Newtons third law and conservation of momentum

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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Whats more basic - Newtons third law or conservation of momentum
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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Conservation of momentum is more basic. It applies in situations where the notion of force can be difficult to even define. For example, in electromagnetism the momentum of the EM field is well-defined, but the idea of a force acting on the EM field is a little strange.
 
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So just like conservation of energy - conservation of momentum is fundamental - it just happens right? - there is no reason why momentum is conserved right?
 
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jd12345 said:
So just like conservation of energy - conservation of momentum is fundamental - it just happens right? - there is no reason why momentum is conserved right?
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.
 

FAQ: Newtons third law and conservation of momentum

1. What is Newton's Third Law?

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.

2. How does Newton's Third Law relate to conservation of momentum?

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.

3. Can you give an example of Newton's Third Law in action?

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.

4. How does Newton's Third Law apply to everyday life?

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.

5. Is Newton's Third Law always true?

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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