Scale-Invariant Field Organization as a Subset of the Universal Quantum Foam Hypothesis: Atoms and Galaxies as Homologous Field-Mechanical Realizations

This preprint addresses a specific sub-area of the Universal Quantum Foam Hypothesis (UQSH) and focuses on the mechanical symmetry between micro- and macrocosmic structures. While the basic conceptual and ontological framework of the UQSH was already presented in the abstract of January 6, 2026 (based on the paper from November 2025), this work focuses on overcoming the fundamental separation between the quantum world and the cosmos. At its core is the thesis that atoms and galaxies are not isolated systems, but rather functionally homologous realizations of the same field-mechanical processes at different scales. In this extension, the atom is defined not as a collection of solid particles, but as a local field node, a zone of increased field tension in which motion is structured and held. Electrons are interpreted as stable vortex modes of the medium, whose discrete states result from the mechanical stability conditions of the field. This multi-scale perspective establishes the field's reorganization rate as the basis for understanding time and entropy. Entropy is understood here as a process of rearranging organization between bound patterns and free field dynamics. This subfield of UQSH complements the existing framework with a perspective that closes the interpretive gap between the Planck scale and the cosmic macrostructure through the principle of scale-invariant field mechanics.