- one trace of an unrolling line on horn torus surface versus various well-known reference objects of physicists -
First we recap the identifications we already have made: the most important, significant and obvious is the axis of symmetry, which we had identified as axis of time, but straightaway had deprived this meaning of its importance, because of the equivalence to horns of very big tori. The total of all big horn tori represents time already. A distinct variable or dimension time is not necessary, is redundant. When using it yet, time will be an auxiliary variable, only for simplification of things, to match our engrams.
The circumferential speed of the tori, when rolling along the axis, shall be the same for all. Constancy is not required, because self-similarity of the whole system equals it instantly, so that within the system it seems to stay constant. Moreover there is nothing outside, no reference, what could define a particular value for the speed. In our world we only know one omnipresent speed, and so it's logical to let the tori perform their revolution (turn of latitudes) with speed of light c.
Now we switch to the imagined unrolling line, that we let emerge on the surface of a dynamic horn torus through its simultaneous rotation (turn of longitudes). Without the extensive explanations in the original (German) text and without mathematical elaboration we try to associate properties of the line with physical objects. Rotation itself can be associated with quantities like energy, frequency, spin of particles etc.
The whole line (the complete cycloid), reaching from infinitesimal small to very big horn tori is one entity, divided in many parts. On big sizes, when the ratio of angular velocities revolution to rotation is small, the line winds very often around the torus including the horns, with small angle to the latitudes - at least off the thin thread near Point S, mostly filling the whole surface after many rotations. At certain ratios, with rational values and especially as integers, the line concentrates to significant patterns, Lissajous figures. The line never shows a discontinuity, but in form of these concentrations different kinds of 'attractors' or 'resonances'. These one can associate with particles, fermions, and the sections of the line between the fermions as their mediators, bosons. See coarse animation.
In this picture elementary particles are local manifestations of one single entity, reaching from inside a nucleon, quark or even smaller to farthest distances of the universe. The outermost boson, with mentioned ratio smaller than 1/2, where there are no significant Lissajous figures, is the photon and at 1/2, as the first striking resonance, we find the electron.
Ratio 1 is a sort of mysterious 'mirror', where the big outer world of 'free' photons and electrons with little manifestation of structure changes into the inverse world with enormous accumulation of resonances, the first being ratio 2, representing a pair of nucleons. Between electron and first half of the two nucleon-loops, which we identify as proton, we find a 'caged' photon as mediator. Further down, at ratio 3, the line next is 'constructing quarks', being not less interesting at ratio 4 then ... and our game has started to be fun.