We could answer: “because Newton’s third law says so”, and that is true. But there is a deeper answer, one that only modern physics has managed to formulate: momentum is conserved because space is homogeneous, that is, the laws of nature are the same here and two metres from here.

This connection between symmetry and conservation is the content of the so-called Noether theorem (1918): to every continuous symmetry there corresponds a conserved quantity.

  • Homogeneity of space \to momentum
  • Homogeneity of time \to energy
  • Isotropy of space \to angular momentum

The three great conservation laws of mechanics have, at their root, a geometric nature: they are not experimental accidents, but the reflection of the fact that space and time have no privileged points, instants, or directions.

Topics: Quantità di moto e urti Concepts: Conservazione della quantità di moto · Terza legge di Newton

Related exercises: Razzo nel vuoto · Terzo principio rotto · Terza legge a senso unico