Re: ACCELERATION

[brian whatcott <inet@INTELLISYS.NET>]

Leigh is always a thought-provoking read.
 I quote his Kittel anecdote at length below.
 And I admit I am surprised.

Leigh felt fooled because Kittel mentioned
he developed a math derivation using cos omega t
rather than sine omega t "which would have made the whole
effect go away".

I take the view that what Kittel meant was that the use
of a sine omega t in a pump frequency expression would have
 made the whole derivation go away - not the physical effect.

 It seems to me there can be cases where a derivation must
take a different course depending critically upon the shape
of the math terms chosen.

 But I fear this story illustrates a not uncommon mindset
- that the math model/derivation etc., call it what you
will *is* the physics.
 I am relieved to believe that math models  are just that.

Brian


At 09:27 9/15/00 -0700, Leigh wrote:
> > ... motion of extended (real) objects
> > can be modeled quite accurately by using a single point.
>
> That is just the <point> I made in my earlier sentence:
>
> > > These kinematic quantities
> > > pertain to the motion of something abstract, usually a point in space
> > > defined by a formal procedure defining the center of mass of some
> > > physical object.
>
> While the description is quite accurate (in fact it is exact, since the
> motion of the center of mass of the object is mathematically defined),
> the description of the motion of an extended object is not *complete*.
> This model is complete for a rigid body, but there are no rigid bodies.
> The rigid body is an abstraction.
>
> In particular, when one asks questions about discontinuous acceleration
> one must consider how the model differs from reality on the shortest of
> timescales. Now hysteresis rears its ugly head. The velocity of a rigid
> body depends upon the velocities of all its constituent particles, and
> on the shortest timescales these velocities are not all the same even
> in the case of nonrotating bodies. The presence of sound waves within
> the body will serve as one of a number of examples.
>
> I think that it is important for us to recognize (and share with our
> students) the fact that we are teaching models having limited validity.
> When a question like "Can a real body have discontinuous acceleration?"
> arises, the only honest answer must recognize the limits of validity of
> the model. Since, above all, we must strive to be honest in teaching,
> these niggling points about validity should be introduced, even though
> you may feel they get in the way of understanding.
>
> When I was in grad school I took a quantum solid state course from
> Charles Kittel. Despite a severe stutter, Kittel is an execellent
> teacher. One lecture he gave in the course, however, left me cold and
> annoyed. Kittel derived the model which demonstrates some effect of
> parallel pumping in solids. After a smooth derivation with no evident
> problems, at the end of the hour he said something like "I suppose I
> should tell you that I've swindled you a little bit here. If I had
> pumped with sine omega t here instead of cosine omega t, the whole
> effect would go away." He left it like that.
>
> I learned no physics from that lecture; it was a waste of my time.
> The very least he should have done was to warn us at the time he
> swindled us (when "the frog jumped into the pond") that he was doing
> so, and he should have made a slightly longer statement at the end
> explaining why this derivation still had merit.
>
> Rigor in the pursuit of learning is no vice.
>
> Leigh
brian whatcott <inet@intellisys.net>  Altus OK
                Eureka!