Symmetry (physics)

A symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is preserved or remains unchanged under some transformation.

A family of particular transformations may be continuous (such as rotation of a circle) or discrete (e.g., reflection of a bilaterally symmetric figure, or rotation of a regular polygon). Continuous and discrete transformations give rise to corresponding types of symmetries. Mathematically, symmetries are described by symmetry groups; continuous symmetries can be described by Lie groups while discrete symmetries are described by finite groups, lattice groups or other discrete groups. Symmetries are frequently amenable to mathematical formulations such as group representations.

Symmetries can be exploited to simplify many problems in physics and explain physical phenomena such as conservation laws, but symmetry principles also play a foundational role in all of the fundamental theories of modern physics.

One of the most important examples of symmetry in physics is that the speed of light has the same value in all frames of reference, which is described in special relativity by a group of transformations of the spacetime known as the Poincaré group. Other important examples include the invariance of the form of physical laws under arbitrary differentiable coordinate transformations in general relativity, and the gauge invariances of electromagnetism and the standard model of particle physics.

As a kind of invariance

Invariance is specified mathematically by transformations that leave some property (e.g. quantity) unchanged.