In physics, conservation of energy and conservation of momentum are both consequences of which of the following?

The story behind the answer

Noether’s Theorem states that every continuous symmetry of a physical system yields a conserved quantity. If the laws of physics are the same at all times (time-translation symmetry), energy is conserved; if they are the same at all places (space-translation symmetry), linear momentum is conserved; and if they are the same in all directions (rotational symmetry), angular momentum is conserved. That is why conservation of energy and momentum both follow from Noether’s Theorem.

Formulated by mathematician Emmy Noether in 1915–1918, the theorem underpins modern physics from classical mechanics to quantum field theory. Remember it with: “Symmetry saves” — symmetries save (conserve) quantities. Contrast: Carnot’s is about heat engine efficiency, Bell’s about quantum nonlocality, and Wick’s about operator ordering in quantum field theory.