We demonstrate that E × B shear, V 0 E×B , governs the dynamics of the cross phase of the peelingballooning-(PB-)mode-driven heat flux, and so determines the evolution from the edge-localized (ELMy) H mode to the quiescent (Q) H mode. A physics-based scaling of the critical E × B shearing rate (V 0 E×B;cr ) for accessing the QH mode is predicted. The ELMy H mode to the QH-mode evolution is shown to follow from the conversion from a phase locked state to a phase slip state. In the phase locked state, PB modes are pumped continuously, so bursts occur. In the slip state, the PB activity is a coherent oscillation. Stronger E × B shearing implies a higher phase slip frequency. This finding predicts a new state of cross phase dynamics and shows a new way to understand the physics mechanism for ELMy to the QH-mode evolution.