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Introduction

The idea of dimensional appearance related to the distance, suggests that the structure of the material points is a function of the distance between the points. If we imagine that two material points are moving towards each other in a process of collision for instance, then the relative motion cannot be described just by the kinematics of their relative position, but also by the variation of their internal structure: the bodies “see” in each other more and more material particles as they come closer and closer. This is the general idea underlying the partonic model (Feynman, 1969). Now, one can frame quantitatively the possible structures of a material point. One can say that its material particles are confined to a region contained in a sphere of radius given by the maximal possible dimensions of that material point according to our experience. Geometry has here a tool which proved effective in giving reality to some strange Non Euclidean geometries: the idea of Absolute (Cayley, 1859). An Absolute is the unreachable bag that contains all the things that happen (By the way, the modern bag model of confinement can be thought of in such geometrical terms). At a certain scale, it is the firmament of our whole experience. If it is a sphere, the regular geometry describing the structure inside is the Lobachevsky or Hyperbolic Geometry.

This is exactly what happened with the assignments of structure to atoms. First they were thought of as impenetrable spheres, then it has been discovered that these spheres are mostly empty and penetrable. These spheres became the maximal spheres – the Absolutes – of existence of the material particles of an atom. The conclusion can be inferred from the Geiger-Marsden experiments. Its first form was the Rutherford model of atom (Rutherford, 1911). By this it becomes explicit the fact that the Hyperbolic Geometry is involved here, inasmuch as the eccentricity of the trajectory in the Kepler problem describing the Rutherford model is confined by physical properties of the structure. Later on the structures related to the atomic nucleus were also related to Hyperbolic Geometry.

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