15. Metric - when dynamic processes induce discrete values|
Several times I used the term 'self-metrification', but didn't explain it. I will do it now: To undertake measurements within a space, be it spanned by coordinates or only a range of numbers, we need a unit to establish relations between occurring values. In a static continuous space formed by linearly independent coordinates no element can be distinguished as particularly eligible for that purpose. We have to choose units arbitrarily and artificially. Different with dynamic horn tori! They can relate revolutions to rotations and vice versa. Their cycloids produce patterns, self-contained curves, Lissajous figures on their surfaces, and they show significant dynamic properties: number of rotations per revolution and number of revolutions per rotation.
There is exactly one situation, where the turns are symmetric, namely when rotations per revolution is the same as revolutions per rotation. With this special case, i.e. revolution : rotation = 1:1, we have an unit, which all other situations and sizes can be related to. Coming from both sides of the numerically obvious symmetry we now have a smallest possible unit for revolution and for rotation: 1 (one) each.
After doing a couple of mental leaps and perhaps mathematical formulations nothing and nobody can inhibit myself to associate one full rotation with reduced Planck's constant and one full revolution with Planck length. Speed of light, as mentioned already, is represented by the circumferential speed of revolution. No matter what value one chooses for c, the geometric situation and all relations persist in a self-similar way. And the well known relations between the mentioned physical quantities achieve imaginable meaning.
Consequently fractions of one full rotation and fractions of one full revolution are not defined, don't occur in the dynamic processes. But that doesn't restrict the variability of the image. The opposite is true! And the analogies to other known and accepted models increase. Example: the electron resp. every horn torus with half-integral ratio of turns (fermion) needs two steps of rotation, two full turns, to match the original shape.
Here we leave the mere imagination, describable in common speech. Here starts physics. In accustomed manner, using sophisticatedly invented formulations of naturally preexisting mathematical rules. - Unfortunately these rules seem to be too simple to match complexities of human perception and thinking. Obviously one has to pay this price for comprehension
- or play a game with reverse relations ...