Symmetry

Symmetry in physics and mathematics is the property of a system that remains unchanged under some transformation — rotation, reflection, translation, or more abstract operations. Noether's theorem (1915) established the deepest fact about symmetry in physics: every continuous symmetry of a physical system corresponds to a conserved quantity. Rotational symmetry yields conservation of angular momentum; time-translation symmetry yields conservation of energy; spatial translation symmetry yields conservation of momentum. The laws of physics are not arbitrary — they are what remains when symmetry has constrained what can change.

Broken symmetry is as important as symmetry itself. The Standard Model acquires its structure from spontaneous symmetry breaking: a symmetric underlying theory whose ground state is not symmetric. The Higgs mechanism is the specific symmetry-breaking that gives particles their mass. Understanding which symmetries hold and which are broken — and why — is the central organizing question of quantum field theory.