Stretch you right arm out, palm up. Try to rotate your palm clockwise about the vertical axis while keeping it facing up at all times. You will notice that it takes a continuous 720 degrees rotation rather than a 360 degrees rotation to bring your arm back to its original state. This is an illustration of the remarkable fact that an object rotated through 360 degrees might not always come back to its original state. Paul Dirac assigned a quantity of 
to the spin of an electron to express the fact that its amplitude changes under a 360 rotation but is restored with a 720 rotation. He justified this assignment with a famous topological insight which has since taken many forms and legends: the Phillipine wine glass trick (which involves sustaining a wineglass placed on the aforementioned palm), the Feynman Plate trick or the Dirac belt trick. Whatever the name, it was probably the first application of algebraic topology to quantum physics. These days it is hard to distinguish one from the other. I will explain this phenomenon in a mathematical framework when I introduce some algebraic topology basics later on in this blog. Here is an excellent visualisation of this trick.
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I believe it is because SU(2) covers SO(2)?
Comment by Anonymous — June 26, 2008 @ 10:49 am
Not S0(2). It is because SU(2) is a double covering of S0(3).
Comment by zetahype — June 26, 2008 @ 2:28 pm
Very interesting, when you say “…it takes a continuous 720 degrees rotation…”, is that hypothetical, I can’t seem to rotate 720 degrees continuously.
Comment by zeeky — June 27, 2008 @ 12:46 am
watch the video in the link zeeky..imagine your palm tracing a spiral!
Comment by zetahype — July 21, 2008 @ 7:58 pm