  In this article, we study the Sagnac effect for spin-$1/2$ particles through
local Wigner rotations according to the framework developed by [H. Terashima
and M. Ueda, Phys. Rev. A 69, 032113 (2004)]. Since the spin of the particle
plays the role of a quantum `clock', as the quanton moves in a superposed path
it gets entangled with the momentum (or the path), and this will cause the
interferometric visibility to drop, since there is a difference in proper time
elapsed along the two trajectories, which is known as the Sagnac time delay.
