In my last post I promised that I would try to build a model that will allow me to see how force is generated. At first, I was considering building an elaborate 3D model with even more curves than in the animation shown in my last post.
However, in the end, I realized that I don’t have to do anything complicated. I just need to draw planes of reflection into the projections. So, this is what I did. Below, in figure a) (the x-z projection from my Blender image) you see five red lines, each of which is a plane of reflection (simplified into a line) for the central dots. The central line is the only plane of reflection shared by the two dots.
To explain the figure, let’s focus on the yellow dot, circled in red. On its left and right are planes of reflection that prevent the movement of the dot to left or right. The line cutting through the yellow dot is further out and can also be seen in the y-z projection in figure b).
This plane prevents the upward movement of the dot, but more importantly it partially prevents the forward movement of the dot. The partiality comes from the blue dot in front moving almost in the same direction, but not quite. So, only the non-linear component of the movement of the dot causes the yellow dot to be reflected downwards. But this downward reflection only affects the non-linear component of the motion of the dot. The movement that was parallel with the blue dot in front isn’t affected.
This isn’t necessarily the absolute best way to explain why there is intrinsic curvature for all movement in space, but it’s the best I can do for today.
And here is the above figure as a 3D animation. I actually think the above projections are better…
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