Re: [Phys-L] force-pair question

[John Denker <jsd@av8n.com>]

On 01/07/2015 07:58 AM, Moses Fayngold wrote:

[snip]

The main points are correct, but perhaps it might be 
worth fine-tuning a couple of side-issues:

> the net momentum of an isolated pair must conserve.

1) There is a difference between constancy and conservation.
It would be better to say
 -- The momentum is always conserved no matter what.
 -- As a corollary, the momentum of an isolated pair
  is constant.
  https://www.av8n.com/physics/conservation-continuity.htm

2) We agree that expressing the third law in terms
 of conservation of momentum is safer than expressing
 it in terms of force-pairs.

3) As several people have pointed out, if you focus
 on pairs of pointlike /objects/ the forces are not
 paired, not even close.  There can be momentum in the
 fields, which are not usually considered pointlike
 particles (although the distinction itself might be
 a mistake).  Consider the spinning disk apparatus in
 Feynman volume II figure 17-5.
   https://www.av8n.com/physics/force-intro.htm#sec-field-momentum

4) On the other hand, we do not need to restrict the
 law to the special case of N=2 objects.  If we focus
 attention on conservation of momentum -- or just redefine
 force to be /any/ transfer of momentum -- then except
 possibly for a set of measure zero, the relevant boundary
 is always automatically the boundary between two regions.
 At any point, the momentum that exits one region enters
 another.  We can always arrange the bookkeeping so that
 every force is paired with another, at the very same
 point.

 They say an expert should be able to see things in more
 than one way, but in this case I find the situation
 very much easier to see in terms of momentum transfer.
 If somebody asks a question about force-pairs, I
 immediately reformulate it in terms of momentum-transfers.

 Many of the FCI and FMCE questions become utterly trivial
 if translated in this way.  For example, is the momentum
 lost by the large truck the same as the momentum gained by
 the small car?  Duh...........

 Operationally, it would be next to impossible to measure
 the forces involved in a car/truck collision.  I have a
 hard time visualizing that, and a hard time caring.  See
 also next message.


> The answer to this would be: "This is a corollary of
> translational invariance of the Minkowsky space" (The Emmy Noether
> theorem).

At that point the student asks, "Why is space translationally
invariant?"  That leads to some deep questions, including some
unanswerable questions.  Actually the better approach is to
assume there is some small non-invariance.  Then we can try
to get experimental bounds on the size of the effect, and
perhaps come up with explanations (inflation?) of how it
came to be so small.
 
That's roughly the response I would have given to Hewitt's
CONCEPT CHECK.  I rather doubt this was what he was expecting
when asked the question.  At this point we are at least
five jumps removed from the original CONCEPT CHECK:
  *) For any given question, start by considering the
   possibility that it is ill-posed.  Try to determine
   what question /should have been asked/.
  *) Force --> momentum transfer
  *) Paired forces --> momentum conservation
  *) Conservation --> symmetry
  *) Why --> how do we know
  *) et cetera

It would be nifty if the book explained how to do any of
those things, but it doesn't.

BTW -- assuming a LOT of groundwork has been laid -- it 
is always amusing to see the look on kids' faces when they 
hear about symmetry <--> conservation for the first time.
Whaaaaaat?!???!!!!