Symmetry, in physics, the concept that particles such as atoms and molecules remain unchanged in properties by symmetry "operations." From the earliest days of natural philosophy (Pythagoras in the 6th century BC), symmetry has furnished insight into the laws of physics and the nature of the cosmos. The two outstanding theoretical achievements of the 20th century, relativity and quantum theory, involve notions of symmetry in a fundamental way.

The application of symmetry to physics leads to the important conclusion that certain physical laws, particularly conservation laws, are unaffected by symmetry operations on the geometric coordinates of the particles concerned, including time, when it is considered as a fourth dimension; i.e., the laws remain valid at all places and times in the Universe. In particle physics, considerations of symmetry can be used to derive conservation laws and to determine which particle interactions can take place and which cannot (the latter are said to be forbidden).

Valid symmetry operations are those that can be performed without changing the appearance of an object. The number and type of such operations depends on the geometry of the object to which the operations are applied. The meaning and variety of symmetry operations may be illustrated by considering a square lying on a table. For the square, valid operations are (1) rotation about its centre through 90, 180, 270, or 360 degrees, (2) reflection through mirror planes perpendicular to the table and running either through any two opposite corners of the square or through the midpoints of any two opposing sides, and (3) reflection through a mirror plane in the plane of the table. There are therefore nine symmetry operations that yield a result indistinguishable from the original square. A circle would be said to have higher symme try because, for example, it could be rotated through an infinite number of angles (not just multiples of 90 degrees) to give an identical circle.

Excerpt from the Encyclopedia Britannica without permission.