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Re: superposition





On Wed, 15 Jan 1997, Richard Taylor wrote:

Don,

I'm not sure you have to rely on the "just because" answer for
superposition. If you have two charges, 3q and 2q, the force is 3 times
as big as from 1q and 2q. But the 3q might just be 3 separate charges of
q each. So the force from 3 charges is the same as just adding them up.
I think that if you accept Coulomb's law, then you accept superposition.

Apparently, judging from several responses, I was less than clear.

Superposition can be of many things. It needn't be simply superposition of
charges, or superposition of vectors, or displacements. We don't know
a-priori which quantities lend themselves to a superposition formulation
in a given physical phenomena. Only experiment can decide that. In the
example above you thought I was referring to superposition of charges. I
had in mind superposition of the *fields* produced by the charges, as
evidenced by their effect on other charges.

I don't know that this is full of universal truth--I've taken the
simplest case where all the charges are together. But I think that
looking at the charges as a sum makes superposition seem reasonable to
students.

There's a trap. Appealing to what seems reasonable. At this point I
usually quote Josh Billings: "There's a mighty big difference between
good, sound reasons, and reasons that sound good."

The students suckered into this version of what's reasonable may then be
inclined, when confronted with a problem where superposition *doesn't*
apply, to apply it anyway, in some form. Surely we can think of some
examples of this error.

If our students' naive intuition and sense of what's right or reasonable
actually worked in the real world, all students would do well in physics.
To lead students to think that because something seems reasonable that it
must be so, is a form of deception. To cite a homely example, is it in any
sense intuitive for students to expect that if you push a spinning
gyroscope in one direction, it moves in a direction perpendicular to your
push? Does the result seem reasonable to them? No, not until you do the
math, understand the concepts of moment of inertia and torque, etc. and so
on. And when the math and physics is understood, you can say "now its'
reasonable" but you are now speaking of reasonable in a much different
sense than it is colloquially understood. Who was it coined the phrase
"the incredible unreasonableness of science"? And I'm sure that's what
Alan Cromer means in his recent book "Uncommon Sense" in which he
characterizes science as a totally uncommon form of thought, not
understood and not appreciated by the majority of mankind.

Are the conclusions of relativity and quantum mechanics in any way
intuitive? If science were limited to what seems reasonable to naive
common sense, we'd still be back in science of the middle ages.

-- Donald

......................................................................
Dr. Donald E. Simanek Office: 717-893-2079
Prof. of Physics Internet: dsimanek@eagle.lhup.edu
Lock Haven University, Lock Haven, PA. 17745 CIS: 73147,2166
Home page: http://www.lhup.edu/~dsimanek FAX: 717-893-2047
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