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Re: imaginary reality II



QM is "different" because the phases of amplitudes become are important,
leading to inaterference effects that have no classical counterpart. A
prime example is the Aharonoff-Boehm effect. Another is the interference
between the "strong interaction" phase shifts and the coulomb phases in
the scattering of charged particles. A third example, closer to "real
life" is the fact that particles passing through a pair of slits show
interference effects resulting from the different phases of ammplitudes
corresponding to different paths.
Regards,
Jack

Adam was by constitution and proclivity a scientist; I was the same, and
we loved to call ourselves by that great name...Our first memorable
scientific discovery was the law that water and like fluids run downhill,
not up.
Mark Twain, <Extract from Eve's Autobiography>

On Sun, 23 Apr 2000, John Denker wrote:

At 08:41 PM 4/23/00 -0400, TIMOTHY WAGNER wrote:

For example would one say..
"Students, you will have to learn a wave amplitude expression
quite different than
the one that models the surface of a ripple tank.

IMHO one should *not* say that.

There is a principle of pedagogy that says:
"learning proceeds from the known to the unknown."

In this case, there are two extreme possibilities:
a) We "could" whine about how different QM is from what has gone before:
-- we used to talk about true and false,
now we talk about probabilities
-- we used to talk about sin and cos,
now we talk about complex exponentials
b) Or we could arrange things so that QM does _not_ come as a big shock.
In a well-designed curriculum, we could say
-- you already know about probabilities. QM uses probabilities.
-- you already know about waves. QM uses lots of waves.
-- you already know about matrices and operators. QM uses them.
-- you already know about complex numbers. QM uses them, too.
-- you already know that the energy of a wave goes like
the square of the amplitude. QM is like that, too.

I recommend item (b).

(OTOH it is possible to design a curriculum so badly that all the tools
that one needs to facilitate QM discussions are lacking at the time QM is
introduced. But let's not discuss how to salvage such a situation. The
correct strategy is to not get caught in such a situation.)

No longer will y=Acos(kx) suffice; rather a complex wave (no
picture)..etc..Later you'll see the practical reality"

This seems to be asking how best to tell students that QM waves are
weird. I really think the question is based on a false premise. QM waves
are not particularly weird. There are some weird things that go on in the
quantum world, but the wave equation isn't one of them. Really it's not.

IMHO any question that assumes that classical waves are somehow
qualitatively different from quantum waves is the wrong question. It would
be poor pedagogy to conjure up a pseudo-distinction where no real
distinction exists.

I realize the question has been asked twice, and I have twice refused to
answer it. It is possible that I didn't understand the question -- but it
is also possible that I did understand the question and I'm doing the right
thing by objecting to the implicit assumptions behind the question.

In particular, consider sunlight scattering off of white fluffy
clouds. ISTM that the quantum wave mechanics of this is for all practical
purposes identical to the classical electromagnetic wave mechanics of
this. Help me out here, folks. If you can think of any physical,
mathematical, or pedagogical reason for saying that the two descriptions
are different, please explain.