Vanadium 50 said:
This is getting more and more complicated. So you want two fields - one massless, left-handed, with electric and weak charge, and another massless, right-handed, with electric but no weak charge. Why would people consider these the same particle?
I'm not following. What do you mean two fields? I was just asking a separate question to try to see if I was understanding your previous answer, sorry if that was not clear. Forgetting about neutrinos, suppose we had a particle that was like a neutrino—massless and left handed—but that also has an electric charge. That would allow us to easily measure its spin along axes orthogonal to its momentum with a Stern-Gerlach device. As I said earlier, that seems weird to me because I don't understand how a measurement of such a spin state makes sense, since it would require the particle to have a non-zero right-handed component. If you think this example is introducing unnecessary complication, that's fine, ignore it, it was just meant to illustrate what I'm asking. Again, I'm just trying to understand whether it makes sense to talk about the spin states of neutrinos along axes orthogonal to their momentum. The example I suggested was just me taking a stab at proposing a way that such a quantity could be easily measurable.
@strangerep, I understand (at least, at a fairly basic level) the mechanics of how spin and helicity arise as irreps of the Poincare group (and I did note right at the outset that I understand chirality and helicity coincide for massless particles). That's not really the issue. Take the photon, for example. It's two helicity states correspond to the two circular polarization states of classical EM. It can also be in superpositions of these states—in particular, in those superpositions that correspond to classical horizontal/vertical and diagonal/antidiagonal polarization states and which, up to a phase, have exactly the same form as the spin states of massive spin half particles along the x- and y-axes, respectively. Maybe this is where the problem lies—I've often heard colleagues in quantum optics talking about measuring the "spin along the x- and y-axes of a photon" just as they would the spin of an electron, but maybe this is just sloppy language that should be avoided? I.e. it's taking the fact that the polarization states of a photon and the spin states of a massive spin-half particle are both described by Bloch sphere too literally?
My confusion, as I described in the above response to Vanadium, is that while it should not (as far I can tell) be possible to have a neutrino in a superposition of helicities, since they are always left handed, if its spin orthogonal to its momentum
were well-defined, such a thing seems like it could be measured. So, I'm getting the feeling is that the answer is that it just does not make sense to talk about the spin of a neutrino orthogonal to its to momentum (and so, presumably, nothing would happen if an electrically charged version of a neutrino were fired through a Stern-Gerlach device).
I hope that was somewhat clear—I'm sort of talking this out to myself as I go—so if it sounds like I'm on the right track, let me know. I suppose maybe a there's simpler question I can distill all this down to, as I alluded to above, that might make things clearer for me:
If a
photon (or just generally any massless spin-1 particle) is propagating along the z-axis of a coordinate system, does it make sense to talk about its spin along the x- and y-axes? Or, as I suggested, is that just a mistaken notion based on the fact that the photon's polarization states are described quantum mechanically in the same way as the components of a massive spin-1/2 particle's spin? If, indeed, it does not make sense to talk about such spin states for a photon than I think my question about neutrinos is answered too.
