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

TL;DR

This paper develops a logical framework linking ionization energies to energy-level spacings in elements, establishing their uniqueness and proportionality, and explores the implications for physical categories and classes of quantum matter.

Contribution

It introduces a formal logical construction connecting ionization energies with energy-level spacings and categorizes physical systems based on these properties.

Findings

Energy-level spacings  can be converted to ionization energies.

 and ionization energies are unique for each element.

Average ionization energies relate proportionally to constituent elements' energies.

Abstract

Logical proofs and definitions are developed to establish (i) the energy-level spacings, \xi for each chemical element (from the periodic table of chemical elements) can be converted to the ionization energies, (ii) both \xi and 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 \xi not = 0 and \xi is 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(\xi) to another P'(\xi). Therefore, the existence of many P(\xi) imply the existence of different categories of physical systems and quantum matter.