  We formulate according to the quantum mechanical uncertainty relation a new
quantum electrodynamical uncertainty relation $\Delta \breve{A} . \Delta l \sim
\hbar/e$ where $\breve{A}$ and $\Delta l \geq l_B$ are the electromagnetic pure
gauge potential, the position uncertainty and the magnetic length,
respectively. Then, we show that the observed potential drops on the edge of
QHE samples are varifications of this uncertainty relation, where the quantum
potential drop of the relevant component of potential can be considered as its
quantum uncertainty $\Delta \breve{A}$.
