  We derive electromagnetomotive force fields for charged particles moving in a
rotating Hall sample, satisfying a twofold U(1) gauge invariance principle. It
is then argued that the phase coherence property of quantization of the line
integral of total collective particle momentum into multiples of Planck's
quantum of action is solely responsible for quantization in the Hall state. As
a consequence, the height of the Hall quantization steps should remain
invariant in a rapidly rotating Hall probe. Quantum Hall particle
conductivities do not depend on charge and mass of the electron, and are
quantized in units of the inverse of Planck's action quantum.
