Can Conservation Laws be Derived from Symmetry and Newton's Laws?

AI Thread Summary
The discussion centers on whether conservation laws, specifically momentum and energy, can be derived from Newton's Laws through symmetry principles. It highlights that Newton himself would not have comprehended such a proof due to the undefined nature of energy during his time. A key point raised is the necessity of postulating a variational principle, as frictional systems can exhibit time invariance without conserving energy. The conversation emphasizes the complexity of linking these concepts directly to Newton's framework. Ultimately, the relationship between symmetry and conservation laws remains a nuanced topic in physics.
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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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xboy said:
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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