Paper detail

Logical Construction of the Ionization Energy Theory and the Origin of Physical Categories

Logical proofs and definitions are developed to establish (i) the energy-level spacings, ξfor each chemical element (from the periodic table of chemical elements) can be converted to the ionization energies, (ii) both ξand the ionization energies are unique, and (iii) the averaged ionization energies of any quantum matter is proportional to the averaged ionization energies of its constituent chemical elements, if and only if ξnot = 0 and ξis not an irrelevant constant. Physical sets are then constructed such that they are members of a specific physical class where each class belongs to a specific physical category, P. However, there is not a single structure-preserving functor from one energy-level spacing physical category, P(ξ) to another P'(ξ). Therefore, the existence of many P(ξ) imply the existence of different categories of physical systems and quantum matter.