The relationship between a particle's ability to change in time and its helicity (or chirality) is a consequence of the relativistic nature of particles and the properties of their respective fields. Let's break it down step by step.
Relativistic Nature of Particles: In the framework of special relativity, particles are described by quantum fields. These fields have associated particles and antiparticles, and the dynamics of these fields are governed by relativistic equations, such as the Dirac equation for fermions like electrons.
Chirality and Helicity: Chirality refers to the property of a particle that distinguishes it as either left-handed or right-handed. In the case of fermions, chirality is associated with the projection of the particle's spin onto its momentum. A left-handed (or left-chiral) fermion has its spin antiparallel to its momentum, while a right-handed (or right-chiral) fermion has its spin parallel to its momentum.
Helicity, on the other hand, is the component of a particle's spin along its direction of motion. For massless particles, helicity and chirality are equivalent because the particle's energy is entirely determined by its momentum. In this case, a left-chiral particle has left-handed helicity, and a right-chiral particle has right-handed helicity.
Changing Chirality and Helicity: The statement you mentioned about an electron flipping between left-chiral and right-chiral states is not accurate for electrons. Electrons are considered left-chiral particles. However, if you were referring to neutrinos, it is true that they can change chirality due to the phenomenon known as neutrino oscillation. Neutrinos have both left-chiral and right-chiral components, and they can oscillate between these states as they propagate through space.
Fixed Helicity for Massless Particles: Massless particles, such as photons, have a fixed helicity in all reference frames. This is a consequence of their relativistic nature. Since the speed of light is constant in all inertial reference frames, the energy of a massless particle is entirely determined by its momentum. Consequently, the helicity, which is the component of the spin along the direction of motion, remains fixed because it is tied to the momentum.
In summary, the correspondence between a particle's ability to change in time (chirality) and having a fixed helicity for massless particles is a consequence of the relativistic nature of particles and the specific properties of their fields.