In physics, symmetry breaking is a phenomenon in which (infinitesimally) small fluctuations acting on a system 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 thought to play a major role in pattern formation.

In his 1972 Science paper titled "More is different"[1] Nobel laureate P.W. Anderson used the idea of symmetry breaking to show that even if reductionism is true, its converse, constructionism, which is the idea that scientists can easily predict complex phenomena given theories describing their components, is not.

Symmetry breaking can be distinguished into two types, explicit symmetry breaking and spontaneous symmetry breaking, characterized by whether the equations of motion fail to be invariant or the ground state fails to be invariant.

Explicit symmetry breaking

Main article: Explicit symmetry breaking

In explicit symmetry breaking, the equations of motion describing a system are variant under the broken symmetry. In Hamiltonian mechanics or Lagrangian Mechanics, this happens when there is at least one term in the Hamiltonian (or Lagrangian) that explicitly breaks the given symmetry.

Spontaneous symmetry breaking

Main article: Spontaneous symmetry breaking

In spontaneous symmetry breaking, the equations of motion of the system are invariant, but the system is not. This is because the background (spacetime) 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.

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 apparently 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. Jacobi[3] 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.

See also

Higgs mechanism

QCD vacuum

Goldstone boson

1964 PRL symmetry breaking papers

References

Anderson, P.W. (1972). "More is Different" (PDF). Science. 177 (4047): 393–396. Bibcode:1972Sci...177..393A. doi:10.1126/science.177.4047.393. PMID 17796623.

"Astronomical Glossary". www.angelfire.com.

Jacobi, C.G.J. (1834). "Über die figur des gleichgewichts". Annalen der Physik und Chemie. 109 (33): 229–238. Bibcode:1834AnP...109..229J. doi:10.1002/andp.18341090808.

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.

Quantum mechanics

Background

Introduction History

timeline Glossary Classical mechanics Old quantum theory

Fundamentals

Bra–ket notation Casimir effect Coherence Coherent control Complementarity Density matrix Energy level

degenerate levels excited state ground state QED vacuum QCD vacuum Vacuum state Zero-point energy Hamiltonian Heisenberg uncertainty principle Pauli exclusion principle Measurement Observable Operator Probability distribution Quantum Qubit Qutrit Scattering theory Spin Spontaneous parametric down-conversion Symmetry Symmetry breaking

Spontaneous symmetry breaking No-go theorem No-cloning theorem Von Neumann entropy Wave interference Wave function

collapse Universal wavefunction Wave–particle duality

Matter wave Wave propagation Virtual particle

Quantum

quantum coherence annealing decoherence entanglement fluctuation foam levitation noise nonlocality number realm state superposition system tunnelling Quantum vacuum state

Mathematics

Equations

Dirac Klein–Gordon Pauli Rydberg Schrödinger

Formulations

Heisenberg Interaction Matrix mechanics Path integral formulation Phase space Schrödinger

Other

Quantum

algebra calculus

differential stochastic geometry group Q-analog

List

Interpretations

Bayesian Consistent histories Cosmological Copenhagen de Broglie–Bohm Ensemble Hidden variables Many worlds Objective collapse Quantum logic Relational Stochastic Transactional

Experiments

Afshar Bell's inequality Cold Atom Laboratory Davisson–Germer Delayed-choice quantum eraser Double-slit Elitzur–Vaidman Franck–Hertz experiment Leggett–Garg inequality Mach-Zehnder inter. Popper Quantum eraser Quantum suicide and immortality Schrödinger's cat Stern–Gerlach Wheeler's delayed choice

Science

Quantum

biology chemistry chaos cognition complexity theory computing

Timeline cosmology dynamics economics finance foundations game theory information nanoscience metrology mind optics probability social science spacetime

Technologies

Quantum technology

links Matrix isolation Phase qubit Quantum dot

cellular automaton display laser single-photon source solar cell Quantum well

laser

Extensions

Dirac sea Fractional quantum mechanics Quantum electrodynamics

links Quantum geometry Quantum field theory

links Quantum gravity

links Quantum information science

links Quantum statistical mechanics Relativistic quantum mechanics De Broglie–Bohm theory Stochastic electrodynamics

Related

Quantum mechanics of time travel Textbooks

Hellenica World - Scientific Library

Retrieved from "http://en.wikipedia.org/"

All text is available under the terms of the GNU Free Documentation License