# Are Newton's Laws just definitions?

• I
• royaljelly

#### royaljelly

TL;DR Summary
Newton's first law follows from the second, the third (if modified) just defines what an inertial frame is, and the second just defines what the force on an object is.
I have read a bunch of articles online regarding my question, and none have helped.

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:

 follows directly from . It contains no more information than  does, so we can scrap it.

 is a definition, but it is not complete. We have no way of knowing whether a frame is an inertial reference frame or not.

 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  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,  gives us no information. It simply defines what an inertial reference frame is.  doesn't give us any information, it just defines what force is and it's incomplete without .

To my understanding, Newton's laws are just definitions and don't make any real claims about this world.

So, how am I wrong? Also, 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.

Last edited:
• davenn

To my understanding, Newton's laws are just definitions and don't make any real claims about this world.
They make very substantial claims. The wisdom before Newton was that objects would naturally slow down and that it took a force to maintain constant motion. This is why the hand of god was required to keep the planets moving.

Newton's laws overturned this, as he saw that on Earth one can hardly avoid resistive forces that cause the dissipation of kinetic energy. And, in the vacuum of space where there are no forces the planets may continue in their motion for a far greater time.

The second law then identified the relationship between force and acceleration; rather than force and speed.

These were fundamental insights about our universe that changed the course of science.

• russ_watters, Klystron, sysprog and 3 others
The wisdom before Newton was that objects would naturally slow down and that it took a force to maintain constant motion
They were talking about a different quantity when they said "force". Newton's first law is true, by definition.

[Post edited by a Mentor]

Last edited by a moderator:
• • davenn, weirdoguy, gmax137 and 1 other person
• • davenn, russ_watters and berkeman
No, I will not read that Wikipedia page. I do not care about what people before Newton thought, and that is completely irrelevant to my post.

I want someone to tell me if I have some flaw in my logic, or if I have misunderstood Newton's laws.

And by the way, people before Newton must have been talking about a different quantity when they said "force". If they were talking about the same quantity that Newton was talking about, they would have reached Newton's first law as a conclusion.

• • • davenn, protonsarecool, russ_watters and 4 others
Here is a flaw in your logic:
Newton's first law is true, by definition.
It was not defined before Newtons Law.

I'm not sure why you think that's irrelevant.

Here is a flaw in your logic:

It was not fact before Newtons Law.

Facts are things widely, nigh-universally understood to be true. And people did not believe it before Newton.

Im not sure why you think that's irrelevant. You talk about it as a definition, but there WAS no such definition before Newton.

2. In an inertial reference frame, the force on an object, ##\vec{F}##, equals ##\frac{d\vec{p}}{dt}##.

=> ##\frac{d\vec{p}}{dt} = \vec{0}## iff ##\vec{F} = \vec{0}## (in an inertial reference frame).

That's Newton's first law. It directly follows from the definition of force.

[Post edited by a Mentor]

Last edited by a moderator:
That is definitely not the same question as mine.

Thread is closed temporarily for Moderation and cleanup...

• Okay, thread cleanup is done for now, and I will reopen the thread tomorrow morning Pacific Daylight Time. I need a little time to calm down. Thanks • 