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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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- Thread starter jd12345
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In summary, it can be argued that conservation of momentum is more basic than Newtons third law. This is because conservation of momentum applies in situations where the concept of force may be difficult to define, such as in electromagnetism. It is also considered fundamental because, according to Noether's theorem, it is linked to a symmetry in the underlying physical theory. Similar to conservation of energy, conservation of momentum is not something that can be explained or derived, but rather it is a fundamental aspect of the universe.

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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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Dale

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jd12345

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AlephZero

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jd12345 said:

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

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Dale

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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.jd12345 said:

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.

Newton's Third Law states that for every action, there is an equal and opposite reaction. This means that when one object exerts a force on another object, the second object will exert an equal and opposite force back on the first object.

Newton's Third Law is directly related to conservation of momentum. When two objects interact, the total momentum of the system remains constant. This means that the momentum lost by one object is equal to the momentum gained by the other object, as dictated by Newton's Third Law.

One example of Newton's Third Law is the recoil of a gun. When a bullet is fired, the force of the expanding gas propels the bullet forward, while an equal and opposite force acts on the gun, causing it to recoil backwards.

Newton's Third Law applies to many everyday situations, such as walking. When you take a step forward, you push against the ground with your foot, and the ground pushes back with an equal and opposite force, propelling you forward. This is also why you can feel the ground pushing against your feet when you jump.

Newton's Third Law is a fundamental law of physics and has been extensively tested and proven to be true. However, it may not apply in extreme situations, such as at the microscopic level or in scenarios involving high speeds or strong gravitational forces.

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