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Re: [Phys-L] The Make-Believe World of Real-World Physics



On 07/24/2013 12:35 PM, William Maddox wrote:
"You maybe a Redneck if ____"

You may be a redneck physicist if you think it makes sense
to shoot varmints after they have let go of the tree branch
and are in free fall.

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

Do you call axb a cross product or a wedge product?

That illustrates how wide is the gulf between alternate
universes.

In my universe:
1) a × b is a cross product. Always was, always will be.
2) In contrast, the wedge product is written a ∧ b.
3) You can calculate the cross product as the Hodge dual
of the wedge product.

The more interesting question is whether you:
1) write angular momentum as a cross product (arm × motion)
i.e. a pseudo-vector along the axis of rotation,
with the aid of the right-hand rule, or
2) write angular momentum as a wedge product (arm ∧ motion)
i.e. a bivector in the plane of rotation,
with no right-hand rules needed, not for anything having
to do with classical mechanics or electromagnetism.

I know I can teach wedge products to your average redneck
high-school student. There is no need for them to unlearn
anything about cross products, because they never learned
any of that stuff to begin with, or if they did, it didn't
stick for more than a few days, and it has long since been
forgotten.

I can explain gyroscopic precession in terms of addition of
bivectors, using three pieces of cardboard, adding them
graphically, edge-to-edge, just as you add vectors graphically,
tip-to-tail.

By way of contrast, I have no idea how to explain precession
to students in terms of cross products and right-hand rules
and axial pseudo-vectors. I've tried. None of it sticks.
If you have a way of explaining precession without bivectors,
something that ordinary rednecks can understand, please
explain. A lot of people would be very interested to see
that.

As I said, I know I can explain wedge products to average
redneck high-school students. It is much more doubtful whether
it is possible to explain such things to average redneck
high-school /teachers/. They're much more set in their ways.