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Symmetry breaking
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This article needs additional citations for verification . Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.<br>Find sources: "Symmetry breaking" – news · newspapers · books · scholar · JSTOR (October 2021) (Learn how and when to remove this message)
Physical process transitioning a system from a symmetric state to a more ordered state
For other uses, see Symmetry breaking (disambiguation).
A ball is initially located at the top of the central hill (C). This position is an unstable equilibrium: a very small perturbation will cause it to fall to one of the two stable wells left (L) or right (R). Even if the hill is symmetric and there is no reason for the ball to fall on either side, the observed final state is not symmetric.<br>In physics, symmetry breaking is a phenomenon where a disordered but symmetric state collapses into an ordered, but less symmetric state.[1] This collapse is often one of many possible bifurcations that a particle can take as it approaches a lower energy state. Due to the many possibilities, an observer may assume the result of the collapse to be arbitrary. This phenomenon is fundamental to quantum field theory (QFT), and further, contemporary understandings of physics.[2] Specifically, it plays a central role in the Glashow–Weinberg–Salam model which forms part of the Standard Model modelling the electroweak sector.<br>A (black) particle is always driven to lowest energy. In the proposed
{\displaystyle \mathbb {Z} _{2}}
-Symmetric system, it has two possible (purple) states. When it spontaneously breaks symmetry, it collapses into one of the two states. This phenomenon is known as spontaneous symmetry breaking.A 3D representation of a particle in a symmetric system (a Higgs Mechanism) before assuming a lower energy stateIn an infinite system (Minkowski spacetime) symmetry breaking occurs, however in a finite system (that is, any real super-condensed system), the system is less predictable, but in many cases quantum tunneling occurs.[2][3] Symmetry breaking and tunneling relate through the collapse of a particle into non-symmetric state as it seeks a lower energy.[4]
Symmetry breaking can be distinguished into two types, explicit and spontaneous. They are characterized by whether the equations of motion fail to be invariant, or the ground state fails to be invariant.
Non-technical description<br>[edit]
This section describes spontaneous symmetry breaking. This is the idea that for a physical system, the lowest energy configuration (the vacuum state ) is not the most symmetric configuration of the system. Roughly speaking, there are three types of symmetry that can be broken: discrete, continuous and gauge, ordered in increasing technicality.
An example of a system with discrete symmetry is given by the figure with the red graph: consider a particle moving on this graph, subject to gravity. A similar graph could be given by the function
{\displaystyle f(x)=(x^{2}-a^{2})^{2}}
. This system is symmetric under reflection in the y-axis. There are three possible stationary states for the particle: the top of the hill at
{\displaystyle x=0}
, or the bottom, at
{\displaystyle x=\pm a}
. When the particle is at the top, the configuration respects the reflection symmetry: the particle stays in the same place when reflected. However, the lowest energy configurations are those at
{\displaystyle x=\pm a}
. When the particle is in either of these configurations, it is no longer fixed under reflection in the y-axis: reflection swaps the two vacuum states.
An example with continuous symmetry is given by a 3d analogue of the previous example, from rotating the graph around an axis through the top of the hill, or equivalently given by the graph
{\displaystyle f(x,y)=(x^{2}+y^{2}-a^{2})^{2}}
. This is essentially the graph of the Mexican hat potential. This has a continuous symmetry given by rotation about the axis through the top of the hill (as well as a discrete symmetry by reflection through any radial plane). Again, if the particle is at the top of the hill it is fixed under rotations, but it has higher gravitational energy at the top. At the bottom, it is no longer invariant under rotations but minimizes its gravitational potential energy. Furthermore rotations move the particle from one energy minimizing configuration to another. There is a novelty here not seen in the previous example: from any of the vacuum states it is possible to access any other vacuum state with only a small amount of energy, by moving around the trough at the bottom of the hill, whereas in the previous example, to...