Scanning the structure of ill‐known spaces: Part 2. Principles of construction of physical space

Abstract

An abstract lattice of empty set cells is shown to be able to account for a primary substrate in a physical space. Space‐time is represented by ordered sequences of topologically closed Poincaré sections of this primary space. These mappings are constrained to provide homeomorphic structures serving as frames of reference in order to account for the successive positions of any objects present in the system. Mappings from one section to the next involve morphisms of the general structures, representing a continuous reference frame, and morphisms of objects present in the various parts of this structure. The combination of these morphisms provides space‐time with the features of a non‐linear generalized convolution. Discrete properties of the lattice allow the prediction of scales at which microscopic to cosmic structures should occur. Deformations of primary cells by exchange of empty set cells allow a cell to be mapped into an image cell in the next section as far as the mapped cells remain homeomorphic. However, if a deformation involves a fractal transformation to objects, there occurs a change in the dimension of the cell and the homeomorphism is not conserved. Then, the fractal kernel stands for a “particle” and the reduction of its volume (together with an increase in its area up to infinity) is compensated by morphic changes of a finite number of surrounding cells. Quanta of distances and quanta of fractality are demonstrated. The interactions of a moving particle‐like deformation with the surrounding lattice involves a fractal decomposition process, which supports the existence and properties of previously postulated inerton clouds as associated to particles. Experimental evidence of the existence of inertons is reviewed and further possibilities of experimental proofs proposed.