#### bhobba

Mentor

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Hi All

I will state the issue succinctly. This is a I level thread so I will suppose people know Newtons Laws. Newtons first law follows from the second which is a definition of force. So it has no actual testable physical content. The third law is equivalent to conservation of momentum as is proven in most texts on Classical Mechanics. This is not just a definition, but a testable statement about nature. However we know of this dandy theorem called Noether's Theorem, and this conservation law is equivalent to symmetry of spatial translation. But this is an assumed property of an inertial frame which is usually defined as a frame that obeys Newton's first law - but we have seen its not a law - but a consequence of the definition of force. Looked at it this way it seems a bit of a mess - yet its importance to many branches of science and engineering is beyond question. Can we disentangle this? (Of course we can - but this is just to set the stage to discuss it).

Thanks

Bill

I will state the issue succinctly. This is a I level thread so I will suppose people know Newtons Laws. Newtons first law follows from the second which is a definition of force. So it has no actual testable physical content. The third law is equivalent to conservation of momentum as is proven in most texts on Classical Mechanics. This is not just a definition, but a testable statement about nature. However we know of this dandy theorem called Noether's Theorem, and this conservation law is equivalent to symmetry of spatial translation. But this is an assumed property of an inertial frame which is usually defined as a frame that obeys Newton's first law - but we have seen its not a law - but a consequence of the definition of force. Looked at it this way it seems a bit of a mess - yet its importance to many branches of science and engineering is beyond question. Can we disentangle this? (Of course we can - but this is just to set the stage to discuss it).

Thanks

Bill

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