Abstract
<jats:p>For more than a century the Sagnac effect has been indispensable to practical metrology, yet there is no consensus on why it occurs — it has been attributed to the ether, to special relativity, to the general-relativistic metric of a rotating frame, and to a synchronization convention. This paper defines a general Sagnac-type effect as the travel-time difference between two counter-propagating beams around a closed optical path, for any medium, any motion, and any frame. We mathematically derive one formula for all such effects and show that they share a common origin: the asymmetry of the observed light velocity along the opposite directions. The formula reproduces the rotational Sagnac effect, its arbitrary-loop generalization, the moving-fiber effect of Wang, and the Fizeau effect, and it predicts two new effects — a Sagnac effect from a linear relative motion along an inertial path in vacuum, and an enhanced Fizeau effect — both testable with a first-order motion-controlled interferometer. As a corollary, the GPS Sagnac correction is shown to be the same observed-velocity effect, absorbed directly when the receiver's velocity in the ECI frame is used in the timing calculation.</jats:p>