Noether's Theorem

Noether's theorem is a foundational result in theoretical physics and mathematics, proved by German mathematician Emmy Noether and published in 1918, stating that every continuous, differentiable symmetry of a physical system's action corresponds to a conserved quantity. Symmetry under translation in time corresponds to conservation of energy, symmetry under translation in space corresponds to conservation of momentum, and symmetry under rotation corresponds to conservation of angular momentum, giving a unified explanation for conservation laws that had previously been treated as separate empirical facts. The theorem was developed within the framework of Lagrangian and Hamiltonian mechanics and became a central tool of twentieth century theoretical physics, underlying the treatment of symmetry in quantum field theory and the Standard Model of particle physics. Noether arrived at the result while working on problems in general relativity at the invitation of David Hilbert and Felix Klein at Gottingen.