picturing spin

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Jeff Lee - 18 May 2005 14:29 GMT

I always hear how, under rotation, a spin 1/2 particle doesn't return to its
origin state until the rotation angle is 4\pi. Mathematically this is no
problem for me being just some facts stemming from the 2-forld cover of the
Lorentz group, but what does this rotation mean practically speaking in the
lab? Is this an active rotation? Is it passive? How do I picture this
operationally?

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PD - 18 May 2005 16:35 GMT

> I always hear how, under rotation, a spin 1/2 particle doesn't return to its
> origin state until the rotation angle is 4\pi. Mathematically this is no
> problem for me being just some facts stemming from the 2-forld cover of the
> Lorentz group, but what does this rotation mean practically speaking in the
> lab? Is this an active rotation? Is it passive? How do I picture this
> operationally?

The best picture is the rotation of an object that tied with a tether
to a fixed point. (I don't have a good feel for *why* this is so, but
I'm doing some reading to find out.)

The classic demonstration is to hold a cup of coffee in the palm of
your hand. Then rotate your hand (if right hand, then rotate ccw
looking down at your hand) so that you don't spill the coffee. After
2*pi, you will not be in your original configuration; in fact, you'll
be on the threshold of pain. But if you continue rotating in the *same*
direction, still palm-up so no coffee spills, you'll find yourself in
comfort in the original state.

This is known as the "Coffee Cup Proof of the Existence of Spinors".

PD

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Richard Schultz - 19 May 2005 05:37 GMT

: This is known as the "Coffee Cup Proof of the Existence of Spinors".

I've seen a series of photographs of Richard Feynman making that demonstration
(was it in _The Feynman Lectures_?), although I believe that he either
called it or strongly implied that it should be called the "Dancing Girl
Proof of the Existence of Spinors."

-----
Richard Schultz schultr@mail.biu.ac.il
Department of Chemistry, Bar-Ilan University, Ramat-Gan, Israel
Opinions expressed are mine alone, and not those of Bar-Ilan University
-----
"Logic is a wreath of pretty flowers which smell bad."

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Natural Science Forum / Physics / Particle Physics / May 2005

picturing spin