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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?

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- Thread starter JDługosz
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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?

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*bump*

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strangerep

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It would be useful if you could give a link/reference/extract to what you read.When it was in the news about neutrinos having mass, I wondered what that meant about left-handed only-ness. 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.

If you google for "helicity chirality" you'll gets heaps of explanations - farWhat is the difference? What exactly are they?

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.

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If you could point me to a link you think would help, I'll start there.

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But now if neutrinos have mass, then you can outrun them, from which perspective they will have opposite helicity. What gives?

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strangerep

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I'm not very good at phrasing things in layman's terms, but here goes...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 semi-layman's terms. Are they two different states, with one permanent and the other mutable?

"Helicity" and "chirality" are not states, they are properties that particles/fields

possess.

To understand

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 anti-clockwise. 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 rotation-sense (clockwise or anti-clockwise) doesn't change, but

the direction of motion

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

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 Lorentz-invariant (although one must

understand that this doesn't include the so-called discrete Lorentz transformation

of parity-reversal, 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,

mirror-images of each other which could not be superimposed upon

one another.

I don't know what you mean by that.What does that have to do with thesinglespin?

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.)

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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

strangerep

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Alas, for this you'll need to understand more of the math in those google

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?

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 right-handed 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 "left-handed" for half of them, and "right-handed" 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 left-handed and right-handed 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

left-handed chirality (always), anti-neutrinos are right-handed (always).

Hope that helps.

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(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.)

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strangerep

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Sorry, I don't know. Someone else will have to help with this question.How would you measure the chirality of an electron

(as opposed to its helicity)? That is, what property is manifested.

Maybe Uncle Al over on sci.physics.research.

That's why I said "hypothetical". But theoretically, a moving electron is still in a(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.)

superposition of LH and RH chirality states, though it's no longer an even 50-50.

- #12

Hans de Vries

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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?

Fermions in the Weyl (chiral) representation have two bi-spinor parts which are each

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

for both chiralities because the electric field E is a

sign under spatial inversion. However, the spin coupling to the B field is the

for both chiral components since the magnetic field B is an

not change sign under spatial inversion. (Bz can be seen as the result of a circular

current in the xy-plane, 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 V-A theory of the Weak force.

Regards, Hans

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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?

Hello,

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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