http://www.physicsforums.com/showthread.php?t=136033

Thoughts on the Spin - Statistics Connection

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If we take an electron and rotate it through 360 degrees, its
wavefunction flips by a sign. That is established fact and we have a
good formalism to treat it (namely the SU(2) generators being the
generators of rotation for fermions).
Now if we take two electrons and interchange their positions, the
wavefuntion of the combination flips by a sign. That too is firmly
established, cause without it the world would literally collapse. The
question is -- IS THERE A CONNECTION BETWEEN THESE TWO FACTS?

The Spin - Statistics Connection is one of the most notoriously
non-intuitive proofs in physics. Though rigorously proved by Pauli,
everyone at one point or another have struggled with creating an
intuitive picture of it.

Like every other self respecting bum who's dabbled in quantum theory, I
have too, and here's my picture:

If one stands in between two electrons (whatever that means), and
watches God interchange the positions of two electrons by His hand, one
sees both electrons 'turning their faces' by 180 degrees each in the
*same* sense of rotation. The combined wavefunction |A>|B> transforms
by exp(i*pi*T/2)|A>exp(i*pi*T/2)|B> = -|A>|B>. (Where T is the third
Pauli matrix).

I suppose watching an electronic collision in the rest frame would look
something like that.

A prediction of such a picture would be to think about the spin of a
hadron-- a proton. It has three fermions inside it. So, if you stand in
the middle and watch God spin the proton around you through 120
degrees, the wavefunction will flip by
exp(i*2pi/3*T/2)|A>exp(i*2pi/3*T/2)|B>exp(i*2pi/3*T/2)|C> = -|A>|B>|C>.
This amounts to saying, the wavefunction of a proton will flip by a
minus sign if you rotate it through 120 degrees.
Flip again to positive through 240 degrees.
And flip to a minus again through a 360 rotation.
Is that true? Have we done, or can we do neutron interferometry
experiments to test this?

-Souvik