Editing Chirality (physics) (section)

== Chirality and helicity ==
{{See also|Helicity (particle physics)}}
The helicity of a particle is positive ("right-handed") if the direction of its [[Spin (physics)|spin]] is the same as the direction of its motion. It is negative ("left-handed") if the directions of spin and motion are opposite. So a standard [[clock]], with its spin vector defined by the rotation of its hands, has left-handed helicity if tossed with its face directed forwards.

Mathematically, ''helicity'' is the sign of the projection of the [[Spin (physics)|spin]] [[vector (geometric)|vector]] onto the [[momentum]] [[vector (geometric)|vector]]: "left" is negative, "right" is positive.

[[Image:Right left helicity.svg|center]]
The '''chirality''' of a particle is more abstract: It is determined by whether the particle transforms in a right- or left-handed [[Group representation|representation]] of the [[Poincaré group]].{{efn|Note, however, that representations such as [[Dirac spinor]]s and others, necessarily have both right- and left-handed components. In such cases, we can define [[projection operator]]s that remove (set to zero) either the right- or left-hand components, and discuss the left- or right-handed portions of the representation that remain.}}

For [[Massless particle|massless particles]] – [[photon]]s, [[gluon]]s, and (hypothetical) [[graviton]]s – chirality is the same as [[helicity (particle physics)|helicity]]; a given massless particle appears to spin in the same direction along its axis of motion regardless of point of view of the observer.

For [[Massive particle|massive particles]] – such as [[electron]]s, [[quark]]s, and [[neutrino]]s – chirality and helicity must be distinguished: In the case of these particles, it is possible for an observer to change to a [[Frame of reference|reference frame]] that is moving faster than the spinning particle is, in which case the particle will then appear to move backwards, and its helicity (which may be thought of as "apparent chirality") will be reversed. 

* Helicity is a [[constant of motion]],<ref>https://cosmology.info/apeiron/pdf/v07no1/v07n1ran.pdf</ref> but it is not [[Lorentz invariant]].<ref>https://faculty.washington.edu/agarcia3/subatomic/helicity-paper.pdf Page 46</ref>
* Chirality is Lorentz invariant,<ref>https://alpha.physics.uoi.gr/foudas_public/APP-UoI-2011/Lecture9-Helicity-and-Chirality.pdf</ref> but is not a constant of motion: a massive left-handed spinor, when propagating, will evolve into a right handed spinor over time, and vice versa.

A ''massless'' particle moves with the [[speed of light]], so no real observer (who must always travel at less than the [[speed of light]]) can be in any reference frame in which the particle appears to reverse its relative direction of spin, meaning that all real observers see the same helicity. Because of this, the direction of spin of massless particles is not affected by a change of inertial reference frame (a [[Lorentz boost]]) in the direction of motion of the particle, and the sign of the projection (helicity) is fixed for all reference frames: The helicity of massless particles is a ''relativistic invariant'' (a quantity whose value is the same in all inertial reference frames) and always matches the massless particle's chirality.

The discovery of [[neutrino oscillation]] implies that [[neutrino#Mass|neutrinos have mass]], leaving the [[photon]] as the only confirmed massless particle; [[gluon]]s are expected to also be massless, although this has not been conclusively tested.{{efn|[[Graviton]]s are also assumed to be massless, but so far are merely hypothetical.}} Hence, these are the only two particles now known for which helicity could be identical to chirality, of which only the [[photon]] has been confirmed by measurement. All other observed particles have mass and thus may have different helicities in different reference frames.{{efn|It is still possible that as-yet unobserved particles, like the [[graviton]], might be massless, and like the [[photon]], have invariant helicity that matches their chirality.}}