Newton's Laws:
1. In an inertial reference frame, an object's momentum doesn't change unless acted upon by a force.
2. In an inertial reference frame, the force on an object equals the time derivative of its momentum.
3. In an inertial reference frame, the total momentum of every isolated system is conserved.
I have explicitly mentioned "inertial reference frame" in all three statements since the force on an object is only defined in an inertial reference frame. Also, the law of conservation of momentum is completely equivalent to the usual statement of Newton's third law.
My observations:
[1] follows directly from [2]. It contains no more information than [2] does, so we can scrap it.
[2] is a definition, but it is not complete. We have no way of knowing whether a frame is an inertial reference frame or not.
[3] makes a real statement, but it is incomplete. We still have no way of knowing if a frame is an inertial frame.
If we assume that the total momentum of every isolated system is conserved only in an inertial frame, then we can use [3] to determine if a frame is an inertial frame. We just check if the total momentum of every isolated system remains constant to determine whether our frame is an inertial reference frame.
But then, [3] gives us no information. It simply defines what an inertial reference frame is. [2] doesn't give us any information, it just defines what force is and it's incomplete without [3].
Newton's laws are just definitions and don't make any real claims about this world.
Newton was a fraud.
imagine newton instead of neumann in picrel
1. In an inertial reference frame, an object's momentum doesn't change unless acted upon by a force.
2. In an inertial reference frame, the force on an object equals the time derivative of its momentum.
3. In an inertial reference frame, the total momentum of every isolated system is conserved.
I have explicitly mentioned "inertial reference frame" in all three statements since the force on an object is only defined in an inertial reference frame. Also, the law of conservation of momentum is completely equivalent to the usual statement of Newton's third law.
My observations:
[1] follows directly from [2]. It contains no more information than [2] does, so we can scrap it.
[2] is a definition, but it is not complete. We have no way of knowing whether a frame is an inertial reference frame or not.
[3] makes a real statement, but it is incomplete. We still have no way of knowing if a frame is an inertial frame.
If we assume that the total momentum of every isolated system is conserved only in an inertial frame, then we can use [3] to determine if a frame is an inertial frame. We just check if the total momentum of every isolated system remains constant to determine whether our frame is an inertial reference frame.
But then, [3] gives us no information. It simply defines what an inertial reference frame is. [2] doesn't give us any information, it just defines what force is and it's incomplete without [3].
Newton's laws are just definitions and don't make any real claims about this world.
Newton was a fraud.
imagine newton instead of neumann in picrel