On 05/09/2003 11:14 AM, Carl E. Mungan wrote:
>
> [the] 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?
I would like to duck the question. I like to
do physics in such a way that the question can't
come up. That is, I consider "the" third law
to be conservation of momentum. Newton's version
of this, expressed in terms of forces, is a
corollary to the more general law. The corollary
is convenient when discussing the forces on
discrete particles. When discussing field
momentum, I wouldn't say any laws are violated,
but some corollaries may be inapplicable or
inconvenient.
> 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?
1) Quantization has nothing to do with it AFAIK. The
classical (non-quantized) fields carry momentum just
fine.
2) Also, "*always*" is awfully strong. As far as we
know at present, it is possible to uphold conservation
of momentum by assigning momentum to the fields in a
sensible way. See Feynman volume II chapter 27.
3) The standard accounting is not provably unique.
The non-uniqueness has no observable consequences
(within the limits of current technology) ... which
is why we cannot sort it out (and why we need not
sort it out).
> ... are [textbooks] a bit deceiving by virtue
> of pretending to rigorously derive conservation of momentum, when
> it's actually an inductive law?
I this context and many others, I think it is a bit
of a swindle to pretend that physics is rigorously
derived. Physics is not like high-school geometry.
There is a tremendous tapestry of evidence tied
together by logic, all supporting the notion of
conservation of momentum. You could delete any
one of the supposedly "basic" facts and the tapestry
would still hold together, because there are so
many other facts and so many connections.
Because communication is largely serial, the
facts and connections must make their _initial_
appearance in some particular order. But things
should not be left in that state. We don't want
the austere minimalism of a Euclidean proof from
high-school geometry. Even in an introductory
class, it's worth making the point that there is
a tremendous accumulation of evidence supporting
conservation of momentum, supporting it from all
directions.
As just one example: if you believe in special
relativity, conservation of momentum is well and
truly wedded to conservation of energy.
> 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.
In a word, yes. Just leave off the "pseudo" from
"pseudoimpulse-momentum". Conservation of momentum is
conveniently applied when you have a given force acting
for a given time. Pseudowork ideas are conveniently
applied when you have a given force acting over a
given distance.
> Any additional thoughts anyone would like to add about conservation
> of momentum and how we discuss it in intro physics would be very
> welcome.
Feynman _The Character of Physical Law_ discusses many of
these issues, including
-- the tapestry of evidence and logic,
-- the way conservation laws are patched up when necessary,
-- and lots of other good stuff.
=========
Sometimes laws need to be patched up. Sometimes this
isn't what's needed. Medieval astronomers patched up
their description of planetary motions by adding more
and more epicycles. Then one fine day Kepler replaced
all the epicycles etc. by ellipses, which were simpler
and better.
So far, the notion of consevation of momentum, including
field momentum, works pretty well, and there's not much
reason to think it is possible or desirable to replace
it with anything else.