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Re: [Phys-l] internal/external conservative/nonconservative forces!?!?



On 12/15/2010 06:54 AM, Philip Keller wrote:
I don't see why this is an issue. "Energy" is an abstract quantity,
not a thing-in-the-world. You can say it "resides" wherever you
like.

There are good physics reasons why it matters.

Yes, energy is somewhat abstract, but not so abstract that
it becomes arbitrary or magical. A magical object can just
disappear without regard to the laws of physics, but energy
cannot.

In particular, the most important thing we know about energy
is that it obeys a strict /local/ conservation law. You cannot
even begin to formulate a /local/ conservation law unless you
know how to localize the energy.

Can you design an experiment that favors one view over another?

That's the great mystery and puzzle. Such an experiment is
possible in principle (Keplerian orbits) but is prohibitively
difficult in practice. Feynman has a long discussion of this.

As for the earlier question: I think I know why it is important to
distinguish between conservative and non-conservative forces, and
think I can design an experiment to see if a force is conservative.

According to long-established convention, a conservative force
field is the gradient of some potential, whereas a non-conservative
force field is not. Distinguishing the two is straightforward:
just carry a test particle around a loop.

A lot of students -- even quite bright ones -- are mystified or
even incredulous when you tell them that not every force field
is the gradient of some potential. I cooked up some diagrams
to help visualize how this works:
http://www.av8n.com/physics/non-grady.htm

The term "conservative force" is just begging to be misunderstood.
It conflicts with the definition of "conservation". For example,
the changing magnetic field (e.g. in a betatron) produces a
force field that is not the gradient of any potential ... but
still it (like everything else) conserves energy.

Let's be clear: a non-conservative force field conserves energy.

The terminology of "exact differentials" versus "inexact differentials"
is almost as bad, for different reasons.

This is such treacherous terminology that I prefer to speak in
terms of "grady" and "ungrady" force fields. A grady force
field is the gradient of some potential. That's simple and
direct.

I don't even make a big deal about "contact" vs. "non-contact" forces
-- in the end, aren't all forces "at a distance"?

I don't make a big deal about contact versus non-contact ...
for the opposite reason: in the end, all forces are contact
forces. Relativity forbids "action at a distance".

For example, Newton's theory of gravitation predicts action
at a distance, which tells you it cannot possibly be entirely
correct. In contrast, general relativity predicts that there
will be gravitons that (a) are produced locally, (b) travel
step-by-step across the distance, and (c) interact locally
with other objects in the system.

So ANY force can be external or internal depending on the choice of
system.

Yes indeed.

Obviously, this has NOTHING at all to do with whether the
force is conservative or not.

Yes indeed.