conservation of momentum (was Re: Heat as an indestructible substance)

["Carl E. Mungan" <mungan@USNA.EDU>]

On Wednesday, May 7, 2000, Bob Sciamanda wrote:

>  I refer to our discovery and development of the conservation
>  of momentum.  It was first derived (and still is in textbooks)
>  from Newton's laws of motion, a crucial premise being the
>  third law.  With the discovery of the magnetic force between
>  moving charges, it was realized that there were forces that
>  did not obey Newton's third law.  Surprisingly, this did not
>  invalidate our conservation of momentum conclusion - we
>  merely raised it to the level of an a-priori hypothesis, assigned
>  the missing momentum to the electromagnetic field, and
>  produced a consistent and testable model of particle interactions.

This interesting paragraph prompts a variety of questions in my mind:

1a. Your example of magnetic force between moving charges is clear. I
suppose "radiation pressure" would be another. Is it safe to say in
general that "field forces" can violate Newton's third law (N3) but
"contact forces" (speaking classically) cannot?

1b. Is it possible to patch up conservation of momentum so that it is
*always* particle-like by quantizing the relevant fields, ie.
introduce photons, gravitons, etc?

2. In parentheses you added "(and still is in textbooks)." Does this
mean you think what textbooks are doing is a bit deceiving by virtue
of pretending to rigorously derive conservation of momentum, when
it's actually an inductive law?

3. I hope no one jumps on me for this, but I'll throw it out anyway.
When it comes to energy, one has the pseudowork-energy (W-E) theorem
which one can rigorously derive by spatially integrating N2. Then one
has the broader conservation of energy law which includes W-E as a
special case, but has been broadened beyond this by consideration of
fields, internal energy, heat, etc. Could one choose to say the same
about momentum: One can derive a "pseudoimpulse-momentum" theorem
that applies to classical masses interacting by contact forces, but
the broader conservation law also handles fields, waves, etc.

Any additional thoughts anyone would like to add about conservation
of momentum and how we discuss it in intro physics would be very
welcome. I confess to never having thought about this clearly enough
before. Carl
--
Carl E. Mungan, Asst. Prof. of Physics  410-293-6680 (O) -3729 (F)
      U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5026
mailto:mungan@usna.edu       http://usna.edu/Users/physics/mungan/