In experiments designed to understand deep shear zones, we show that periodic porous sheets emerge spontaneously during viscous creep and that they facilitate mass transfer. These findings challenge conventional expectations of how viscosity in solid rocks operates and provide quantitative data in favour of an alternative paradigm, that of the dynamic granular fluid pump model. On this basis, we argue that our results warrant a reappraisal of the community's perception of how viscous deformation in rocks proceeds with time and suggest that the general model for deep shear zones should be updated to include creep cavitation. Through our discussion we highlight how the integration of creep cavitation, and its Generalised Thermodynamic paradigm, would be consequential for a range of important solid Earth topics that involve viscosity in Earth materials like, for example, slow earthquakes.