Here's an easy (and I suppose well known) way to demonstrate the double twist phenomenon. Take an ordinary belt. Anchor the "tongue" end, make a double twist and hold the buckle "shiny side up". The aim is to untwist the belt without ever rotating the buckle, i.e. keep it shiny side up at all times so it is always parallel to its original position. It's possible for 720 but not 360 degrees as you will easily see. DG At 07:52 AM 4/7/2004 -0500, you wrote:
Thane:
Dirac visited SIUC around 1978 for an Einstein symposium. When I met him, I mentioned to him that I recalled having seen -- around 1965 -- a brief reference to his spinor-related trick in Time magazine. The article suggested that he had discovered it around 1932. He confirmed that that was probably about the right date.
I suggest that you ask my physicist colleague Jerzy Kocik (jkocik@math.siu.edu) to fill you in on the details of the spinor connection. He has demonstrated the trick (with flailing arms) and he has expert knowledge of quantum mechanics. I'll send a copy of this email to Jurek (Jerzy).
Alan
At 01:47 PM 4/4/2004, you wrote:
(This is the same thing that says you can hold a full cup of coffee in one hand, and without letting go or spilling, turn it around twice and get back in the same position. However, if you turn it around just once, your arm will be in a different, probably awkward, position.)
I read that Dirac illustrated this fact, that a 360 degree rotation isn't the same as a 720 degree one, using strings tied to a pair of scissors, right?
My question: where/when did he do it?
Thane Plambeck 650 321 4884 office 650 323 4928 fax http://www.plambeck.org
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun