Force, Newtons second law

Question

In the book "An Introduction to Mechanics - Second edition" by Kleppner D., Kolenkow R, I came across a paragraph:

pg. 54 , sec 2.5.2(force)

It is worth emphasizing that force is not merely a matter of definition. For instance, if we observe that an air track rider of mass $m$ starts to accelerate at rate $\vec a$, it might be tempting to conclude that we have just observed a force $\vec F=m\vec a$. Tempting, but wrong. The reason is that forces always arise from real physical interactions between systems. Interactions are scientifically significant: accelerations are merely their consequence. Consequently, if we eliminate all interactions by isolating a body sufficiently from its surroundings —an inertial system— we expect it to move uniformly.

I can not understand why it is wrong. Please explain to me the reason author gave.

Answer 1

Yes, the author's statement is weirdly worded to say the least. Unless Newton's laws are incorrect, you can obviously conclude that if an object is accelerating, then the net force acting on it is mass times acceleration (assuming you're in the inertial frame).

However, what the author is trying to convey is the theoretical structure of our model of the world in Newtonian mechanics. That is that we ought to think of acceleration as the consequence of the forces acting on the particle rather than the other way around. In other words, you have to have a formalism where you can calculate forces acting on a particle independently of the acceleration of the particle (say, for example, as a function of the charges of the particles and the distances between them) and then you should verify if the acceleration produced due to this force according to the formula $F=ma$ matches with the experimentally observed acceleration of the particle. If you don't have an independent way of deducing what the force acting on a particle is independent of just observing the acceleration of the particle then you'd have learnt nothing about the world. Because you'd just see some acceleration and just define a force as $ma$ but you'd have no predictive power because you didn't really say anything about how this acceleration is arising.

Answer 2

The author is trying to convey the message that it was not the acceleration which made us observe a force, the force was already there. In other words, force is not the consequence of acceleration, rather it's the other way around, acceleration is the consequence of force, which implies forces are more fundamental.

Answer 3

Let us say you have two charged particles of charge $q_1$ and $q_2$. The force between them will be given by- $$\textbf {F}=\dfrac{q_1q_2}{4 \pi \epsilon_0 r^3}\textbf{r}$$ Now, what is the cause of the force? The Field. It was the field which developed in space due to one particle, and the other particle experienced that field. What you will observe will just be the acceleration of the objects. Not the force. Force was a result of the field produced. And that force led to acceleration, which you observed. I think this clears your doubt.

Answer 4

I now understand what the author is trying to say. He is saying that by mere observation of acceleration, we can not conclude that some force is acting on the body. It is because we can observe acceleration sometimes which is not due to any force but is merely an artifact of being in a non-inertial system. For example, while sitting in an accelerating car, we observe a tree accelerating in opposite direction without any force because we are in non inertial frame. To know whether an acceleration results from a real force, we need Newton's Third Law, which states that there must be an equal and opposite force in the system, if we can not find the partner force, the acceleration is not due to a force but only because of non-inertial system.