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Re: corrupting the youth



paul o johnson wrote:

You were kind enough to give references to Clifford Algebra, which I had
never heard of. But now you introduce chiral belts, which I also have never
heard of.

Sorry. I shouldn't have said chiral belts.
I should have said bivectorish belts.
Or omitted the adjective entirely.
See below for detailed correction.

Bob Sciamanda wrote:

This would then mean that a compass needle has chirality and that its
reflection changes chirality. (No?)

This is tricky, depending on exactly what you mean
by "compass needle".

1) Start with a macroscopically-symmetric long thin
cylindrical needle of _non_magnetized steel. That has
very high symmetry. It really is as symmetric as it
looks.
-- It is not chiral.
-- It has no sense of circulation.

2) Magnetize it. Better yet, let your Martian friend
magnetize it and give it back. It is now less symmetric
than its macroscopic shape would suggest:
-- It is still not chiral.
-- It now has a bivectorish circulation.
You can think of this as being due to microscopic
"Amperian currents".
Represent this by a belt, with arrowhead markings
indicating the direction of circulation.

3) Continue by painting one end of it red. (This is the
traditional marking for the north-pointing pole of a
compass needle.)
-- It is now for the first time chiral.

Note that you cannot perform this paint-job without
invoking the right-hand rule (to define what you mean
by "north") --- whereas all the previous steps could
be done without any notion of north or any notion of
right-handedness.

4) Demagnetize it. Even if you keep the paint-job,
-- It is no longer chiral.
-- It no longer has microscopic circulation.

So ... fully-marked compass needles are chiral, even
if that isn't obvious from their macroscopic shape.
The belt, representing the microscopic Amperian
currents, is _part_ of what makes them chiral, but
the belt is not by itself chiral.

You need both the circulation (to create a bivector)
_and_ the red paint (to indicate which side of the
bivector is called "north") before you have something
that is chiral.

==========

And yes, this is the physically-correct answer.
Fully-marked compass needles are chiral even if
they don't look it. In particular, if somebody
sent you a mirror-image snapshot of Prof. Wu's
famous cobalt-60 decay apparatus, and you tried
to replicate it based on that image, it wouldn't
work. To fix it you would need to repaint all
the bar magnets, putting the red paint on the
other end.