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Helicity vs. Chirality? 
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#1
Aug1607, 04:14 PM

P: 346

When it was in the news about neutrinos having mass, I wondered what that meant about lefthanded onlyness. You could catch up to one and pass it, or slow one down.
More recently, I read that the helicity of the neutrino is invariant but the chirality can still change. What is the difference? What exactly are they? 


#2
Aug2107, 06:13 PM

P: 346

*bump*



#3
Aug2107, 06:32 PM

Sci Advisor
P: 1,927

more than I could write here. Have a read of some of them. If it's still not clear, bump the thread again and say what remains mysterious. 


#4
Aug2207, 11:37 PM

P: 346

Helicity vs. Chirality?
Actually, I didn't understand any of it. I saw explanations that dealt with the math, but no lucid explanation of what they were in semilayman's terms. Are they two different states, with one permanent and the other mutable? What does that have to do with the single spin?
If you could point me to a link you think would help, I'll start there. 


#5
Aug2307, 01:29 AM

P: 2,051

Wasn't it accepted that neutrinos always have the same helicity?
But now if neutrinos have mass, then you can outrun them, from which perspective they will have opposite helicity. What gives? 


#6
Aug2307, 02:12 AM

P: 77

My take= Helicity represents direction of motion and Chirality represents orientation. My Opinion= Both are ridiculous words that serve to confuse when put together and serve nothing better when separated. But then, I may be being a bit cynical. It's just that I've never heard either of them used in the context of a discussion. What's the origin of these strange words and why do you care? Why do I? These are good questions.



#7
Aug2307, 03:01 AM

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P: 1,927

"Helicity" and "chirality" are not states, they are properties that particles/fields possess. To understand helicity heuristically, do the following experiment. Extend your index finger out in front of you. As you extend it, rotate it clockwise (about the axis of the finger). I.e: there's a clockwise twisting helical motion as you extend your arm forward. Now do it again, this time rotating anticlockwise. These two things correspond roughly to opposite helicities: different rotations about the direction of motion. Now imagine moving your body and head forward faster than you're extending your arm. The rotationsense (clockwise or anticlockwise) doesn't change, but the direction of motion relative to your head reverses. This roughly illustrates what is meant when people say that a Lorentz boost (of your head) that overtakes the particle (your finger) changes the helicity that your head "measures" when observing your finger. In contrast, to understand chirality heuristically, hold your left hand in front of you and arrange the thumb, 1st finger, and 2nd finger so that they all point in mutually perpendicular directions. Do the same thing simultaneously with your right hand. The finger arrangements on your two hands form mirror images of each other, and this corresponds to opposite "chirality". Now, there is no way you can move you head around that will make your left hand's finger arrangement look like your right hand's. That's what is meant when people say that chirality is Lorentzinvariant (although one must understand that this doesn't include the socalled discrete Lorentz transformation of parityreversal, i.e: exchange of "left" and "right" senses). I think the word "chiral" has its origins in crystallography  when people noticed that certain substances could occur in different crystalline forms, mirrorimages of each other which could not be superimposed upon one another. BTW, Idjot: you should definitely care about understanding the difference between helicity and chirality, at least if you wish to understand particle physics and its associated relativistic quantum theory. Many people get seriously confused otherwise when trying to learn about the weak nuclear interaction for the first time. (I speak from personal experience.) 


#8
Aug2307, 11:23 PM

P: 346

Thank you strangerep, that starts to help. I understand from what you wrote that chirality is Lorentzinvariant and helicity depends on the observer.
What about other particles, such as electrons? The spin along the motion vector in the frame of whatever interaction is about to take place is the helicity. But do electrons have two different types of chirality that are different from each other? 


#9
Aug2407, 01:03 AM

Sci Advisor
P: 1,927

references I alluded to earlier. An electron (indeed, any massive fermion), does not have a deterministic chirality in general. When an electron is a rest, it is a quantum superposition of left and righthanded chirality states in equal amounts. If (hypothetically) we measured the chiralities of a large number of electrons at rest (separated far enough from each other so we can neglect their electromagnetic interactions), we'd get the result "lefthanded" for half of them, and "righthanded" for the other half. I.e: "chirality" is not a deterministic property of electrons. To make things even more complicated, as an electron propagates forward in time along its worldline, the lefthanded and righthanded components of the superposition will mix together. But you'll need to learn about the "Dirac eqn" to understand more of that. For a massless neutrino however, (at least, before we began to suspect there is no such thing), the chirality is definite (i.e: deterministic). Massless neutrinos have lefthanded chirality (always), antineutrinos are righthanded (always). Hope that helps. 


#10
Aug2407, 01:10 AM

P: 346

How would you measure the chirality of an electron (as opposed to its helicity)? That is, what property is manifested.
(As an aside, how do you, in principle make a measurement on a stationary particle? The observation is due to an interaction and the particle will be moving in the frame of the center of momentum of the interaction.) 


#11
Aug2507, 03:29 AM

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P: 1,927

Maybe Uncle Al over on sci.physics.research. superposition of LH and RH chirality states, though it's no longer an even 5050. 


#12
Aug2507, 07:41 AM

Sci Advisor
P: 1,135

others spatial inversions which can be seen from the definition of the gamma matrices: [tex]\gamma^0 = \left(\begin{array}{cc} 0 & \ \ I\ \ \\ \ \ I\ \ & 0 \end{array} \right), \qquad \gamma^i = \left(\begin{array}{cc} 0 & +\sigma_i\\ \sigma_i & 0 \end{array} \right)[/tex] Where the first represents the time component which isn't reversed and the other three represent the spatial components (i=x,y,z) which are reversed. Now, an electron has both chiralities but the amount of them depends on the relative speed. In the electron's rest frame both are equal but at v = +c or v = c only the first or the latter survives. The chirality which survives depends on the sign of the speed but also on the sign of the spin along the direction of motion. Since both chiral components are each other spatial inversions, they couple differently to normal or axial vectors, for instance: The spin coupling to the E field is opposite for both chiralities because the electric field E is a normal vector which changes sign under spatial inversion. However, the spin coupling to the B field is the same for both chiral components since the magnetic field B is an axial vector which does not change sign under spatial inversion. (Bz can be seen as the result of a circular current in the xyplane, reversing the x and y axis leaves the clockwise direction of the current unchanged) Thus an electron at rest has no spin coupling to the E field since both chiralities cancel each other but it does couple to the B field: The electron has an intrinsic magnetic moment. An electron at higher speed does couple with the E field. In classical electro dynamics this is because the moving electron sees the E field partly transformed into a B field in its own rest frame. For the charge coupling (as opposed to the spin coupling), both chiral components couple the same to the E and B fields because F = q( E + v x B), and both E as well as v x B are normal vectors. The Weyl (chiral) representation became a very important representation of the electron after it was established that only one of the two chiralities couples to the Weak force. From the above we can see that this is possible if the Weak force field is a combination of both a V(ector) and A(xial) current with equal strength. The couplings add for one chirality while they cancel each other for the other chirality. This became the successful VA theory of the Weak force. Regards, Hans 


#13
Aug2907, 04:22 AM

P: 79

I do not understand why the helicity of the neutrino should be invariant now it has a mass ? Indeed if neutrinos have mass, it just implies that LH and RH chirality states are no more solutions of Weyl equations and so are no more eigenvalues of helicity operator. Which means we can no more relate helicity to chirality exactly for neutrinos. Does it mean we could observe right helicity neutrinos even in the lab frame ? 


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