Excellent, John! I was surmising as much, but needed your clarification.
Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net http://www.velocity.net/~trebor
----- Original Message -----
From: "John S. Denker" <jsd@MONMOUTH.COM>
To: <PHYS-L@lists.nau.edu>
Sent: Monday, September 02, 2002 12:42 PM
Subject: Re: corrupting the youth
| . . .
| 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.
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