The Operational Now - Coherence Volumes and the Geometric Limits of Simultaneity

Relativity shows that simultaneity is frame-dependent. This work asks a different question: when can a physical system maintain internal synchronization despite gravitational time dilation? We derive a geometric condition comparing two timescales: the light-crossing time required for internal communication and the gravitational shear time over which proper-time differences accumulate across an extended body. When synchronization cannot occur faster than gravitationally induced desynchronization, a shared notion of time loses operational meaning. This leads to a coherence length determined solely by the local gravitational acceleration. Within this coherence volume, temporal simultaneity can be maintained. Beyond it, a system may remain spatially rigid but cannot sustain synchronized timekeeping. The result applies both to systems in external gravitational fields and to self-gravitating bodies. For terrestrial conditions the coherence scale is enormous, but near compact objects or for sufficiently massive systems the limit becomes physically relevant. Combined with the mechanism derived in When Reference Frames Fail Themselves (Zenodo: 10.5281/zenodo.18461843) and the geometric interpretation in Rigidity vs. Simultaneity (Zenodo: 10.5281/zenodo.18600601), this work shows that gravitational time dilation becomes an irreducible source of temporal noise once quantum positional uncertainty is accounted for. A shared time parameter is therefore not a primitive feature of spacetime, but an emergent operational property restricted to regions where geometric shear remains subdominant to internal synchronization.