I am exceedingly fond of this trick. I keep the paraphernalia hanging on
the wall of my office. Every so often, somebody takes the bait: they ask
what it is. That makes my day. I leap into action and demonstrate the
trick to them.
My version is a piece of Vectorbord (about 4" by 5"). http://www.vectorelect.com/Products/Prototyping/Vectorbord/vectorbord.htm
I drew a picture of a hand on it (to make it easy to distinguish front from
back, and easy to recognize orientation). There are strings attached to
each corner. The far end of each string is attached to a magnet, so I can
stick it onto a doorframe on a moment's notice.
DDDDDDDDDDDDDDDDDDDDD
D D
Ds sD
D s s D V = Vectorbord
D s s D
Ds sVVVVVs sD s = string
D s VVVVV s D
D s VVVVV s D D = doorframe
D sVVVVVs D
D D
D D
D D
D D
First I rotate the Vectorbord by 2pi, whereupon the strings are obviously
tangled, and there's nothing you can do about it. I then rotate it by a
further 2pi (for a total of 4pi) and show that the strings can be untangled
without moving the Vectorbord or unhooking anything.
(This works with three strings, or any larger number.)
================
Also: The Philippine Wine Glass Trick is almost as much fun as the Dirac
String Trick.
While remaining seated, or standing in one spot, you can rotate something
by 4pi (about a !single! axis) and return to the original situation without
shifting your grip -- but 2pi is impossible.
Some hints:
1) Rather than a wine glass, it is better to demonstrate this with a
coffee-cup or some such, because the handle makes it easier for the
audience to keep track of the rotation.
2) For the first 2pi of rotation, tuck it under your elbow. For the second
2pi of rotation, it passes above the same elbow. It's an unfamiliar
motion, but perfectly doable.
3) Practice a few times with an empty cup, or a cup containing something
non-messy (perhaps a spoon or two). The contents are an important part of
the demo, to prove that you rotated around one axis only.
====================================
You may be wondering what this has to do with physics.
"Everybody knows" that ordinary objects have a 2pi rotational
symmetry. And "everybody knows" that if rotating by 360 degrees doesn't
restore the original configuration, rotating by 720 degrees will only make
it worse. But just because "everybody knows" it doesn't make it true. In
fact, in our universe, 4pi is the fundamental rotational symmetry.
This comes up when discussing the wavefunction for an electron (or any
spinor particle, i.e. anything with half-integer spin), which is *not*
unchanged if you rotate it by 2pi (whereas 4pi is the same as zero). A
vector particle such as a deuteron is invariant under 2pi rotations, which
is easy to understand if you think of it as two spinors.
All this goes to show that my piece of Vectorbord with strings doesn't
behave like a vector particle. Really we ought to call it Spinorbord.