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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.

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.

[[图一：一个小球位于中央山丘的山峰处（C）这是一种不稳定的平衡位置，具体表现为:一个很小的扰动会使它下降到稳定井左(L)或右(R)中的一个。即使是对称的,没有理由让球落在两侧,观察到的最终状态是不对称的]]

[[图一：一个小球位于中央山丘的山峰处（C）这是一种不稳定的平衡位置，具体表现为:一个很小的扰动会使它下降到稳定井左(L)或右(R)中的一个。即使山丘是对称的,没有理由让球落在两侧,观察到的最终状态是不对称的]]

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，对系统作用一个很小的力使其达到临界点产生波动，从而决定去向分岔的哪个分支。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。在斑图形成中对称性破缺起着重要作用。

在物理学中，'''<font color="#ff8000"> 对称性破缺</font>'''是一种现象，在这种现象中，对系统作用一个很小的力使其达到临界点产生波动，从而可以决定去向分岔的哪个方向。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。在'''<font color="#ff8000"> 斑图生成</font>'''中对称性破缺起着重要作用。

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.

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，诺贝尔奖得主P·W·安德森(P.W.Anderson)在《科学》(Science)杂志上发表了一篇名为《More is different》的论文，文中利用对称性破缺的概念来表明，即使还原论是正确的，但与之相反的建构主义(construcism)却是错误的。建构主义认为，在给出描述其组成部分的理论的情况下科学家可以轻易地预测复杂现象。

1972年，诺贝尔奖得主P·W·安德森(P.W.Anderson)在《科学》(Science)杂志上发表了一篇名为《More is different》的论文，文中利用对称性破缺的概念来表明，即使'''<font color="#ff8000"> 还原论</font>'''是正确的，但与之相反的'''<font color="#ff8000"> 建构主义 Construcism</font>''' 却是错误的。建构主义认为，在给出描述其组成部分的理论的情况下科学家可以轻易地预测复杂现象。

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 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 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.

在20世纪90年代,明显对称性破缺描述一个系统的运动方程在对称性破缺的情况下是不同的。在哈密顿力学或拉格朗日力学中，假若系统的哈密顿量或拉格朗日量本身存在一个或多个违反某种对称性的项目，导致系统的物理行为不具备这种对称性，则称此为明显对称性破缺。这术语特别适用于大致具有对称性、违反对称项目很小的系统。

在20世纪90年代,'''<font color="#ff8000">明显对称性破缺</font>'''描述一个系统的运动方程在对称性破缺的情况下是不同的。在哈密顿力学或拉格朗日力学中，假若系统的哈密顿量或拉格朗日量本身存在一个或多个违反某种对称性的现象，导致系统的物理行为不具备这种对称性，则称此为明显对称性破缺。这术语特别适用于大致具有对称性、违反对称项目很小的系统。

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.

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，但系统不是。这是因为系统的背景(时空)是非恒定的。这种对称破缺用序参量进行参数化。这类对称破缺的一个特殊情况是动力学对称性破缺。

在'''<font color="#ff8000">自发对称性破缺</font>'''中，系统的运动方程是不变的，但系统不是。这是因为系统的背景(时空)是非恒定的。这种对称破缺用序参量进行参数化。这类对称破缺的一个特殊情况是'''<font color="#ff8000">动力学对称性破缺</font>'''。

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，这个问题的平衡解是三轴椭球。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。

 

==See also==

==See also==