Title: Theoretical Analysis of Generalized Sagnac Effect in the Standard Synchronization,
Abstract: The Sagnac effect has been shown in inertial frames as well as rotating
frames. We solve the problem of the generalized Sagnac effect in the standard
synchronization of clocks. The speed of a light beam that traverses an optical
fiber loop is measured with respect to the proper time of the light detector,
and is shown to be other than the constant c, though it appears to be c if
measured by the time standard-synchronized. The fiber loop, which can have an
arbitrary shape, is described by an infinite number of straight lines such that
it can be handled by the general framework of Mansouri and Sexl (MS). For a
complete analysis of the Sagnac effect, the motion of the laboratory should be
taken into account. The MS framework is introduced to deal with its motion
relative to a preferred reference frame. Though the one-way speed of light is
other than c, its two-way speed is shown to be c with respect to the proper
time. The theoretical analysis of the generalized Sagnac effect corresponds to
the experimental results, and shows the usefulness of the standard
synchronization. The introduction of the standard synchrony can make
mathematical manipulation easy and can allow us to deal with relative motions
between inertial frames without information on their velocities relative to the
preferred frame.