Symmetry and newton's laws

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Is it possible to show directly from Newton's Laws that conservation of momentum and energy follow from principles of symmetry?
 

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AlephZero
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vanesch
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Is it possible to show directly from Newton's Laws that conservation of momentum and energy follow from principles of symmetry?

I think you also need to postulate that there is some variational principle. After all, frictional systems can be time invariant, and nevertheless, there is no conservation of energy.
 

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