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In the context of non relativistic quantum mechanics, or better, if I consider the neutrino's mass to be zero, the phrase

Neutrino are left-handed. The spin is in the opposite direction of motion.

seems to me puzzling. What I know is that if I know the direction of motion, I know the spin projection onto that direction, say z-direction. But to not violate Heisenberg's Uncertainty, if I manage to measure Spin in a perpendicular direction of motion, say $S_x$, now helicity must be undetermined. And to be consistent if I subsequently measure $S_z$ (or helicity), I can have the same or the opposite helicity. So, if a measure change helicity (to not to violates Heisenberg), it would be more precise to talk about left-handed neutrinos only in the context of some interaction, without excluding a priori that I can change it's helicity by an accurate measurement of Spin on the perpendicular direction of motion?

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Well, you have considered neutrinos to be massless. Since massless particles move at the speed of light, one can't actually choose or be in a frame where the particle appears to relatively change or reverse its Spin. Therefore, the helicity remains the same for all frames. Helicity of massless particles is actually a relativistically invariant quantity.

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  • $\begingroup$ I agree with that, but my question was about changing helicity not with a change of reference, but with a measure of the particle Spin. And by the nature of quantum measurement I assume the Spinor must collapse in a superposition of $S_z$ and $S_y$ eigeinstates say, if I choose to measure $S_x$ $\endgroup$ – Coltrane8 May 8 at 14:51

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