Asymmetry, the Cutoff Radius, and Scale-Dependent Symmetry

This paper presents an entropic approach to gravitation, where the emergence of gravitational phenomena is governed not directly by mass-energy densities but by informational degrees of freedom distributed across a finite entropic domain. A key structural parameter in such frameworks is an unavoidable gravitational cutoff radius rs, which specifies the scale beyond which a particle or composite system no longer contributes to spacetime curvature via entropic gradients. The presence of the cutoff radius violates Newton’s third law, which stems from the conservation of momentum. This violation reveals an inherent translational asymmetry, appearing at cosmological and atomic scales but masked at intermediate scales. Such dual-scale asymmetry may explain puzzling features of the universe that ΛCDM cannot account for without free parameters. The goal of achieving a Grand Unification of Nature across all scales based on a priori axioms may be completely out of reach as a consequence of Gödel’s incompleteness theorems: There must be an underlying asymmetry due to Noether’s theorem leading to inconsistencies across the full range of scales for a self-referential universe in the spirit of Wheeler’s “Law of no law.”