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You can prove newtons third law by conservation of momentum but you can also prove conservation of momentum by newtons third law. What comes first?

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- Thread starter jd12345
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You can prove newtons third law by conservation of momentum but you can also prove conservation of momentum by newtons third law. What comes first?

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AlephZero

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See http://en.wikipedia.org/wiki/Noether's_theorem

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According to Noether's theorem (see the link provided by AlephZero above) there is a reason. Noether's theorem applies to any physical theory which can be expressed in terms of a Lagrangian. If the Lagrangian has some differential symmetry (i.e. it does not change under some specific transformation) then there is a quantity which is conserved. This link between symmetry and conservation is so fundamental that the most basic theories are expressed in terms of their symmetries, and everything follows from those.

Energy is conserved because the Lagrangian does not change with small translations in time. Momentum is conserved because the Lagrangian does not change with small translations in space. Angular momentum is conserved because the Lagrangian does not change with small rotations in space. Charge is conserved because the Lagrangian does not change with small changes in potential. Etc.

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