Four-Leaved Reflection

In today’s post I’m talking about a four-leaved reflection model. I would have wanted to call today’s post “The Shamrock Reflection”, but apparently shamrock is only a three-leaved clover. The four-leaved version is no longer a shamrock. You live and learn.

Anyhow, the topic of today’s post is that when you fit two folding bicones into a single unit sphere of reflection, you’re bound to get a ‘scissor-like’ reflection pattern. That is, the connection point between the four cones (or the center of both bicones) is at the center of the unit sphere. Because the bicones are folded, it is impossible to get their both ends to touch. That is, if you tilt the bicones to just the right angle, so that the distance of neighboring motion vectors is the same for three pairs, but the distance of the fourth pair must always be longer. It’s like when you squeeze scissors, the handles never touch each other no matter how hard you squeeze, because the blades are closer to each other than the handles. In real life, there is usually a neat trick to prevent the blades from going past the ‘level point’, which is where the analogy here breaks a bit.

Here is a very rough model of the four-leaved reflection:

The three green vectors connecting the bases of the cones in this model aren’t actually of equal length just yet. To do that I need to do a bit of math.

I think this model means that when the shape describes the reflections of molecules, one side of the molecule is reflected twice as often as the other side. However, the reason for this is so new to me that I won’t try to explain it in this post. But I’m quite confident that this is the first version of the theory where I don’t need to resort to “then a miracle occurs” logic.

I’m becoming increasingly more convinced that this is the final theory, even though I seem to be adding bits and bobs to it from post to post. This might just be the final bit. But only equations will tell me whether I’m right or wrong.