# Just clearing doubts about the obviousness of newton's laws [duplicate]

I have edited this question because I thought that I had not conveyed my problem in the non edited one.

I want to ask that how 3rd law was so obvious to Newton.How Newton guessed that for an action there is always equal and opposite reaction.How can one so accurately perform an experiment in 17th century and state a law which is universal?How he isolated two bodies in the lab and said that force exerted by two bodies on each other is equal and opposite?Based on some finite experiments how he guessed that it is a universal law.

Well,I am nothing in front of newton to question his laws which are governing whole macroscopic phenomena but I think that I should be able to ask about these laws which are so obvious for Sir Issac Newton.

Coming to 2nd law how he guessed that force is directly proportional to time derivative of linear momentum?Well,one could say that he defined force in this manner but my motive is to ask here that if we expand this derivative then we come to know that if mass is not constant then force is directly proportional to rate of change of mass.See it is not very intuitive for anyone to say that if mass is changing with time there would be a force on an object.But one would say that he was a genius so his intuition was very strong but I think that this would not be the answer because according to one's intelligence and intuition he can not frame laws of physics.

By just observing these phenomenon by finite no. of experiments how Newton can universalise these laws for each and every entity in universe.

As per one comment I want to ask here that is 3rd law a consequence of law of conservation of linear momentum?If it is true then why 3rd law is a law?

• Violating the 3rd law means violating conservation of momentum, if that helps. – Ben51 Nov 27 '18 at 14:57
• I'm voting to close this question as off-topic because it's more a question of Philosophy than Physics. – Kyle Kanos Nov 27 '18 at 15:20
• @K_inverse Action-reaction pairs still hold perfectly well in electrodynamics. The misconception is in assuming that two charges form an action-reaction pair. In reality, charges do not directly exert forces on other charges; instead, each charge forms an action-reaction pair with the electromagnetic field, where the "reaction force" on the electromagnetic field is defined the same as usual: $F=dp_{field}/dt$. – probably_someone Nov 27 '18 at 15:36
• @Kyle Kanos : please, do not be too fast in judging the question as off-topics. Showing that the 3rd law can be related to a specific form of the potential energy is physics, I guess, not philosophy. – GiorgioP Nov 27 '18 at 17:44
• @GiorgioP With 3-body interactions, Newton's Third Law is not violated. Each body forms an action-reaction pair with the extended object formed by the other two bodies. – probably_someone Nov 27 '18 at 18:13

Newton's Third Law, as it is most commonly worded, reads:

Every action has an equal and opposite reaction.

Note that there is nothing in this statement about the action and reaction forces being "on a line between the two objects." This is because this addition is not in general true, both because there are explicit counterexamples (take any non-central force, like friction, for instance) and because there are situations where a "line between the two objects" makes no sense (for example, in the case where a charge interacts with a field).

In any case, if we want to understand why the properly-written form of Newton's Third Law always applies, we have to make sure that the terms here are properly defined.

When we say action and reaction in Newton's Third Law, we are referring to a pair of forces that a pair of interacting objects (sometimes called an "action-reaction pair") exert on each other. A force is defined as an interaction in which momentum is transferred over time from object A to object B (where the convention is to refer to "the force exerted by A on B"). The magnitude of each component of the force is precisely the rate of momentum transfer in that direction, which is why we write $$\vec{F}=\frac{d\vec{p}}{dt}$$. (Incidentally, this is equivalent to the general case of Newton's Second Law.)

So, if we were being precise about our terminology, Newton's Third Law would read:

If objects A and B form an action-reaction pair, then the force exerted by A on B has the same magnitude and the opposite direction as the force exerted by B on A.

Using the definition of force, this statement reads:

If objects A and B form an action-reaction pair, then the rate at which the momentum of A is changing due to interaction with B has the same magnitude and the opposite direction as the rate at which the momentum of B is changing due to interaction with A.

In plainer language:

When objects A and B interact, any momentum lost by A due to that interaction is gained by B, and vice versa.

So, once we have properly defined action and reaction, Newton's Third Law is essentially a statement that momentum doesn't appear or disappear in an interaction. Applied over any possible interaction, this is a restatement of conservation of momentum.

So the next question one might ask is, "Why is momentum conserved in the first place?" The answer to this relies on a very deep result by celebrated mathematical physicist Emmy Noether. Noether's theorem essentially states that every conserved quantity of a system arises from a fundamental symmetry of that system. In the case of momentum, that symmetry is translational symmetry. So momentum is conserved because the fundamental laws of physics do not change as you change position in the universe.

Of course, you could also ask, "Why don't the laws of physics change as you change position in the universe?" I don't know that there is a widely-accepted answer for this question as of yet, other than the fact that we have observed it to be the case, and that dropping this assumption generally leads to theories in which it is very difficult or impossible to calculate much of anything.

Many times, you will hear that "Newton's Third Law is violated" in certain situations (a common one that tends to pop up is the case of two moving electric charges). This is a misconception borne from the fact that oftentimes people attach additional assumptions to Newton's Third Law, which are not in general true. Most of the time, this additional assumption is a restriction on the types of objects that can form an action-reaction pair. For example, in the case of two moving charges, the people who say that Newton's Third Law is violated are implicitly assuming that the two charges are the action-reaction pair. This is not true; in reality, the charge and the electromagnetic field are the action-reaction pair. The only thing that Newton's Third Law guarantees is that for every object that is feeling a force, there exists some generalized abstract object that forms an action-reaction pair with it.

