What is the hidden link between energy and the fact that the laws do not change tomorrow?

An experience can be moved, rotated, or restarted later. If its physical description retains certain symmetries, this stability has much deeper consequences than a simple like result. In 1918, Emmy Noether established a mathematical link between continuous transformations and quantities conserved during the movement.

In the context where his theorem applies, time translational invariance is related to energy conservation. Translations and rotations in space are associated with other conservations, those of the amount of motion and the kinetic moment. Rules that could be learned separately are thus revealed as relatives.

The surprise is not that a phenomenon observed once repeats itself out of habit. It is a demonstration that makes it possible to move from the structure of the laws to what must remain constant. The theorem provides physicists with a tool to examine their models, with precise assumptions: it does not promise that any apparent resemblance hides a conservation.