Quantum-Cosmological Scale Unification through Spacetime Diffusivity

Time appears to flow for observers, yet general relativity’s block universe is static. We propose a potential resolution to this “problem of time’’ by introducing a scale‑invariant spacetime diffusivity field, ϵ(s) (units [L2T−1]), which limits how finely causal information can be resolved—loosely analogous to thermal diffusivity in heat flow, though of purely quantum‑informational origin. Two Lorentz‑invariant postulates, (i) ds/dt=c and (ii) dϵ/ds=c, promote ϵ^ and m^ to a canonical pair obeying [ϵ^,m^]=iℏ and suggest a Cosmological Uncertainty Principle (CUP), ΔϵΔm≥ℏ/2. An area-diffusion parameter Z≡4πc2κ02 reproduces both Planck time (tP=ℓP/c) and Hubble time (tH=1/H0) when evaluated at the corresponding horizon scales, unifying quantum and cosmological regimes without additional constants. Within this framework, we derive a cosmological horizon temperature, TCUP=πTdS≃9×10−30K, similar to the Gibbons–Hawking de Sitter temperature. Because reducing diffusivity uncertainty inevitably enlarges mass uncertainty, the framework produces falsifiable signatures in high‑precision galaxy‑cluster kinematics and, ultimately, pulsar‑timing arrays. By recasting temporal flow as an epistemic bound set by information transport, our theory links quantum information, diffusion physics, and cosmology, offering possible observational probes of spacetime’s quantum structure.