The Physicality of Scales: An Emergent Hierarchy from Minimal Axioms in Quantum-Geometry Dynamics

This paper proposes physically grounded definitions of object and scale within the framework of Quantum-Geometry Dynamics (QGD) and the Minimal Physically Derivable Theories (MPDT) programme established by the Uniqueness Theorem. Both definitions have been absent from the existing literature on the framework and are developed here for the first time. An object is defined by a behavioral criterion: a structure is an object if, under the influence of any force, its response is entirely describable by its total mass and the resultant of the intrinsic momentum vectors of all its constituent preons(+). The criterion is independent of the type of force acting on the structure and independent of the internal mechanism — gravitational, electromagnetic, or any combination — that produces the coherent response. A scale is defined as the level of the hierarchy at which a collection of objects satisfies this criterion collectively, constituting a new object at the next scale. The hierarchy extends from the single preon(+) at the fundamental scale upward through particles, atoms, molecules, macroscopic bodies, planetary systems, stellar systems, galaxies, and galaxy clusters. The universe as a whole is excluded from the hierarchy because no external force acts on it and the behavioral criterion therefore does not apply — the universe is the boundary condition of the hierarchy, not a member of it. The behavioral criterion is applied to so-called elementary particles. Within QGD, no particle is ontologically elementary: all matter is constituted by preons(+), and every particle is a composite object above the fundamental scale. What physics designates as elementary particles are objects whose internal preon(+) degrees of freedom are not accessible under any experimentally realized interaction — they are behaviorally elementary, not ontologically so. Their apparent elementarity is a consequence of scale, not of ontology. This dissolves the Standard Model's positing of 17 fundamental particles as primitives: they are objects whose internal structure is behaviorally inaccessible at the scales the Standard Model describes, which is precisely what the Uniqueness Theorem identifies as the source of the Standard Model's non-minimality. Scale is shown to be an emergent property of the MPDT axiom set, subordinate to dimensionality: the scale hierarchy presupposes the full structural conditions established by the Uniqueness Theorem, including discrete space, intrinsic momentum, and the two-force balance between p-gravity and n-gravity. The result is situated against existing treatments of scale in renormalization group theory, cosmology, and philosophy of science, including Wimsatt's account of levels of organization, Ladyman and Ross's ontic structural realism, and Batterman's work on inter-level relations and descriptive autonomy. The behavioral criterion provides the principled foundation that all of these treatments presuppose but do not supply. This paper is part of a series developed in conjunction with Quantum-Geometry Dynamics: An Axiomatic Approach to Physics (Burnstein, 2026) and the companion papers on the Uniqueness Theorem, the Physicality of Logic, the three-dimensionality of space, Quantum Computing under QGD, and Bell correlations under QGD.