I have read a bunch of articles online regarding my question but none have helped.
Newton's Laws:
In an inertial reference frame, an object's momentum doesn't change unless the object is acted upon by a force.
In an inertial reference frame, the force on an object equals the time derivative of its momentum.
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 defined only in an inertial reference frame. Also, the law of conservation of momentum is completely equivalent to the usual statement of Newton's third law. It's just much easier to work with the law of conservation of momentum.
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 only 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].
To my understanding, Newton's laws are just definitions and don't make any real claims about this world.
So, how am I wrong? Please note that I have no problems with defining mass through experiment. I have seen many posts where people claim that Newton's laws are "circular" because they don't define mass without using force, but this has nothing to do with that.
Unrelated sidenote:
I had posted this exact same question on physicsforums a while back, but I was accused of being a troll (and was banned) for signing up with my completely legitimate and verified cock.li email address. Also, a so-called mentor edited some of my replies after I had posted them. It was a very upsetting experience.
Best Answer
From a mathematical point of view, they are definitions: they relate mathematical abstractions. But from a physical point of view, they are not definitions: they capture real behavior of real physical objects through the metaphors that relate the mathematical abstractions to the phenomena.
Other definitions might yield perfectly good math, but physics is more constrained.