question.
- Spontaneous symmetry breaking where the laws
*are*invariant but the system is not because the background of the system, its vacuum, is non-invariant. Such a symmetry breaking is parametrized by an order parameter. A special case of this type of symmetry breaking is dynamical symmetry breaking.

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.

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. Jacobi and soon later Liouville, 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.

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### Famous quotes containing the words breaking and/or symmetry:

“All the aspects of this desert are beautiful, whether you behold it in fair weather or foul, or when the sun is just *breaking* out after a storm, and shining on its moist surface in the distance, it is so white, and pure, and level, and each slight inequality and track is so distinctly revealed; and when your eyes slide off this, they fall on the ocean.”

—Henry David Thoreau (1817–1862)

“What makes a regiment of soldiers a more noble object of view than the same mass of mob? Their arms, their dresses, their banners, and the art and artificial *symmetry* of their position and movements.”

—George Gordon Noel Byron (1788–1824)