Zig-zag model illuminates helicity vs. chirality?

[Spinnor]

Can we use the Zig-Zag model of the electron to get an intuitive understanding of the difference between helicity and chirality?

Suppose we have a long and narrow cylinder where the spin 1/2 massless zig and zag particles bounce between the top and bottom of the inside of the cylinder at the speed of light. Label one end of the cylinder as the top. The zig and zag particles change into each other when they bounce off the top or bottom of the cylinder. There are two possibilities, the top end of the cylinder changes zig to zag or zag to zig, this gives spin up and down? (The zig and zag particles have opposite chirality and spin.)

Edit: The zig and zag particles have opposite chirality and the same spin.

With the cylinder at rest and pointing in some direction the zig and zag particles exist for equal times, have equal magnitudes of momentum, and left and right chirality exist for equal times. Now consider what a person sees if they move rapidly past the cylinder with the top of the cylinder "leading the way". Now zig and zag particles don't exist for equal times, they don't have equal magnitudes of momentum, and left and right chirality don't exist for equal times, the zig-zag particle "becomes" chiral?

The faster we move past the cylinder with a given orientation It will "flatten" and "appear" rotated into alignment with our velocity? Helicity and chirality become the same?

Thanks!

 

[eljose79]

Your idea of using the Zig-Zag model to understand the difference between helicity and chirality is an interesting one. However, there are a few things that need to be clarified.

Firstly, the Zig-Zag model is a simplified model used to explain the behavior of spin 1/2 massless particles. In reality, particles do not actually zig-zag between two points but rather exist as a wave function that can be described by probability amplitudes.

Secondly, in your model, you mention that the zig and zag particles have opposite chirality and spin. This is not entirely accurate. In fact, the zig and zag particles have opposite chirality and the same spin. This is because chirality refers to the handedness of a particle while spin refers to its intrinsic angular momentum.

Moving on to your question, if a person moves rapidly past the cylinder with the top leading the way, the particles will indeed appear to have different properties due to the relativistic effects of time dilation and length contraction. However, this does not necessarily mean that helicity and chirality become the same. Helicity is a property that remains unchanged regardless of the observer's frame of reference while chirality can change depending on the observer's perspective.

In conclusion, while the Zig-Zag model can provide some intuitive understanding of the behavior of particles, it is important to remember that it is a simplified model and may not accurately reflect the complexities of quantum mechanics. It is always best to consult with established theories and experiments when trying to understand scientific concepts.