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{{Use American English|date = March 2019}}

{{Use American English|date = March 2019}}

{{expert|Physics|date=May 2014}}

{{expert|Physics|reason=Lacking. It discusses symmetry breaking like a dictionary without saying why its so critically important in nearly every field of physics. Does not even discuss [[Noether's theorem]] here or in subpages. Originally set in May 2014|date=October 2020}}

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 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.

在物理学中，对称性破缺是一种现象，在这种现象中，作用于系统的小涨落通过一个临界点决定了系统的命运，通过决定分岔的哪一个分支。对于一个不知道波动(或“噪音”)的外部观察者来说，这个选择看起来是任意的。这个过程被称为对称性“破缺” ，因为这种跃迁通常使系统从一个对称但无序的状态进入一个或多个确定的状态。对称性破缺被认为在模式形成中起着重要作用。

在物理学中，对称性破缺是一种现象，在这种现象中，作用于系统的小涨落通过一个临界点决定了系统的命运，通过决定分岔的哪个分支。对于一个不知道波动(或“噪音”)的外部观察者来说，这个选择看起来是随意的。这个过程被称为对称性“破缺” ，因为这种跃迁通常使系统从一个对称但无序的状态进入一个或多个确定的状态。对称性破缺被认为在模式形成中起着重要作用。

In 1972, [[Nobel prize in physics|Nobel laureate]] [[Philip Warren Anderson|P.W. Anderson]] used the idea of symmetry breaking to show some of the drawbacks of the constructionist converse of [[reductionism]] in his paper titled "More is different" in [[Science (journal)|''Science'']].<ref>{{cite journal | last=Anderson | first=P.W. | title=More is Different | journal=Science | volume=177 | issue=4047| pages=393–396 | year=1972 | url=http://robotics.cs.tamu.edu/dshell/cs689/papers/anderson72more_is_different.pdf | doi=10.1126/science.177.4047.393 | pmid=17796623 | format=|bibcode = 1972Sci...177..393A }}</ref>

In his 1972 [[Science (journal)|''Science'']] paper titled "More is different"<ref>{{cite journal | last=Anderson | first=P.W. | title=More is Different | journal=Science | volume=177 | issue=4047| pages=393–396 | year=1972 | url=http://robotics.cs.tamu.edu/dshell/cs689/papers/anderson72more_is_different.pdf | doi=10.1126/science.177.4047.393 | pmid=17796623 | format=|bibcode = 1972Sci...177..393A }}</ref> [[Nobel prize in physics|Nobel laureate]] [[Philip Warren Anderson|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.

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

In his 1972 Science paper titled "More is different"  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.

1972年，诺贝尔经济学奖得主 p.w。在《科学》杂志上发表的题为《更多是不同的》的论文中，Anderson 用对称性破缺的思想来展示了还原论反向的建构主义的一些缺点。

在他1972年发表的题为“更多是不同的”的科学论文中，诺贝尔奖获得者 p.w。用对称性破缺的观点来表明，即使还原论是正确的，其反向的构造论---- 即认为科学家可以轻易地预测复杂现象的理论来描述它们的组成部分---- 也是不正确的。

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.

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.

In explicit symmetry breaking, the [[equations of motion]] describing a system are variant under the broken symmetry.

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.

In explicit symmetry breaking, the equations of motion describing a system are variant under the broken symmetry.

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.

In spontaneous symmetry breaking, the [[equations of motion]] of the system are invariant, but the system is not because the background ([[spacetime]]) of the system, its [[Vacuum state|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 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 state|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 spontaneous symmetry breaking, the equations of motion of the system are invariant, but the system is not 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.

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.

在自发对称性破缺中，系统的运动方程是不变的，但是这个系统不是因为系统的背景(时空) ，它的真空是非不变的。这样的对称性破缺是由一个序参数参数化的。这种类型的对称性破缺的一个特例是动力学对称性破缺。

在21自发对称性破缺，系统的运动方程是不变的，但是系统不是。这是因为这个系统的背景(时空) ，它的真空，是非不变的。这样的对称性破缺是通过一个序参数参数化的。这种类型的对称性破缺的一个特例是动力学对称性破缺。

对称性破缺可以涵盖以下任何一种情况:

对称性破缺可以涵盖以下任何一种情况:

:* The breaking of an exact symmetry of the underlying laws of physics by the random formation of some structure;  

:* The breaking of an exact symmetry of the underlying laws of physics by the apparently random formation of some structure;  

* The breaking of an exact symmetry of the underlying laws of physics by the random formation of some structure;  

* The breaking of an exact symmetry of the underlying laws of physics by the apparently random formation of some structure;  

* 某些结构的随机形成破坏了物理学基本定律的精确对称性;

* 某些结构的明显随机形成破坏了物理学基本定律的精确对称性;

:* A situation in physics in which a [[ground state|minimal energy state]] has less symmetry than the system itself;  

:* A situation in physics in which a [[ground state|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 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);  

* 系统的实际状态因明显对称的状态不稳定而不能反映动力学的基本对称性(以局部不对称为代价获得稳定性)的情况;

* 系统的实际状态由于明显对称的状态不稳定而不能反映动力学的基本对称性的情况(稳定性是以局部不对称为代价的) ;

:* Situations where the equations of a theory may have certain symmetries, though their solutions may not (the symmetries are "hidden").

:* 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 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.

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.

在物理学文献中讨论的首批对称性破缺案例之一与不可压缩流体在重力和流体静力平衡中的均匀旋转物体的形式有关。在1834年，Jacobi 和后来的 Liouville 讨论了这样一个事实: 当旋转物体的动能相对于引力势能超过一定的临界值时，三轴椭球是这个问题的平衡解。在这个分叉点上，麦克劳林椭球体的轴对称性被破坏。此外，在这个分叉点之上，对于常数角动量，使动能最小化的解是非轴对称的 Jacobi 椭球，而不是 Maclaurin 椭球。

在物理学文献中讨论的首批对称性破缺案例之一，与不可压缩流体在重力和流体静力平衡中的均匀旋转物体的形式有关。在1834年，Jacobi 和后来的 Liouville 讨论了这样一个事实: 当旋转物体的动能相对于引力势能超过一定的临界值时，三轴椭球是这个问题的平衡解。在这个分叉点上，麦克劳林椭球体的轴对称性被破坏。此外，在这个分叉点之上，对于常数角动量，使动能最小化的解是非轴对称的 Jacobi 椭球，而不是 Maclaurin 椭球。