Re: [Phys-L] force-pair question

[Moses Fayngold <moshfarlan@yahoo.com>]

On 06/01/2015, at 4:40 PM, John Denker wrote:

> A while back I came across the following question:
>   "Why do forces always occur in pairs?"


  I think that asking this is an attempt to get the right answer to a wrong, or at least ambiguous, question. In my view, the forces do not always come in pairs. They do so only if we consider a pair of mutually interacting objects. 
  If in a certain problem we are dealing with an object singled out from the given environment, and that object can be considered as a point, we have a single force on it. And even that force is single only with an adjective "net" before it. For N objects we have N such forces. They come in pairs only in a special case N=2. If, in addition, we neglect the forces from the environment, then the remaining two forces satisfy Newton's third law. Usually we mean this very special case when we say that the forces "always" come in pairs. If we ask "Why?" for this case, the answer will be "Because the net momentum of an isolated pair must conserve." In other words, the paired forces are the corollary of conservation law for momentum. So if we want to find out how the properties of one concept relate to another concept considered as given, Physics can, in principle, answer the "Why" questions.   We can keep on going down this venue and ask "Why should momentum conserve?" The answer to this would be: "This is a corollary of translational invariance of the Minkowsky space" (The Emmy Noether theorem). Of course we will have to stop at some point and say: "Here Physics does not answer the question "Why?". Take it as given by evidence." 
  BTW, getting back to the original question in conventional understanding, it is not always trivial to isolate a pair of objects so that the respective pair of forces would satisfy Newton's third law. If we have two electrical charges - one stationary and the other passing by, the forces on them do not satisfy Newton's third law, so their net momentum does not conserve. Conservation is satisfied only when we also take into account the momentum of EM field  of the system. 
Moses Fayngold,NJIT
  
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