What is the Difference Between Chirality and Helicity?

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Chirality and helicity are related concepts in physics, but they are not the same thing. Here are the differences between the two:

  • Chirality refers to the property of a particle that makes it distinguishable from its mirror image. It is a fundamental property of a particle, like either being left-handed or right-handed.
  • Helicity is an extrinsic property related to the direction of a particle's spin relative to its momentum. If the spin is aligned with the momentum, the helicity is positive (right-handed); if the spin is anti-aligned with the momentum, the helicity is negative (left-handed).

For massless particles, chirality and helicity are linked. In this case, if a particle is chiral right-handed, it will have right-handed helicity, and if it is chiral left-handed, it will have left-handed helicity. However, for massive particles, helicity is not an inherent property due to relativity. You can change a massive particle's helicity by boosting it to a different frame, but you cannot change its chirality.

In summary, chirality is an intrinsic property of a particle that determines whether it is left-handed or right-handed, while helicity is an extrinsic property related to the direction of a particle's spin relative to its momentum. For massless particles, chirality and helicity are related, but for massive particles, they are not, and helicity can be changed by altering the frame of reference.

Comparative Table: Chirality vs Helicity

Chirality and helicity are two distinct concepts related to particles, particularly in the context of particle physics and electromagnetism. Here is a table comparing the differences between them:

Property Chirality Helicity
Definition Chirality refers to the "handedness" of a particle, such as left-handed or right-handed. Helicity is the alignment or anti-alignment of a particle's spin with its momentum.
Relation to Spin Chirality is a property that makes particles different from each other in a way that is reversed through a mirror image. Helicity is a measure of the direction of a particle's spin in relation to its momentum.
Inherent Property Helicity is not an inherent property of a particle due to relativity, meaning it can be changed by changing the frame of reference. Chirality, on the other hand, is an inherent property of a particle and is not affected by changes in the frame of reference.
Massless Particles For massless particles, chirality and helicity are the same. In the case of massless particles, the chirality and helicity of a particle are the same, regardless of the reference frame.
Massive Particles Chiral particles have a specific chirality, meaning a massive left-chiral particle may have either left- or right-helicity depending on the reference frame.
Applications Chirality is used to study molecules and other systems with handedness. Helicity is used to analyze the propagation of light through various media and scattering processes.

In summary, chirality is a property that distinguishes between left-handed and right-handed particles, while helicity is a measure of spin alignment with momentum. Chirality is an inherent property, whereas helicity can change due to relativistic effects.