Symmetry in Physical Laws: Feynman's Physics Explained
There is a deep, beautiful link between the symmetries of the universe and its conservation laws. Because the laws are the same everywhere (symmetry under moving in space), momentum is conserved. Because they do not change over time, energy is conserved. Because there is no special direction in space, angular momentum is conserved. For every symmetry of Nature, there is a matching conserved quantity.
The big idea
Every symmetry of Nature hides a conservation law.
Think about it
Conservation of energy comes from the laws not changing over time. What does that suggest about why energy is conserved?
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