Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: operational F, m, and a



I recommended
++ a direct operational definition of force (in terms of fish scales)
++ an operational definition of acceleration (2nd derivative of position)
++ an operational definition of mass (additive if we conglomerate massive
objects)

Others pointed out that we also have
-- an operational definition of force in terms of mass * acceleration.

which is true. Yes, that is an operational definition.

Two responses:

1) OK, I wasn't 100% clear. I should have said that I was recommending
++ a direct AND INDEPENDENT operational definition of force (in terms of
fish scales)

where "independent" means independent of mass and acceleration.

2) Now the question remains, _why_ should we prefer the
direct-and-independent fish-scale definition.

Well, it turns out that there are lots of possible definitions.
-- We could define F in terms of ma.
-- We could define F in terms of d(momentum)/dt
-- We could define F in terms of G M m / r^2
-- We could define F in terms of fish scales.
-- et cetera
And there are lots of criteria for judging definitions:
-- We might want forces to uphold the 3rd law of motion.
-- We might want forces to rotate according to the vector rotation law,
and form resultants according to the vector addition law, and permit
multiplication by scalars, and do all the other good things vectors do.
-- et cetera.

I wrote F=ma first on this list, but not that does _not_ give it more
validity than the others. You may have learned F=ma chronologically before
the others when you were in school, but again that does not bestow any
extra validity on it.

And it turns out that you are forced to choose. When relativity comes into
play, you must choose either F=ma or F=dP/dt -- you can't have both. Nine
out of ten doctors surveyed recommend defining F in terms of momentum,
since that will guarantee that the 3rd law will be upheld. If one adopts
this definition, there is a deep correspondence between the 3rd law of
motion and conservation of momentum. This demotes F=ma to an
approximation, valid in the low-velocity limit.

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

Another way of saying almost the same thing:

If you define F in terms of ma, then F=ma becomes a tautology. That means
it becomes impossible in principle to even imagine an experiment to
determine how accurately F equals ma. It becomes impossible in principle
to design an experiment to check for small violations of the F=ma law.

If that's how you want it, go ahead -- but be careful. You could start a
new religion in which F=ma is the 11th commandment -- but you probably
don't want to. The other properties that we want force to have, such as
upholding the 3rd law and satisfying the vector axioms, are more important
IMHO.

I am not saying that choosing to define F in terms of ma is wrong. I'm
just saying that it is a choice, and it is not the only choice, and it is
not the choice I would recommend. My preference is for the independent
fish-scale definition, but I'm not prepared to prove this is superior on
physical or pedagogical grounds; I'll have to think about it some more. I
am sure that the fish-scale choice is a viable option, and at least as good
as the others.

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

Finally, let us examine the assertion that F is conceptually the same as
mass * acceleration "because" NIST and IUPAC define the unit of force in
terms of mass * acceleration.

This assertion is a non-starter. There is more to physics than dimensional
analysis. Are we to believe that the Lagrangian is conceptually identical
to the Gibbs free energy, because they both have units of Joules? I don't
think so.