I think it is based on observation. When you push a wall it pushes back : you feel yourself pushed away from the wall. The same goes when climbing a stair; indeed when you push against the stair you are pushed up. If the third law was not here then you would only apply a force on the stair, not on yourself.

Well, it is not always true that "there is always an equal and opposite reaction for an action along the line joining the particles exerting forces on each other".

It is a statement about how forces behave, which does have a certain number of well known and not so well known exceptions.

Well known exceptions are:

1. inertial forces: if one is using the newtonian second law in a non inertial reference system, she/he has to introduce force-like terms in the equations of motion which originate from the $$bad$$ choice of the reference system and for those terms there is nothing like an actio-reaction pair;
2. interactions mediated by fields whose configurations vary with a finite speed. Electromagnetic interactions are an obvious prototype, but also hydrodynamic interactions in colloidal solutions may be a different example.

Not so well known examples are actually very widespread in condensed matter: all the forces described by non-pairwise interactions (in practice almost all the effective interactions in condensed matter) do not strictly obey Newton's third law. This point is quite easy to check.

If the potential energy is a sum of central pairwise interactions: $$U({\bf r_1, r_2, ..., r_N})= \sum_{i it is easy to show that the force on particle $$i$$ is a sum of terms, each corresponding to the force due to a second particle $$j$$ (for all $$j\neq i$$) and the the force due to $$j$$ on $$i$$ is a vector of equal modulus but opposite direction than the force on $$j$$ due to $$i$$ ($$\bf F_{ij} = - F_{ji}$$).

However the sum of pairwise interaction is exact only in few cases. If the interaction is described by many-body potential energy, like for example a sum of three-body interactions, it is not possible to say that each body interacts on another as if there were no other body around. In such a case, the force of particle 1 on particle 2 depends explicitly on where a third particle is. In a more formal way, one could write the potential energy of the system of N bodies as a sum of three-body interaction terms: $$U_3({\bf r_1, r_2, ..., r_N})= \sum_{i In correspondence with this potential energy, one could write the force on each atom $$i$$, as a sum, over all the pairs $$(j,k)$$ of two other atoms, of three-body forces $$\bf F_{ijk}$$.

So, while for the two-body interaction we have the usual form of the third law ($$\bf F_{ij} = - F_{ji}$$), with a three-body interaction, we would find a modified form: $$\bf F_{ijk} = -F_{jki} -F_{kij}$$.

It is clear that this relation, even if it looks unusual, plays the same role as the usual action-reaction: it ensures the conservation of the total momentum of a system of N particles.

In summary, the Newton third law is a statement on how a special set of forces work. It is very useful and convenient if one is working with really pairwise interactions (like the gravitational or the electrostatic forces between pointlike charges) or many other force laws which can be used to approximate the behavior of real systems. But one has to be prepared to the existence of dynamic systems where the original formulation by Newton has to be adapted to more complicate interactions.

• I agree that the statement "there is always an equal and opposite reaction for an action along the line joining the particles exerting forces on each other" is incorrect. But your counterexamples don't actually address this point. For counterexample 1, "force-like terms" are not the same thing as forces, and so Newton's Third Law says nothing about them. For counterexample 2, the "every action has an equal and opposite reaction" statement of Newton's Third Law actually applies perfectly well here, where the action-reaction pair is the charge and the field. – probably_someone Nov 27 '18 at 16:25
• Even in the case of non-pairwise interactions, the problem is not Newton's Third Law, but rather the fact that the proper action-reaction pair has not been identified. In particular, each particle forms an action-reaction pair with the non-rigid extended object consisting of the other $N-1$ particles. – probably_someone Nov 27 '18 at 16:40
• In counterexample 1, I used the term force-like to stress the origin iof inertial forces as not due to "physical interactions". However, inertial forces determine acceleration through $ma=F$ equation like any other force. The only differerence with other forces is in connection with the action-reaction dualism. Counterexample 2: the statement that the action-reaction pair is the charge and the field looks possible but questionable: while it is clear what a force on a particle, due to a field is, it is not obvious what a force of a charge on a field could be. – GiorgioP Nov 27 '18 at 17:27
• @probably_someone : As far as the last comment you made, your re-interpretation of the action-reaction pairs is possible but I would say that it goes very far from the Newton's statement of the principles of dynamics. My point is simply that Newton did not took into account the possibility of many-body forces. But nowadays we know they exist and they are also much more widespread than people would have thought. The observation that 3-body forces do not obey the third law in the usual form is trivial for anybody who has implemented a Molecular Dynamics simulation for that kind of interaction. – GiorgioP Nov 27 '18 at 17:35
• For counterexample 1, our disagreement largely seems to be a matter of definition. I am defining forces as arising from interactions, and you are not (so, under my definition, inertial "forces" are not really forces, while in your definition, they apparently are, otherwise we wouldn't be having this argument). There are two confusing things about this: one is that you yourself admit that inertial "forces" are not actually forces, calling them "force-like terms" in your answer. – probably_someone Nov 27 '18 at 17:47

It's because everyday objects, what Newton's laws are best at describing, interact mainly through electromagnetic interactions.

Let's take for example two pool balls which are colliding. The same idea applies elsewhere though. So, what happens when the balls hit each other? The electrons in each of the balls repel each other, according to Coulomb's law. Now, asking "which ball feels the force" is a little silly: they both do! So, they repel each other: Newton's third law!

Essentially, "contact forces" are just like electromagnetic forces. You know from experience that when you have two magnets with the same poles facing each other, they are both repelled.

As for the next "why," Feynman addresses why questions very well in this video: https://youtu.be/36GT2zI8lVA