Beyond the Shell: The Implicit Closed Surface Theory in Engineering and Chemistry

This paper explores how practical language and methodology in chemistry and engineering implicitly assume a closed surface structure for electrons, despite the prevailing quantum view of electrons as point-like probabilistic entities. By analyzing the widespread use of spatial concepts such as electron shells, orbitals, and molecular surfaces, the paper demonstrates that practitioners already operate under a surface-based model of electronic structure. The closed surface theory makes this implicit understanding explicit, offering a coherent geometric framework that aligns with empirical practices in crystallography, catalysis, and materials science.