Unveiling the Mysteries of Photon Helicity

[Usaf Moji]

I'm perplexed about something that Wikipedia says about photon helicity:

The magnitude of its spin is $$\sqrt{2}$$ $$\hbar$$ and the component measured along its direction of motion, its helicity, must be $$\pm$$$$\hbar$$.

(see http://en.wikipedia.org/wiki/Photon)

But for a photon, doesn't the spin vector always point in the same direction as the momentum vector - and therefore, shouldn't the magnitude of a photon's helicity equal it's spin magnitude, i.e. $$\sqrt{2}$$ $$\hbar$$?

 

[James R]

The spin vector is always at an angle to the propagation vector, such that its component in the direction of propagation is $\pm \hbar$ and its magnitude is $\sqrt{s(s+1)}\hbar = \sqrt{2}\hbar$.

In theory, one might expect that the photon could also have a spin projection of zero. However, apparently this would require that the photon have non-zero rest mass (which it doesn't), so a zero helicity state is not observed.

If somebody can explain why a zero spin projection is ruled out by relativity in more detail, I would be grateful.

 

[malawi_glenn]

Usaf Moji: WHY must the spin of the photon be aligned in the same direction as its momentum-vector?