symmetry
An operation under which a system is unchanged — in physics, the source of every conservation law via Noether's theorem.
Definition
A symmetry of a physical system is a transformation under which the laws governing the system, and the system itself, are unchanged. The classic examples are geometric: a square has rotational symmetry by 90° and reflection symmetry across its diagonals. In physics the concept is more general — it covers not just shapes but operations on space, time, fields, and internal variables, and it includes both discrete symmetries (parity, time reversal) and continuous symmetries (translation, rotation, Lorentz boosts, gauge transformations).
Continuous symmetries are of particular importance because of Noether's theorem (1918), which says every continuous symmetry of a system's action implies a conserved quantity. Time-translation symmetry gives energy conservation; space-translation symmetry gives momentum conservation; rotational symmetry gives angular-momentum conservation. In quantum field theory the same theorem ties charge conservation to phase-rotation symmetry, and the full Standard Model of particle physics is built around the continuous symmetries of a product of unitary gauge groups.
Symmetry-breaking — where a symmetry of the underlying laws is not respected by a particular state — is an equally important idea. The Higgs mechanism, ferromagnetism, and the chiral structure of the weak interaction are all examples. Observing that a conservation law is violated is direct evidence that a symmetry is broken, and broken symmetries are how new physics is usually discovered.