  The Sagnac effect is a time or phase shift observed between two beams of
light traveling in opposite directions in a rotating interferometer. We show
that the standard description of this effect within the framework of general
relativity misses the effect of deflection of light due to rotational inertial
forces. We derive the necessary modification and demonstrate it through a
detailed analysis of the square Sagnac interferometer rotating about its
symmetry axis in Minkowski space-time. The role of the time shift in a Sagnac
interferometer in the synchronization procedure of remote clocks as well as its
analogy with the Aharanov-Bohm effect are revised.
