Stochastic Diffusion and Drift from Spacetime Foam in the Zhang Effective Metric

The search for quantum gravitational effects has led to the study of spacetime foam, where the metric undergoes stochastic fluctuations at microscopic scales. In this paper, we demonstrate that the rotational-order geometric unification framework provides a concrete realization of spacetime foam. We show that the stochastic fluctuations of the internal S³ orientation field, governed by the Zhang Effective Metric, induce phase diffusion and energy-dependent drift on propagating photons. We derive the phase broadening and decoherence rates for high-energy astrophysical sources. Unlike phenomenological models with arbitrary parameters, the geometric diffusion is strictly controlled by the internal topology. We show that the energy-dependent time delay (drift) provides a falsifiable signature for next-generation gamma-ray telescopes, such as LHAASO and CTA.