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Direction of Pseudovectors

  1. Nov 21, 2011 #1
    The Wikipedia article on http://en.wikipedia.org/wiki/Pseudovector" [Broken] initally suggests that they do change direction after reflection.

    But in a later http://en.wikipedia.org/wiki/Pseudovector#Physical_examples" angular momentum remains invariant under reflection.

    A pseudovector is direction invariant under reflection or not?

    I tried to devise a trick on the Right Hand Rule - if I were to switch to a left hand rule (left hand appears to be a mirror image of the right hand), and curl my left palm as in right hand rule. I noticed that if the left hand is to be maintained as a mirror image of the right, the direction of both the thumbs is same, suggesting that it is invariant.
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Nov 21, 2011 #2

    D H

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    Well, that's wikipedia for ya'. Sometimes very good, sometimes poorly written and confusing, sometimes flat out wrong. This article falls in the second category.

    You are talking about this image in the wiki article:
    500px-Impulsmoment_van_autowiel_onder_inversie.svg.png

    Think of the car on the left as the real car, the car on the right as the car's reflection. Imagine a vector on the car's rear bumper, with the tail in the middle of the red/gray hatched region and the head in the middle of the red/blue hatched region. In the car on the left, this vector is parallel to the angular momentum vectors of the car's wheels. Upon reflection, this vector reverses direction: It is points to the right upon reflection. This displacement vector is a real vector rather than a pseudovector. It's reflected image is the reverse of the real image in this particular example. The angular momentum pseudovectors are reflected and reversed. Reflection alone would reverse the direction of the pseudovectors. Reversing the reflections of these pseudovectors leaves those pseudovectors unchanged in this particular example.
     
    Last edited by a moderator: May 5, 2017
  4. Nov 22, 2011 #3
    Actually, the original statement is not complete and not correct. It is true that a pseudovector, reflected in a mirror perpendicular to the vector, does not change sign. If you reflect a pseudovector in a mirror parallel to the vector, it does change sign.
     
  5. Nov 22, 2011 #4

    D H

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    You misread that statement in the wikipedia article. The statement is correct, just very poorly worded.
     
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