Lately I've been brushing up on some of my old Physics texts from college. Most recently, I've been rereading parts of "Classical Dynamics of Particles and Systems (5th ed.)" by Thornton and Marion.
In the second chapter, the authors discuss Newton's Laws of Motion, and point out about the Third Law that
We must hasten to add, however that the Third Law is not a general law of nature. The law does apply when the force exerted by one (point) object on another (point) object is directed along the line connecting the objects. Such forces are called central forces. (Pg 50)
I know that gravity and the electrical attraction between static charges are central forces, and so I know that these forces certainly obey Newton's Third Law. However, aside from briefly mentioning that velocity-dependent forces do not generally follow the Third Law, the authors do not elaborate. So my question is two-fold.
First, is Newton's Third Law not universally true? It was my understanding the the Third Law was a necessary consequence of the homogeneity of space, and conservation of momentum.
Second, what would be a familiar example of a non-relativistic force that does not follow the Third Law. Am I correct in understanding that drag would not necessarily follow the Third Law, because the magnitude of the force is velocity-dependent?
Best Answer
I have Marion-Thornton 4th ed. around here somewhere. It is an older book and presents some material differently than we are used to in more modern books (for instance they even use the old imaginary time method when discussing some things in special relativity, which I personally dislike). However I agree with DanielSank, different pedagogy does not equal "nonsense".
Newton's laws are presented slightly differently by different books. For instance, it can be argued Newton meant his second law to be $F=dp/dt$ (although he didn't write it in this modern notation), although many books present it as $F=ma$. Some people go even further and try to extract a modern meaning, as I've seen some people say Newton's third law is the conservation of momentum. This may be pedagogically useful, but not historically accurate. It is worth reminding that some debate over the exact statements translated to modern language is understandable. Even though Newton invented calculus, some concepts in mechanics still took long after Newton to come into their modern understanding, such as the concept of kinetic energy was put in its modern form much later.
Thus to answer this question requires agreeing on a statement for Newton's third law. I don't have Marion-Thornton handy, so using wikipedia
The force between two particles in electromagnetism can violate this. For a concrete example consider a positive charged particle A pulled along the x axis at a constant velocity in the positive direction, and another positive charged particle B pulled along the y axis at a constant velocity in the positive direction. If it is arranged such that when A is at (0,0), B is at (0,1), then we can calculate the fields and find:
If we include the person or device pulling these charges along as part of the system (so there are no external forces), then we should expect the momentum of the system to be conserved.
I constructed this scenario specially to also help break a bad habit of some descriptions of this phenomena. Because the charges are moving at a constant velocity, there is no radiation. We don't need radiation to provide a force back on the partices or something to solve this. Momentum can be stored in the fields themselves. (While not shown in this example, even static fields can have non-zero momentum.)