Re: F=ma: law or theory?

["John S. Denker" <jsd@MONMOUTH.COM>]

At 01:43 PM 10/16/01 -0400, Robert Cohen wrote:
> OK, F=ma can be derived from something else.  Are you saying that the
> "something else" is a theory?  Can you be more clear on what might make
> F=ma a theory instead of a law?  I interpret "theory" to imply "explanatory"
> whereas "law" implies "empirical".

Let me totally and explicitly duck the vocabulary question;  see below for
discussion of the underlying physics issue.  I don't find it useful to
dissect such words in any great detail.  We have
  -- Einstein's theory
  -- Newton's laws
  -- Maxwell's equation
  -- Bianchi's identities
  -- Simpson's rule
  -- Shannon's formula
  -- Bell's theorem
  -- Zorn's lemma

I don't see any significant metaphysical distinction between Newton's "law"
of gravitation and Einstein's "theory" of gravitation.  Both give
mathematical formulas that purport to predict how Nature behaves.
Maxwell's "equations" are in the same category.

OTOH I recognize that in other contexts these words might have wildly
divergent connotations.

I refuse to worry about it.  Sometimes it's nice to be able to communicate
by choosing the exactly-right word.  Sometimes that's not feasible;
instead you may find that:
 -- communicating the exact nuance is not worth the trouble;  any meaning
in the ballpark is good enough, or
 -- it may take an entire sentence, or paragraph, or tome to pin down the
exact nuance.

===========================

The physics (if not the vocabulary) is reasonably clear
 -- We don't have an exact description of nature.
 -- Quantum mechanics is pretty good, give or take a few divergences,
paradoxes, and conundrums.  It's accuracy and relevance have been
established empirically.
 -- Classical mechanics is, under typical macroscopic conditions, a good
approximation to QM.
 -- F=ma is, under typical nonrelativistic conditions, a good approximation
to the above.
 -- None of the above is relevant for an introductory course.  I recommend
saying that F=ma is well established empirically.  This puts you on
perfectly reasonable metaphysical foundations.  Griding out a "derivation"
wouldn't improve the situation, metaphysically or pedagogically.


[There is an entire branch of science called "mathematical physics" which
starts from various axioms and hypotheses and sees where they lead, without
reference to empirical checks.  This is a radical departure from what most
list-members appear to be interested in, so I won't discuss it unless
somebody asks specifically.]