Re: left/right symmetry, manifest or not

[Robert Cohen <Robert.Cohen@PO-BOX.ESU.EDU>]

I wouldn't blame the cross product.  I would say the *coordinate system* is
flipped in the mirror and the cross product follows suit.

For example, meteorologists may use a left-handed coordinate system where
one axis points toward the east, another points toward the north, and the
third points in the direction of increasing pressure (down).  If we define
ixj=k then the cross product in this coordinate system follows the LHR.  As
far as I am concerned, this is just math.  The physics is contained in the
circulation, which is the same in both coordinate systems.  Likewise, the
wedge product is the same in both coordinate systems.  I think.

____________________________________________
Robert Cohen; rcohen@po-box.esu.edu; 570-422-3428; http://www.esu.edu/~bbq
Physics, East Stroudsburg Univ., E. Stroudsburg, PA 18301

> -----Original Message-----
> From: Bob Sciamanda [mailto:trebor@VELOCITY.NET]
> Sent: Wednesday, August 28, 2002 1:09 PM
> To: PHYS-L@lists.nau.edu
> Subject: Re: left/right symmetry, manifest or not
>
>
> If I may add another novice's appreciation,
> Draw two (non-parallel) vectors (A and B) from a common
> vertex on a sheet
> of paper.
> Now look at this in a mirror.  If you define and represent the cross
> product AxB as a (pseudo) vector following the right hand rule in the
> "real world", the reflected objects will follow the left hand
> rule in the
> "mirror world".
> OTOH, if you define and represent the wedge product by a directed
> (circulation) arc going form the tip of A to the tip of B,
> this definition
> carries over into the "mirror world".