Belt trick, spin 1/2 and spin sqrt(3/4)
- From: frank_k_sheldon@xxxxxxxxxxx
- Date: Sun, 6 Jan 2008 11:03:01 -0500 (EST)
It is well known that Dirac's belt trick models the behaviour of
spin 1/2 particles. For example, if one turns the end of the
belt (the particle) by 4 pi, the belt can be untwisted even while
keeping the particle fixed. This illustrates that for spin 1/2
particles,
rotations by 4 pi and 0 pi are equivalent, whereas rotations
by 2 pi are not.
But there is another point. Spin 1/2 hbar is in fact the projection
on the z axis; the absolute value of the spin is sqrt(3/4) hbar.
How can one see both the 1/2 and the sqrt(3/4) values
in the belt visualization?
Or:
Is there a way to visualize the sqrt(3/4) value as well,
in the belt trick?
Frank
.
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