Spontaneous symmetric breaking is a spontaneous process of symmetry breaking, whereby a physical system in a symmetric state ends up in an asymmetric state.

By definition, spontaneous symmetry breaking requires the existence of physical laws (e.g. quantum mechanics) which are invariant under a symmetry transformation, so that any pair of outcomes differing only by that transformation have the same probability distribution. For example, if the measurement of any two observables at two different locations have the same probability distribution, the observable has translational symmetry.

Spontaneous symmetry breaking occurs when this relation breaks down, while the underlying physical laws remain symmetrical.

In particle physics

Note

This is an active area of research, and the details are still being worked on. Nevertheless, this is the best explanation we have for the existence of mass.

In particle physics, the force carrier particles are normally specified by field equations with gauge symmetry. Their equations predict that certain measurements will be the same at any point in the field. For instance, field equations might predict that the mass of two quarks is constant. Solving the equations to find the mass of each quark might give two solutions - one in which quark A is heavier than quark B, and other in which quark B is heavier than quark A by the same amount. The symmetry of the equations is not reflected by the individual solutions, but it is reflected by the range of solutions.

Actual measurement reflects only one solution, representing a breakdown in the symmetry of the underlying theory. "Hidden" is a better term than "broken", because the symmetry is always there in these equations. The phenomenon is called spontaneous symmetry breaking because nothing we know of breaks the symmetry in the equations.

Chiral Symmetry

Higgs Mechanism

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