The misunderstood Sagnac effect

The Sagnac effect of first order (in one-way light) is shown to explain the aberration observed in the very long base interferometry tests. This fact is also consistent with Sagnac’s results and with the observed stellar aberration. The Sagnac effect of second order (in two-way light) is shown to be real, but not observable, in the experiments that were done by Michelson and Morley. However, it is also shown that the same second order effect is observable in the Pioneer anomaly. The Doppler effect of second order is also demonstrated to explain the cosmic red shift, due to a radial ether wind.

Wavelength and throughput tuning of FORR-based optical filter using Sagnac effect

In this paper, analysis of tunable optical filter based on Sagnac effect tuning is presented using a fiber-optic ring resonator (FORR) and the responses of the filters for different FORR and Sagnac loop parameters under steady-state conditions are investigated. Formulation of the optical filter response is presented by considering with/without single and multiple Sagnac loop effects. Effects of the FORR parameters of filter response are studied and analyzed under different parametric conditions for the maximum transmission intensity. The simulation results show that the filter responses are affected strongly by the Sagnac loop and the FORR parameters. With the Sagnac effect, it is shown that full-width at half maximum (FWHM) would increase by increasing the phase difference Δϕ from 0 to 0.20 radian, beyond which it will start decreasing. The difference in FWHM value in this range of Δϕ variations is found to be about 3.77 nm. Between the first and the second resonances at wavelengths 1395 and 1538 nm, the free spectral range (FSR) is found to be 140 nm. In multiple loops effects, by increasing the number of loop turn N, the values of FSR would reduce. For Δϕ = 0.3 and N = 1, 2, 3, the values of FSR are obtained as 144, 74, 47 nm, respectively.

Multi-loop atomic Sagnac interferometry

The sensitivity of light and matter-wave interferometers to rotations is based on the Sagnac effect and increases with the area enclosed by the interferometer. In the case of light, the latter can be enlarged by forming multiple fibre loops, whereas the equivalent for matter-wave interferometers remains an experimental challenge. We present a concept for a multi-loop atom interferometer with a scalable area formed by light pulses. Our method will offer sensitivities as high as $$2\times 10^{-11}$$ 2 × 10 - 11 rad/s at 1 s in combination with the respective long-term stability as required for Earth rotation monitoring.

Fermat Metrics

In this paper we present a survey of Fermat metrics and their applications to stationary spacetimes. A Fermat principle for light rays is stated in this class of spacetimes and we present a variational theory for the light rays and a description of the multiple image effect. Some results on variational methods, as Ljusternik-Schnirelmann and Morse Theory are recalled, to give a description of the variational methods used. Other applications of the Fermat metrics concern the global hyperbolicity and the geodesic connectedeness and a characterization of the Sagnac effect in a stationary spacetime. Finally some possible applications to other class of spacetimes are considered.

Optical data implies a null simultaneity test theory parameter in rotating frames

The simultaneity framework describes the relativistic interaction of time with space. The two major proposed simultaneity frameworks are differential simultaneity, in which time is offset with distance in “moving” or rotating frames for each “stationary” observer, and absolute simultaneity, in which time is not offset with distance. We use the Mansouri and Sexl test theory to analyze the simultaneity framework in rotating frames in the absence of spacetime curvature. The Mansouri and Sexl test theory has four parameters. Three parameters describe relativistic effects. The fourth parameter, [Formula: see text], was described as a convention on clock synchronization. We show that [Formula: see text] is not a convention, but is instead a descriptor of the simultaneity framework whose value can be determined from the extent of anisotropy in the unidirectional one-way speed of light. In rotating frames, one-way light speed anisotropy is described by the Sagnac effect equation. We show that four published Sagnac equations form a relativistic series based on relativistic kinematics and simultaneity framework. Only the conventional Sagnac effect equation, and its associated isotropic two-way speed of light, is found to match high-resolution optical data. Using the conventional Sagnac effect equation, we show that [Formula: see text] has a null value in rotating frames, which implies absolute simultaneity. Introducing the empirical Mansouri and Sexl parameter values into the test theory equations generates the rotational form of the absolute Lorentz transformation, implying that this transformation accurately describes rotational relativistic effects.

Assessment of the relativistic rotational transformations

Rotational transformations describe relativistic effects in rotating frames. There are four major kinematic rotational transformations: the Langevin metric; Post transformation; Franklin transformation; and the rotational form of the absolute Lorentz transformation. The four transformations exhibit different combinations of relativistic effects and simultaneity frameworks, and generate different predictions for relativistic phenomena. Here, the predictions of the four rotational transformations are compared with recent optical data that has sufficient resolution to distinguish the transformations. We show that the rotational absolute Lorentz transformation matches diverse relativistic optical and non-optical rotational data. These include experimental observations of length contraction, directional time dilation, anisotropic one-way speed of light, isotropic two-way speed of light, and the conventional Sagnac effect. In contrast, the other three transformations do not match the full range of rotating-frame relativistic observations.