Theoretical analysis of generalized Sagnac effect in the standard synchronization

Abstract

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.

Uniqueness of the Isotropic Frame and Usefulness of the Lorentz Transformation

“…The generalized Sagnac effect that involves both linear and circular motions can be analyzed based on TCL [18]. We can also make an analysis of the effect by using the MS framework [11], taking account of the motion of the laboratory frame. These theoretical analyses, which correspond with the experimental results, indicate that the one-way speed of light is anisotropic in inertial frames as well as in rotating frames.…”

“…Hence there are an infinite number of isotropic frames. Recently the relationship of time dilation and the formula of the Doppler effect have been derived under the uniqueness of the isotropic frame by exploiting the MS framework [11,12]. The unique isotropic frame is the preferred reference frame.…”

“…Proper times and Doppler-shifted frequencies, which are independent of the synchronization of clocks [2,3,11,12], can be obtained by regarding any inertial frame as isotropic. Nonetheless, their values are demonstrated not to be uniquely determined unless the isotropic frame is unique.…”

“…Though a variety of explanations and analyses on the Sagnac effect are available based on these theories [19,20], even the problem of time gap that multiple times are defined at the same place in the rotating frame has not been resolved. The generalized Sagnac effect [11,[16][17][18]21] that shows the anisotropy of the speed of light in inertial frames as well may be a more perplexing conundrum to the theory of relativity based on its isotropy. We demonstrate, as an example to show the usefulness of LT, that the difference between the travel times of counter-propagating light beams in the experiment of the generalized Sagnac effect can be exactly obtained by exploiting it.…”

Consistent Coordinate Transformation for Relativistic Circular Motion and Speeds of Light

“…The generalized Sagnac effect [10][11][12][13], which involves linear motion as well as circular motion, indicates that the speed of light is anisotropic not only in rotating frames but also in inertial frames.…”