Symmetry and conservation

Under the conditions of Noether's theorem, a continuous symmetry of a physical action yields a conserved quantity.

In suitable variational systems, invariance under time translations is associated with energy conservation, spatial translations with momentum, and rotations with angular momentum. The connection turns a geometric property of the description into a constraint on motion.

For example: A freely rotating system with no external torque conserves angular momentum even as its parts change their arrangement.

Keep in mind: The theorem has mathematical assumptions and concerns symmetries of the action. An informal visual symmetry or every discrete symmetry does not automatically supply the same result.

Think about it

If a model treats one time or place differently from another, which conservation claim would you re-examine?

Connected ideas

Entropy and open systems · The ship of Theseus · The map is not the territory

Sources and further reading

• Emmy Noether: Invariant Variation Problems (English translation)

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