What does Noether's theorem express?

Noether's theorem establishes a profound and fundamental connection between conservation laws and symmetries in physics. Specifically, it states that for every continuous symmetry of a physical system, there is a corresponding conservation law. For example, if a system exhibits symmetry in time (the laws of physics are the same at all times), then energy is conserved. Similarly, if a system is symmetric in space (the laws of physics are the same at every point in space), then momentum is conserved. This relationship is crucial because it provides a unifying framework for understanding various conservation laws that apply across different physical systems, making it a cornerstone of theoretical physics.