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@ everexpanding
2023-05-02 07:16:55Every fundamental particle carries an intrinsic angular momentum, which we call 'spin'. It is important to remember that this is an intrinsic quantum mechanical property of particles. There is no such thing as a spinning sphere in the classical sense. Nevertheless, the image of a spinning sphere is often a good analogue to understand what is going on.
Helicity
The helicity of a particle is the projection of its spin vector onto its linear momentum. In the spinning analogy, it is the relation of its spin direction to its direction of motion. The particle helicity is called either right-handed or left-handed. We say that the particle has right-handed helicity if the spin is aligned with the direction of motion, and left-handed helicity if the spin and motion have opposite orientations. In the spinning analogy, we can immediately understand where the names come from and what they mean. We look at your hands, make a fist and spread the thumbs. The thumbs indicate the direction of motion and the curled fingers indicate the direction of spin. We point our thumbs in the direction of motion and compare the fingers with the direction of spinning we see: If they are in the same direction as the right hand, we call it right-handed helicity, and conversely.
Since massless particles (e.g. photons) travel at the speed of light, we will never find a reference frame in which this particle is at rest, i.e. we cannot find a rest frame. Therefore, the helicity will never change, since the spin is fixed and the direction of motion is the same in all reference frames.
On the other hand, massive particles travel at a speed less than that of light, so in principle we can find a rest frame. In fact, we can even find a reference frame in which the particle appears to be moving in the opposite direction. Yet the spin of a particle never changes. This leads to the fact that for massive particles the helicity can change because the direction of motion can be reversed, resulting in the opposite helicity. Note that this is not possible for massless particles, because we cannot move faster than them.
Thus we see that the mass of a particle tells us whether the helicity of a particle is an intrinsic property of the particle. For a massless particle, the helicity is fixed in all reference frames, whereas for a massive particle this is not the case, because different observers can infer different helicities for the same particle.
As physicists, we like to find fundamental properties of a particle. We therefore ask whether there is a related property to helicity that is intrinsic to particles. We call this fundamental property chirality.
Chirality
Chirality and helicity are closely related. Just as we say a particle has right-handed or left-handed helicity, we say a particle has right-handed or left-handed chirality. Sometimes we can drop the '-handed' and just say right-/left-helicity or right-/left-chirality. For massless particles, helicity and chirality are the same thing, so a right-chiral particle will also have right-helicity. For massive particles, however, helicity and chirality are different. A massive particle has a certain chirality but can have both helicity states, e.g. a right-chiral particle can have right or left helicity depending on the frame of reference.
Chirality is an abstract concept that refers to a fundamental intrinsic quantum mechanical property of a particle. However, a useful and nice visualisation can be made by looking at our hands. We hold our hand in front of us. The left and right hands are mirror images of each other. No matter how we rotate, flip or move one hand, it will never look exactly like the other hand. Our hands have different chirality.
In physics, particles with different chirality can be considered as completely different particles. It refers to how a particle's quantum mechanical wave function behaves under rotation. The quantum wave functions of left- and right-chiral particles behave differently under rotation.
The measurable physical effect of a particle's chirality can be seen in the theory of the weak interaction. The weak interaction only affects left-chiral particles and not right-chiral ones. As a result, neutrinos, which are weakly interacting particles, are only observed in left-handed chiral states.
I hope this post has helped you understand the concept of helicity and chirality in physics. If anything is still unclear, or if an explanation could be improved to make it easier to understand, please comment or write to me. I am happy to answer. I'm looking forward to your feedback. PV 🤙
v0 @ 785591; v1 @ 785712: fixed typos and added a missing sentence; v2 @ 787922: slight changes to the layout