Running Critical Acceleration from Gravitational Information Processing: Unifying the Radial Acceleration Relation from Galaxies to Galaxy Clusters

The radial acceleration relation (RAR) observed in spiral galaxies constitutes one of the tightest em- pirical correlations in extragalactic astronomy, yet its extension to galaxy clusters reveals a systematic decit: standard MOND under-predicts cluster dynamics by a factor of ∼2. We propose that the critical acceleration a0 is not a universal constant but a running quantity that increases with the total enclosed baryonic mass of the gravitational system: a0,eff(M) = a0 1 + Ξmax M M + Msat . Using a0 = 1.20 ×10−10 m/s2 xed from 175 SPARC galaxies with zero free parameters, and tting only Ξmax = 4.2 and Msat = 2.5 ×1012 M⊙ to ve well-studied clusters (Coma, Perseus, Virgo, Abell 1689, Bullet), we reduce the cluster residual from 0.337 dex (MOND) to 0.110 dexa threefold improvementwhile preserving the galaxy RAR at 0.147 dex. The physical interpretation is natural: in the Unied Theory of Quantum Gravity (UTQG) framework, a0 encodes the accumulated deco- herence history of spacetime. More mass implies more gravitational interactions, more decoherence, and a stronger memory eld χ, yielding a higher eective a0. We derive six falsiable predictions that distinguish this model from both ΛCDM and standard MOND, including a mass-dependent boost in galaxy groups and redshift evolution of the cluster decit. Keywords: modied gravity, dark matter, radial acceleration relation, galaxy clusters, quantum gravity, MOND, decoherence